These pages provide information on the people, research interests, teaching activities and projects at the chair of mathematical physics, consisting of the quantum field theory / operator algebras group (Gandalf Lechner) and the quantum mechanics / group (Hermann Schulz-Baldes).
Professors
Prof. Dr. Gandalf Lechner
Chair of Mathematics (Operator Algebras) (Heisenberg Professorship)
Professors
Address
Cauerstraße 11 91058 Erlangen
Contact
Prof. Dr. Hermann Schulz-Baldes
Professorship for Mathematics (Mathematical Physics)
Professors
Address
Cauerstraße 11 91058 Erlangen
Contact
Secretary
Irmgard Moch
Department of Mathematics
Administrative staff
Address
Cauerstraße 11 91058 Erlangen
Contact
Substitute professor
Prof. Dr. Markus Fröb
Chair of Mathematics (Algebra and Geometry)
Professors
Address
Cauerstraße 11 91058 Erlangen
Contact
PostDocs and PhD students
Timo Feistl
Professorship for Mathematics (Mathematical Physics)
Research associates
Address
Cauerstraße 11 91058 Erlangen
Contact
Johannes Große
Chair of Mathematics (Operator Algebras) (Heisenberg Professorship)
Research associates
Address
Cauerstraße 11 91058 Erlangen
Contact
Lars Koekenbier
Professorship for Mathematics (Mathematical Physics)
Research associates
Address
Cauerstraße 11 91058 Erlangen
Contact
Ian Koot
Chair of Mathematics (Operator Algebras) (Heisenberg Professorship)
Doctoral candidates
Address
Cauerstraße 11 91058 Erlangen
Contact
Dragan Markovic
Professorship for Mathematics (Mathematical Physics)
Research associates
Address
Cauerstraße 11 91058 Erlangen
Contact
MSc students
- Moritz Lanz
- Andreas Rothemund
- Benedikt Wenzel
Emeritus
Prof. Dr. Andreas Knauf
Faculty of Sciences
Retired professors
Address
Cauerstraße 11 91058 Erlangen
Contact
Publications at the chair of mathematical physics and operator algebras
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Integral representations of f-divergences for general von Neumann algebras
(2026)
URL: https://arxiv.org/abs/2607.05195
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The classification problem for unitary R-Matrices with two eigenvalues
(2026)
DOI: 10.48550/arXiv.2603.20158
URL: https://arxiv.org/abs/2603.20158
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Unitary R-matrices, mostly with two eigenvalues
Oberwolfach Mini-Workshop: The Yang–Baxter Equation and Representations of Braid Groups (Oberwolfach, 27.10.2025 - 31.10.2025)
DOI: 10.4171/owr/2025/49
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Causal quantum-mechanical localization observables in lattices of real projections
(2026)
DOI: 10.48550/arXiv.2602.11392
URL: https://arxiv.org/abs/2602.11392
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Inclusions of Standard Subspaces
In: Communications in Mathematical Physics 406 (2025), Article No.: 283
ISSN: 0010-3616
DOI: 10.1007/s00220-025-05458-4
URL: https://arxiv.org/abs/2506.16085
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Standard Subspaces and twisted Araki-Woods subfactors
Subfactors and Applications (Mathematisches Forschungsinstitut Oberwolfach, 28.07.2025 - 01.08.2025)
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Scaling of the Lyapunov Exponent at a Balanced Hyperbolic Critical Point
In: Annales Henri Poincaré (2025)
ISSN: 1424-0637
DOI: 10.1007/s00023-025-01594-8
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Topological indices for periodic gapped Hamiltonians and fuzzy tori
In: Mathematical Physics Analysis and Geometry 28 (2025), Article No.: 13
ISSN: 1385-0172
DOI: 10.1007/s11040-025-09508-0
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Relative positions of half-sided modular inclusions
In: Letters in Mathematical Physics 115 (2025), Article No.: 118
ISSN: 0377-9017
DOI: 10.1007/s11005-025-02008-w
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Superdiffusion, normal diffusion, and chaos in semiclassical Bose-Hubbard chains
In: Physical Review E 112 (2025), p. 024211-
ISSN: 1063-651X
DOI: 10.1103/4k8x-fd1j
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Standard Subspaces in Quantum Field Theory and Representation Theory
2024
(Oberwolfach Reports, Vol.20)
DOI: 10.14760/OWR-2023-50
URL: https://publications.mfo.de/handle/mfo/4092
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Operator-Algebraic Constructions of QFT Models in Two Dimensions
In: Encyclopedia of Mathematical Physics (Second Edition), 2024, p. 291-303
DOI: 10.1016/B978-0-323-95703-8.00268-8
URL: https://www.sciencedirect.com/science/article/abs/pii/B9780323957038002688?via=ihub
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Local Markers for Crystalline Topology
In: Physical Review Letters 132 (2024), Article No.: 073803
ISSN: 0031-9007
DOI: 10.1103/PhysRevLett.132.073803
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Crossing symmetry and the crossing map
In: Reviews in Mathematical Physics (2024)
ISSN: 0129-055X
DOI: 10.1142/S0129055X24610051
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KMS states on Z2-crossed products and twisted KMS functionals
In: Annales Henri Poincaré (2024)
ISSN: 1424-0637
DOI: 10.1007/s00023-024-01516-0
URL: https://arxiv.org/abs/2402.15574
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Transfer matrix analysis of non-Hermitian Hamiltonians: asymptotic spectra and topological eigenvalues
In: Journal of Spectral Theory 14 (2024), p. 1563-1622
ISSN: 1664-039X
DOI: 10.4171/JST/524
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Twisted Araki-Woods Algebras, the Yang-Baxter Equation, and quantum field theory
In: Geometric Methods in Physics XL, Birkhäuser, 2024, p. 127-144 (Trends in Mathematics)
ISBN: 978-3-031-62406-3
DOI: 10.1007/978-3-031-62407-0
URL: https://link.springer.com/book/10.1007/978-3-031-62407-0
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Numerical results on quantum energy inequalities in integrable models at the two-particle level
In: Physical Review D 109 (2024), Article No.: 085022
ISSN: 2470-0010
DOI: 10.1103/PhysRevD.109.085022
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Topological Indices in Condensed Matter
Elsevier, 2024
ISBN: 9780323957069
DOI: 10.1016/B978-0-323-95703-8.00041-0
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Levinson theorem for discrete Schrödinger operators on the line with matrix potentials having a first moment
In: Communications in Contemporary Mathematics (2023)
ISSN: 0219-1997
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Bayesian Inference with Nonlinear Generative Models: Comments on Secure Learning
In: IEEE Transactions on Information Theory (2023), p. 1-1
ISSN: 0018-9448
DOI: 10.1109/TIT.2023.3325187
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Spectral localizer for line-gapped non-Hermitian systems
In: Journal of Mathematical Physics 64 (2023), Article No.: 082102
ISSN: 0022-2488
DOI: 10.1063/5.0150995
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Modular Structure and Inclusions of Twisted Araki-Woods Algebras
In: Communications in Mathematical Physics (2023)
ISSN: 0010-3616
DOI: 10.1007/s00220-023-04773-y
URL: https://link.springer.com/article/10.1007/s00220-023-04773-y
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Partially hyperbolic random dynamics on Grassmannians
In: Journal of Mathematical Physics 64 (2023), Article No.: 082702
ISSN: 0022-2488
DOI: 10.1063/5.0146402
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Footprint of a topological phase transition on the density of states
In: Letters in Mathematical Physics 113 (2023), Article No.: 96
ISSN: 0377-9017
DOI: 10.1007/s11005-023-01719-2
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Classification of unitary R-matrices by braid group characters
Oberwolfach Workshop 2309a "Skew Braces and the Yang-Baxter Equation" (Oberwolfach, 26.02.2023 - 04.03.2023)
DOI: 10.4171/OWR/2023/9
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Spectral Flow. A Functional Analytic and Index-Theoretic Approach
Berlin / Boston: De Gruyter, 2023
(De Gruyter Studies in Mathematics, Vol.94)
ISBN: 9783111169897
DOI: 10.1515/9783111172477
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Spectral flow: A functional analytic and index-Theoretic approach
Berlin, Boston: De Gruyter, 2023
(De Gruyter Studies in Mathematics)
ISBN: 9783111172477
DOI: 10.1515/9783111172477
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Inclusions of Standard Subspaces
Mini-Workshop on Standard Subspaces in Quantum Field Theory and Representation Theory (Oberwolfach, 29.10.2023 - 03.11.2023)
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Callias-type operators associated to spectral triples
In: Journal of Noncommutative Geometry 17 (2023), p. 527-572
ISSN: 1661-6952
DOI: 10.4171/JNCG/505
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Spectral localization for semimetals and Callias operators
In: Journal of Mathematical Physics 64 (2023), Article No.: 081901
ISSN: 0022-2488
DOI: 10.1063/5.0093983
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The generators of the K-groups of the sphere
In: Expositiones Mathematicae 41 (2023), Article No.: 125519
ISSN: 0723-0869
DOI: 10.1016/j.exmath.2023.125519
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Band Edge Limit of the Scattering Matrix for Quasi-One-Dimensional Discrete Schrodinger Operators
In: Complex Analysis and Operator Theory 16 (2022)
ISSN: 1661-8254
DOI: 10.1007/s11785-022-01196-w
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Secure Coding via Gaussian Random Fields
2022 IEEE International Symposium on Information Theory, ISIT 2022 (Espoo, 26.06.2022 - 01.07.2022)
In: IEEE International Symposium on Information Theory - Proceedings 2022
DOI: 10.1109/ISIT50566.2022.9834788
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Analysis of Sparse Recovery Algorithms via the Replica Method
In: Gitta Kutyniok, Holger Rauhut, Robert J. Kunsch (ed.): Compressed Sensing in Information Processing, Cham: Birkhäuser, 2022, p. 145-179 (Applied and Numerical Harmonic Analysis)
DOI: 10.1007/978-3-031-09745-4_5
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RANDOM MOBIUS DYNAMICS ON THE UNIT DISC AND PERTURBATION THEORY FOR LYAPUNOV EXPONENTS
In: Discrete and Continuous Dynamical Systems-Series B (2022), p. 945-976
ISSN: 1531-3492
DOI: 10.3934/dcdsb.2021076
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Deformations of half-sided modular inclusions and non-local chiral field theories
In: Communications in Mathematical Physics (2022)
ISSN: 0010-3616
DOI: 10.1007/s00220-022-04324-x
URL: https://link.springer.com/article/10.1007/s00220-022-04324-x
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Reduced transfer operators for singular difference equations
In: Journal of Difference Equations and Applications (2022)
ISSN: 1023-6198
DOI: 10.1080/10236198.2022.2147002
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Applications to Solid State Systems
DOI: 10.1007/978-3-031-12201-9_5
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Besov Spaces for Isometric G-Actions
DOI: 10.1007/978-3-031-12201-9_2
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Duality for Toeplitz Extensions
DOI: 10.1007/978-3-031-12201-9_4
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Harmonic analysis in operator algebras and its applications to index theory and topological solid state systems
Cham: Springer, 2022
(Mathematical Physics Studies)
DOI: 10.1007/978-3-031-12201-9
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Invariants of disordered semimetals via the spectral localizer
In: EPL - Europhysics Letters 136 (2022)
ISSN: 0295-5075
DOI: 10.1209/0295-5075/ac1b65
URL: https://iopscience.iop.org/article/10.1209/0295-5075/ac1b65/pdf
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Preface and Overview
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Preliminaries on Crossed Products
DOI: 10.1007/978-3-031-12201-9_1
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Quantum Differentiation and Index Theorems
DOI: 10.1007/978-3-031-12201-9_3
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Analyticity properties of the scattering matrix for matrix Schrödinger operators on the discrete line
In: Journal of Mathematical Analysis and Applications 497 (2021), Article No.: 124856
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2020.124856
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High Energy Bounds On Wave Operators
In: Journal of Operator Theory 86 (2021), p. 61-91
ISSN: 0379-4024
DOI: 10.7900/jot.2020feb01.2285
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Yang–Baxter endomorphisms
In: Journal of the London Mathematical Society-Second Series 103 (2021), p. 633-671
ISSN: 0024-6107
DOI: 10.1112/jlms.12387
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Skew localizer and Z2-flows for real index pairings
In: Advances in Mathematics 392 (2021), Article No.: 108038
ISSN: 0001-8708
DOI: 10.1016/j.aim.2021.108038
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Braid groups, the Yang–Baxter equation, and subfactors
In: Snapshots of Modern Mathematics from Oberwolfach (2021)
ISSN: 2626-1995
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The spectral localizer for semifinite spectral triples
In: Proceedings of the American Mathematical Society 149 (2021), p. 121-134
ISSN: 0002-9939
DOI: 10.1090/proc/15230
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Dimensional Reduction and Scattering Formulation for Even Topological Invariants
In: Communications in Mathematical Physics 381 (2021), p. 119-142
ISSN: 0010-3616
DOI: 10.1007/s00220-020-03886-y
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On Z(2)-indices for ground states of fermionic chains
In: Reviews in Mathematical Physics 32 (2020)
ISSN: 0129-055X
DOI: 10.1142/S0129055X20500282
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Approximate symmetries and conservation laws in topological insulators and associated Z-invariants
In: Annals of Physics 419 (2020), Article No.: 168238
ISSN: 0003-4916
DOI: 10.1016/j.aop.2020.168238
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Pseudo-gaps for random hopping models
In: Journal of Physics A: Mathematical and Theoretical 53 (2020)
ISSN: 1751-8113
DOI: 10.1088/1751-8121/ab5e8c
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Fock representations of ZF algebras and R-matrices
In: Letters in Mathematical Physics 110 (2020), p. 1623-1643
ISSN: 0377-9017
DOI: 10.1007/s11005-020-01271-3
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The spectral localizer for even index pairings
In: Journal of Noncommutative Geometry 14 (2020), p. 1-23
ISSN: 1661-6952
DOI: 10.4171/JNCG/357
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Space versus energy oscillations of prÜfer phases for matrix sturm-liouville and jacobi operators
In: Electronic Journal of Differential Equations 2020 (2020), p. 1-23
ISSN: 1072-6691
URL: https://ejde.math.txstate.edu/
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Statistical Mechanics of MAP Estimation: General Replica Ansatz
In: IEEE Transactions on Information Theory 65 (2019), p. 7896-7934
ISSN: 0018-9448
DOI: 10.1109/TIT.2019.2937335
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Spectral flow for skew-adjoint Fredholm operators
In: Journal of Spectral Theory 9 (2019), p. 137-170
ISSN: 1664-039X
DOI: 10.4171/JST/243
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Spectral Flow of Monopole Insertion in Topological Insulators
In: Communications in Mathematical Physics 370 (2019), p. 895-923
ISSN: 0010-3616
DOI: 10.1007/s00220-019-03310-0
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Parity as Z2-valued spectral flow
In: Bulletin of the London Mathematical Society 51 (2019), p. 836-852
ISSN: 0024-6093
DOI: 10.1112/blms.12282
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Random perturbations of hyperbolic dynamics
In: Electronic Journal of Probability 24 (2019), p. 23 pp.
ISSN: 1083-6489
DOI: 10.1214/19-EJP340
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Erratum: Oscillation theory for the density of states of high dimensional random operators (International Mathematics Research Notices DOI: 10.1093/imrn/rnx246)
In: International Mathematics Research Notices 2019 (2019), p. 4898-
ISSN: 1073-7928
DOI: 10.1093/imrn/rnx317
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Yang-Baxter representations of the infinite symmetric group
In: Advances in Mathematics 355 (2019), Article No.: 106769
ISSN: 0001-8708
DOI: 10.1016/j.aim.2019.106769
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Spectral flow argument localizing an odd index pairing
In: Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 62 (2019), p. 373 - 381
ISSN: 0008-4395
DOI: 10.4153/CMB-2018-013-x
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Chern numbers as half-signature of the spectral localizer
In: Journal of Mathematical Physics 60 (2019), Article No.: 0721011
ISSN: 0022-2488
DOI: 10.1063/1.5094300
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Application of Semifinite Index Theory to Weak Topological Phases
In: 2016 MATRIX Annals, Cham: Springer, 2018, p. 203-227
DOI: 10.1007/978-3-319-72299-3_10
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SO(d, 1) -Invariant Yang–Baxter Operators and the dS/CFT Correspondence
In: Communications in Mathematical Physics 357 (2018), p. 159-202
ISSN: 0010-3616
DOI: 10.1007/s00220-017-2942-6
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Approximation numbers of weighted composition operators
In: Journal of Functional Analysis 274 (2018), p. 1928-1958
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2018.01.010
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Topological edge states for disordered bosonic systems
In: Journal of Mathematical Physics 59 (2018), Article No.: 031901
ISSN: 0022-2488
DOI: 10.1063/1.5002094
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The non-commutative topology of two-dimensional dirty superconductors
In: Journal of Geometry and Physics 124 (2018), p. 100-123
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2017.10.016
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Inverse Scattering and Local Observable Algebras in Integrable Quantum Field Theories
In: Communications in Mathematical Physics 354 (2017), p. 913-956
ISSN: 0010-3616
DOI: 10.1007/s00220-017-2891-0
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Replica Symmetry Breaking in Compressive Sensing
Information Theory and Applications Workshop (ITA) (San Diego, CA, 12.02.2017 - 17.02.2017)
DOI: 10.1109/ITA.2017.8023461
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Quantum backflow and scattering
In: Physical Review A 96 (2017), Article No.: 012112
ISSN: 1050-2947
DOI: 10.1103/PhysRevA.96.012112
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Oscillation theory for the density of states of high dimensional random operators
In: International Mathematics Research Notices 2019 (2017), p. 4579–4602
ISSN: 1073-7928
DOI: 10.1093/imrn/rnx246
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Topological boundary invariants for Floquet systems and quantum walks
In: Mathematical Physics Analysis and Geometry 20 (2017), Article No.: 22
ISSN: 1385-0172
DOI: 10.1007/s11040-017-9253-1
URL: https://link.springer.com/article/10.1007/s11040-017-9253-1
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Finite volume calculation of K-theory invariants
In: New York Journal of Mathematics 22 (2017), p. 1111 - 1140
ISSN: 1076-9803
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Signatures for J-hermitians and J-unitaries on Krein spaces with Real structures
In: Mathematische Nachrichten 290 (2017), p. 1840-1858
ISSN: 0025-584X
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Recent Mathematical Developments in Quantum Field Theory
In: Oberwolfach reports 13 (2016), p. 2069-2122
ISSN: 1660-8933
DOI: 10.4171/OWR/2016/36
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RSB decoupling property of MAP estimators
2016 IEEE Information Theory Workshop (ITW) (Cambridge, London)
In: 2016 IEEE Information Theory Workshop (ITW) 2016
DOI: 10.1109/ITW.2016.7606860
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Index Pairings in Presence of Symmetries with Applications to Topological Insulators
In: Communications in Mathematical Physics 343 (2016), p. 477-513
ISSN: 0010-3616
DOI: 10.1007/s00220-015-2530-6
URL: http://link.springer.com/article/10.1007/s00220-015-2530-6
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Modular nuclearity: A generally covariant perspective
In: Axioms 5 (2016), Article No.: 5
ISSN: 2075-1680
DOI: 10.3390/axioms5010005
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Thermal equilibrium states for quantum fields on non-commutative spacetimes
In: Felix Finster, Johannes Kleiner, Christian Röken, Jürgen Tolksdorf (ed.): Quantum Mathematical Physics, Springer International Publishing, 2016, p. 179-199
ISBN: 9783319269023
DOI: 10.1007/978-3-319-26902-3_10
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Strict deformation quantization of locally convex algebras and modules
In: Journal of Geometry and Physics 99 (2016), p. 111-144
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2015.09.013
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Bulk and Boundary Invariants for Complex Topological Insulators
Springer International Publishing, 2016
(Mathematical Physics Studies)
ISBN: 978-3-319-29350-9
DOI: 10.1007/978-3-319-29351-6
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Generalized Connes-Chern characters in KK-theory with an application to weak invariants of topological insulators
In: Reviews in Mathematical Physics 28 (2016), Article No.: 1650024
ISSN: 0129-055X
DOI: 10.1142/S0129055X16500240
URL: https://www.worldscientific.com/doi/abs/10.1142/S0129055X16500240
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Non-commutative odd Chern numbers and topological phases of disordered chiral systems
In: Journal of Functional Analysis 271 (2016), p. 1150-1176
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2016.06.001
URL: http://de.arxiv.org/abs/1402.5002
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The density of surface states as the total time delay
In: Letters in Mathematical Physics 106 (2016), p. 485-507
ISSN: 0377-9017
DOI: 10.1007/s11005-016-0825-y
URL: http://link.springer.com/article/10.1007/s11005-016-0825-y
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Topological insulators from the perspective of non-commutative geometry and index theory
In: Jahresbericht der deutschen Mathematiker-Vereinigung 118 (2016), p. 247–273
ISSN: 0012-0456
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Krein signatures of transfer operators for half-space topological insulators
In: Journal of Physics A: Mathematical and Theoretical 49 (2016), p. 19pp
ISSN: 1751-8113
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Spectral flows associated to flux tubes
In: Annales Henri Poincaré 17 (2016), p. 1-35
ISSN: 1424-0637
DOI: 10.1007/s00023-014-0394-5
URL: http://link.springer.com/article/10.1007/s00023-014-0394-5
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Gaussian fluctuations of products of random matrices distributed close to the identity
In: Journal of Difference Equations and Applications 21 (2015), p. 467-485
ISSN: 1023-6198
DOI: 10.1080/10236198.2015.1024672
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Algebraic constructive quantum field theory: Integrable models and deformation techniques
In: Romeo Brunetti, Claudio Dappiaggi, Klaus Fredenhagen, Jakob Yngvason (ed.): Advances in Algebraic Quantum Field Theory, Springer International Publishing, 2015 (Mathematical Physics Studies)
ISBN: 9783319213538
DOI: 10.1007/978-3-319-21353-8_10
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Localization in Nets of Standard Spaces
In: Communications in Mathematical Physics 336 (2015), p. 27-61
ISSN: 0010-3616
DOI: 10.1007/s00220-014-2199-2
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Linear hyperbolic PDEs with noncommutative time
In: Journal of Noncommutative Geometry 9 (2015), p. 999-1040
ISSN: 1661-6952
DOI: 10.4171/JNCG/214
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Z_2 indices and factorization properties for odd symmetric Fredholm operators
In: Documenta Mathematica 20 (2015), p. 1481-1500
ISSN: 1431-0643
URL: https://www.math.uni-bielefeld.de/documenta/vol-20/vol-20.html
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Localization and Chern numbers for weakly disordered BdG operators
In: Markov Processes and Related Fields 21 (2015), p. 463-482
ISSN: 1024-2953
URL: http://de.arxiv.org/abs/1310.0207
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Spectral flows of dilations of Fredholm operators
In: Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques 58 (2015), p. 51-68
ISSN: 0008-4395
DOI: 10.4153/CMB-2014-055-3
URL: http://de.arxiv.org/abs/1405.0410
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Quantization of interface currents
In: Journal of Mathematical Physics 55 (2014), Article No.: 121901
ISSN: 0022-2488
DOI: 10.1063/1.4902377
URL: http://de.arxiv.org/abs/1405.0408
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Towards an Operator-Algebraic Construction of Integrable Global Gauge Theories
In: Annales Henri Poincaré 15 (2014), p. 645-678
ISSN: 1424-0637
DOI: 10.1007/s00023-013-0260-x
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Signature and spectral flow for J-unitary S^1 Fredholm operators
In: Integral Equations and Operator Theory 78 (2014), p. 323-374
ISSN: 0378-620X
DOI: 10.1007/s00020-013-2094-9
URL: http://de.arxiv.org/abs/1210.0184
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Topological invariants of edge states for periodic two-dimensional models
In: Mathematical Physics Analysis and Geometry 16 (2013), p. 136-170
ISSN: 1385-0172
DOI: 10.1007/s11040-012-9123-9
URL: http://de.arxiv.org/abs/1202.0537
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Wick rotation for quantum field theories on degenerate Moyal space(-time)
In: Journal of Mathematical Physics 54 (2013), Article No.: 022307
ISSN: 0022-2488
DOI: 10.1063/1.4790886
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Scattering zippers and their spectral theory
In: Journal of Spectral Theory 3 (2013), p. 47-82
ISSN: 1664-039X
URL: http://de.arxiv.org/abs/1112.4959
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On the Equivalence of Two Deformation Schemes in Quantum Field Theory
In: Letters in Mathematical Physics 103 (2013), p. 421-437
ISSN: 0377-9017
DOI: 10.1007/s11005-012-0599-9
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Lyapunov spectra for all symmetry classes of quasi-one-dimensional disordered systems of non-interacting Fermions
In: Journal of Statistical Physics 152 (2013), p. 275-304
ISSN: 0022-4715
DOI: 10.1007/s10955-013-0764-2
URL: http://de.arxiv.org/abs/1212.0322
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Persistence of spin edge currents in disordered quantum spin Hall systems
In: Communications in Mathematical Physics 324 (2013), p. 589-600
ISSN: 0010-3616
DOI: 10.1007/s00220-013-1814-y
URL: http://de.arxiv.org/abs/1207.2480
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Orbital polarization and magnetization for independent particles in disordered media
In: Communications in Mathematical Physics 319 (2013), p. 649-681
ISSN: 0010-3616
DOI: 10.1007/s00220-012-1639-0
URL: http://de.arxiv.org/abs/1201.4812
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Scattering theory for lattice operators in dimension d ≥ 3
In: Reviews in Mathematical Physics 24 (2012), p. 1250020-1250071
ISSN: 0129-055X
DOI: 10.1142/S0129055X12500201
URL: http://de.arxiv.org/abs/1109.5459
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Transport in the random Kronig-Penney model
In: Journal of Mathematical Physics 53 (2012), p. 122109
ISSN: 0022-2488
DOI: 10.1063/1.4769219
URL: http://de.arxiv.org/abs/1207.0295
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Deformations of Quantum Field Theories and Integrable Models
In: Communications in Mathematical Physics 312 (2012), p. 265-302
ISSN: 0010-3616
DOI: 10.1007/s00220-011-1390-y
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Sturm intersection theory for periodic Jacobi matrices and linear Hamiltonian systems
In: Linear Algebra and Its Applications 436 (2012), p. 498-515
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.06.052
URL: http://de.arxiv.org/abs/1105.6219
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Scaling limits of integrable quantum field theories
In: Reviews in Mathematical Physics 23 (2011), p. 1115-1156
ISSN: 0129-055X
DOI: 10.1142/S0129055X11004539
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Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories
In: Communications in Mathematical Physics 304 (2011), p. 95-123
ISSN: 0010-3616
DOI: 10.1007/s00220-010-1137-1
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Deformations of Quantum Field Theories on Spacetimes with Killing Vector Fields
In: Communications in Mathematical Physics 305 (2011), p. 99-130
ISSN: 0010-3616
DOI: 10.1007/s00220-011-1210-4
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Deformations of operator algebras and the construction of quantum field theories
XVIth International Congress on Mathematical Physics
DOI: 10.1142/9789814304634_0040
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Random phase property and the Lyapunov spectrum for disordered multi-channel systems
In: Journal of Statistical Physics 140 (2010), p. 122-153
ISSN: 0022-4715
DOI: 10.1007/s10955-010-9986-8
URL: http://de.arxiv.org/abs/0910.5808
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Random Dirac operators with time reversal symmetry
In: Communications in Mathematical Physics 295 (2010), p. 209-242
ISSN: 0010-3616
DOI: 10.1007/s00220-009-0956-4
URL: http://de.arxiv.org/abs/0902.1935
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Random Lie Group actions on compact manifolds: a perturbative analysis
In: Annals of Probability 38 (2010), p. 2224-2257
ISSN: 0091-1798
DOI: 10.1214/10-AOP544
URL: http://de.arxiv.org/abs/0802.2909
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Geometry of Weyl theory for Jacobi matrices with matrix entries
In: Journal D Analyse Mathematique 110 (2010), p. 129-165
ISSN: 0021-7670
DOI: 10.1007/s11854-010-0004-5
URL: http://de.arxiv.org/abs/0804.3746
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Spectral averaging techniques for Jacobi matrices with matrix entries
In: Journal of Physics A: Mathematical and Theoretical A 42 (2009), p. 185204-185217
ISSN: 1751-8113
DOI: 10.1088/1751-8113/42/18/185204
URL: http://de.arxiv.org/abs/0902.1937
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Noncommutative deformations of Wightman quantum field theories
In: Journal of High Energy Physics (2008), Article No.: ARTN 131
ISSN: 1029-8479
DOI: 10.1088/1126-6708/2008/09/131
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Construction of quantum field theories with factorizing S-matrices
In: Communications in Mathematical Physics 277 (2008), p. 821-860
ISSN: 0010-3616
DOI: 10.1007/s00220-007-0381-5
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Positive Lyapunov exponents and localization bounds for strongly mixing potentials
In: Advances in Theoretical and Mathematical Physics 12 (2008), p. 1377-1400
ISSN: 1095-0761
URL: http://de.arxiv.org/abs/math-ph/0702052
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Spectral averaging techniques for Jacobi matrices
In: Journal of Mathematical Physics 49 (2008), p. 023507-023520
ISSN: 0022-2488
DOI: 10.1063/1.2840910
URL: http://de.arxiv.org/abs/0802.2913
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Wedge-local quantum fields and noncommutative Minkowski space
In: Journal of High Energy Physics (2007), Article No.: ARTN 012
ISSN: 1029-8479
DOI: 10.1088/1126-6708/2007/11/012
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Upper bounds on wavepacket spreading for random Jacobi matrices
In: Communications in Mathematical Physics 273 (2007), p. 601-618
ISSN: 0010-3616
DOI: 10.1007/s00220-007-0252-0
URL: http://de.arxiv.org/abs/math-ph/0607029
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Towards the construction of quantum field theories from a factorizing S-matrix
In: Rigorous Quantum Field Theory, Springer Basel, 2007, p. 175-197 (Progress in Mathematics, Vol.251)
DOI: 10.1007/978-3-7643-7434-1_13
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Scaling diagram for the localization length at a band edge
In: Annales Henri Poincaré 8 (2007), p. 1595-1621
ISSN: 1424-0637
DOI: 10.1007/s00023-007-0347-3
URL: http://de.arxiv.org/abs/math-ph/0702051
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Lyapunov Exponents at Anomalies of SL(2, ℝ)-actions
In: Jan Janas, Pavel Kurasov, Ari Laptev, Sergei Naboko, Günter Stolz (ed.): Operator Theory, Analysis and Mathematical Physics, Basel: Birkhäuser, 2007, p. 159-172 (Operator Theory: Advances and Applications, Vol.174)
ISBN: 978-3-7643-8134-9
DOI: 10.1007/978-3-7643-8135-6_10
URL: http://de.arxiv.org/abs/math-ph/0607026
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Rotation numbers for Jacobi matrices with matrix entries
In: Mathematical Physics Electronic Journal 13 (2007), p. 1-40
ISSN: 1086-6655
URL: http://de.arxiv.org/abs/math-ph/0702050
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Gaussian fluctuations for random matrices with correlated entries
In: International Mathematics Research Notices 15 (2007), p. 1-36
ISSN: 1073-7928
DOI: 10.1093/imrn/rnm047
URL: http://de.arxiv.org/abs/math-ph/0607028
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Mott law as lower bound for a random walk in a random environment
In: Communications in Mathematical Physics 263 (2006), p. 21-64
ISSN: 0010-3616
DOI: 10.1007/s00220-005-1492-5
URL: http://de.arxiv.org/abs/math-ph/0407058
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Low density expansion for Lyapunov exponents
In: J. Asch, J. Joye (ed.): Mathematical Physics of Quantum Mechanics, Erlangen: Springer Verlag, 2006, p. 343-350 (Lecture Notes in Physics, Vol.690)
ISBN: 3540310266
DOI: 10.1007/b11573432
URL: http://de.arxiv.org/abs/math-ph/0607027
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On the existence of local observables in theories with a factorizing S-matrix
In: Journal of Physics A: Mathematical and General 38 (2005), p. 3045-3056
ISSN: 0305-4470
DOI: 10.1088/0305-4470/38/13/015
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Semicircle law and freeness for random matrices with symmetries or correlations
In: Mathematical Research Letters 12 (2005), p. 531-542
ISSN: 1073-2780
URL: http://de.arxiv.org/abs/math-ph/0505003
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Modular nuclearity and localization
In: Annales Henri Poincaré 5 (2004), p. 1065-1080
ISSN: 1424-0637
DOI: 10.1007/s00023-004-0190-8
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Boundary maps for C**-crossed products with R with an application to the quantum Hall effect
In: Communications in Mathematical Physics 249 (2004), p. 611-637
ISSN: 0010-3616
DOI: 10.1007/s00220-004-1122-7
URL: http://de.arxiv.org/abs/math-ph/0405022
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Quantization of edge currents of continuous magnetic operators
In: Journal of Functional Analysis 209 (2004), p. 388-413
ISSN: 0022-1236
DOI: 10.1016/S0022-1236(03)00174-5
URL: http://de.arxiv.org/abs/math-ph/0405021
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Weak disorder expansion for localization lengths of quasi-1D systems
In: EPL - Europhysics Letters 68 (2004), p. 247-253
ISSN: 0295-5075
DOI: 10.1209/epl/i2004-10190-9
URL: http://de.arxiv.org/abs/cond-mat/0405125
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Perturbative test of single parameter scaling for 1D random media
In: Annales Henri Poincaré 5 (2004), p. 1159-1180
ISSN: 1424-0637
DOI: 10.1007/s00023-004-0195-3
URL: http://de.arxiv.org/abs/cond-mat/0405125
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Lifshitz tails for the 1D Bernoulli-Anderson model
In: Markov Processes and Related Fields 9 (2004), p. 795-802
ISSN: 1024-2953
URL: http://de.arxiv.org/abs/math-ph/0405020
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Perturbation theory for Lyapunov exponents of an Anderson model on a strip
In: Geometric and Functional Analysis 14 (2004), p. 1089-1117
ISSN: 1016-443X
DOI: 10.1007/s00039-004-0484-5
URL: http://de.arxiv.org/abs/math-ph/0405018
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Delocalization in random polymer models
In: Communications in Mathematical Physics 233 (2003), p. 27-48
ISSN: 0010-3616
DOI: 10.1007/s00220-002-0757-5
URL: http://de.arxiv.org/abs/math-ph/0405024
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Polarization-free quantum fields and interaction
In: Letters in Mathematical Physics 64 (2003), p. 137–154
ISSN: 0377-9017
DOI: 10.1023/A:1025772304804
URL: http://arxiv.org/abs/hep-th/0303062
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Phase-averaged transport for quasiperiodic Hamiltonians
In: Communications in Mathematical Physics 227 (2002), p. 515-539
ISSN: 0010-3616
DOI: 10.1007/s002200200642
URL: http://de.arxiv.org/abs/math-ph/0405023
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Edge channels and Chern numbers in the integer quantum Hall effect
In: Reviews in Mathematical Physics 14 (2002), p. 87-119
ISSN: 0129-055X
DOI: 10.1142/S0129055X02001107
URL: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=00-266
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Homotopy arguments for quantized Hall conductivity
In: Journal of Mathematical Physics 42 (2001), p. 3439-3444
ISSN: 0022-2488
DOI: 10.1063/1.1379070
URL: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=02-4
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Anomalous transport in aperiodic media
XIIIth International Congress on Mathematical Physics, (Imperial College, London,)
In: Proceedings of the ICMP 2000, Boston: 2001
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Subdiffusive quantum transport for 3D-Hamiltonians with absolutely continuous spectra
In: Journal of Statistical Physics 99 (2000), p. 587-594
ISSN: 0022-4715
DOI: 10.1023/A:1018613227308
URL: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=99-344
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Edge versus Bulk Currents in the Integer Quantum Hall Effect
In: Journal of Physics A: Mathematical and Theoretical 33 (2000), p. L27-L32
ISSN: 1751-8113
URL: http://de.arxiv.org/abs/cond-mat/9912186
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Simultaneous quantization of edge and bulk Hall conductivity
In: Journal of Physics A: Mathematical and General 33 (2000)
ISSN: 0305-4470
DOI: 10.1088/0305-4470/33/2/102
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Anomalous transport in presence of singular continuous spectral measures
In: Annales de l'Institut Henri Poincaré - Physique Théorique 71 (1999), p. 539-559
ISSN: 0246-0211
URL: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=99-47
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Intermittent lower bound on quantum diffusion
In: Letters in Mathematical Physics 49 (1999), p. 317-324
ISSN: 0377-9017
DOI: 10.1023/A:1007610717491
URL: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=99-342
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Lower bounds on wave packet propagation by packing dimensions of spectral measures
In: Mathematical Physics Electronic Journal 5 (1999), p. 1-18
ISSN: 1086-6655
URL: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=98-457
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Upper bounds for quantum dynamics governed by Jacobi matrices with self-similar measures
In: Reviews in Mathematical Physics 11 (1999), p. 1249-1268
ISSN: 0129-055X
DOI: 10.1142/S0129055X99000398
URL: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=98-382
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Pointwise dimensions on real Julia sets
In: Journal of Physics A: Mathematical and General 32 (1999), p. 2887-2894
ISSN: 0305-4470
DOI: 10.1088/0305-4470/32/15/014
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A Kinetic Theory for Quantum Transport in Aperiodic Media
In: Journal of Statistical Physics 91 (1998), p. 991-1026
ISSN: 0022-4715
DOI: 10.1023/A:1023084017398
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Anomalous transport: a mathematical framework
In: Reviews in Mathematical Physics 10 (1998), p. 1-46
ISSN: 0129-055X
DOI: 10.1142/S0129055X98000021
URL: http://de.arxiv.org/abs/cond-mat/9706239
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Rigorous spectral analysis of the metal-insulator transition in a limit-periodic potential
In: Journal of Statistical Physics 91 (1998), p. 801-806
ISSN: 0022-4715
DOI: 10.1023/A:1023094030969
URL: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=97-346
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Anomalous Drude Model
In: Physical Review Letters 77 (1997), p. 2176
ISSN: 0031-9007
DOI: 10.1103/PhysRevLett.78.2176
URL: http://de.arxiv.org/abs/cond-mat/9702220
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Anomalous transport in quasicrystals
5th International Conference on Quasicrystals (Avignon, 22.05.1995 - 26.05.1995)
In: C. Janot, R. Mosseri (ed.): Proceedings of the 5th International Conference on Quasicrystals, Singapore: 1995
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The non-commutative geometry of the quantum Hall effect
In: Journal of Mathematical Physics 35 (1994), p. 5373-5451
ISSN: 0022-2488
DOI: 10.1063/1.530758
URL: http://de.arxiv.org/abs/cond-mat/9411052
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Projects at the chair of mathematical physics and operator algebras
Term: 16.08.2026 - 15.08.2028
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
In recent years, the Tomita-Takesaki theory of modular flows of von Neumann algebras has been extensively used both in high energy and condensed matter physics, as a tool for studying energy, entropy and entanglement in quantum field theory (QFT) and semiclassical gravity. The central object in modular theory, the modular or entanglement Hamiltonian associated to a given quantum state and spacetime region, is however only known in a handful of examples. These mainly include theories and regions…
Term: 01.04.2023 - 31.03.2026
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader:
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader:
Topological invariants and their index theory, the bulk-boundary correspondence and the more recently introduced spectral localizer are well-established mathematical concepts for disordered topological insulators and are also influential for numerical studies of such materials. This proposal is about extending prior results and techniques to systems with crystalline defects, disordered semimetals and topological metals, as well as non-hermitian topological systems stemming from (leaky and driven…
Term: 01.09.2021 - 31.08.2026
Funding source: DFG-Einzelförderung / Heisenberg-Programm (EIN-HEI)
Project leader:
Funding source: DFG-Einzelförderung / Heisenberg-Programm (EIN-HEI)
Project leader:
Das Ziel des Heisenberg-Programms ist es, herausragenden Wissenschaftlerinnen und Wissenschaftlern, die alle Voraussetzungen für die Berufung auf eine Langzeit-Professur erfüllen, zu ermöglichen, sich auf eine wissenschaftliche Leitungsfunktion vorzubereiten und in dieser Zeit weiterführende Forschungsthemen zu bearbeiten. In der Verfolgung dieses Ziels müssen nicht immer projektförmige Vorgehensweisen gewählt und realisiert werden. Aus diesem Grunde wird bei der Antragstellung und auch später b…
Term: 01.04.2020 - 31.03.2023
Funding source: Deutsche Forschungsgemeinschaft (DFG)
Project leader:
Funding source: Deutsche Forschungsgemeinschaft (DFG)
Project leader:
The first goal of index theory is to relate topological invariants to indices of Fredholm operators. The most famous result in this direction is the Atiyah-Singer index theorem, but there exist far reaching non-commutative generalizations. While there is a general theory, such index theorems have to be established case by case in applications. The second goal of index theory is to connect invariants and indices of problems related via exact sequences. For example, this allows to read off the top…
Term: 01.07.2018 - 31.12.2021
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader: ,
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader: ,
The theoretical limits of distributed compressive sensing are studied bytools from both information theory and statistical physics. The investigationscover both noise-free and noisy distributed compressive sensing. The theoretical insightsare utilized to design approximate message passing algorithms for joint recovery of large distributed compressive sensing networks with feasible computational complexity. These algo-rithms enable us to verify the non-rigorous results obtained by the replica met…
Term: 01.03.2016 - 28.02.2019
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader: ,
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader: ,
The project will investigate the performance limits of compressive sensing and propose practical algorithms that approach these performance limits closely.The project will focus on the regime of high compression ratios where L1-norm regularization is suboptimal.Compressive sensing will be investigated from the viewpoint of statistical physics and considered as a particular instance of a spin glass system.Both average distortion and minimax distortion will be addressed as objective functions (Ham…
Term: 01.01.2016 - 01.10.2019
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader:
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader:
The first goal of index theory is to relate topological invariants to indices of Fredholm operators. The most famous result in this direction is the Atiyah-Singer index theorem, but there exist far reaching non-commutative generalizations. While there is a general theory, such index theorems have to be established case by case in applications. The second goal of index theory is to connect invariants and indices of problems related via exact sequences. For example, this allows to read off the top…
Term: 01.06.2010 - 31.03.2016
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader:
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Project leader:
Das Forschungsvorhaben kann in zwei Problembereiche unterteilt werden:I Untersuchung der Topologie, der Dynamik und der Spektren von ungeordneten zeitumkehrinvarianten Systemen mit ungeradem Spin II Topologische und spektrale Aspekte der Streutheorie in Medien mit einem periodischen Hintergrundpotential oder an HyperflächenDas Hauptziel im Problembereich I ist eine detaillierte mathematische Analysis von Spin- Randströmen, die zum Beispiel in Graphenschichten auftreten und in Zukunft so genannte…
Term: 01.02.2006 - 30.09.2009
Funding source: Deutsche Forschungsgemeinschaft (DFG)
Project leader:
Funding source: Deutsche Forschungsgemeinschaft (DFG)
Project leader:
Im Rahmen diese Projektes wurden verschiedene Fragestellungen aus dem Bereich der Fest-körperphysik ungeordneter Systeme rigoros analysiert. Die meisten Fortschritte wurden beider kontrollierten Störungstheorie für quasi-eindimensionale zufällige Medien gemacht, die esnun erlauben, auch so genannte Anomalien zu untersuchen. Dies erlaubt insbesondere auchVerbindungen zur Theorie der vollen Zufallsmatrizen herzustellen. Es wurde Delokalisierungfür bestimmte quasi-eindimensionale ungeordnete System…
Publications of the group of Prof. Andreas Knauf (since 1987)
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NONDETERMINISTIC PARTICLE SYSTEMS
In: Discrete and Continuous Dynamical Systems 51 (2026), p. 193-229
ISSN: 1078-0947
DOI: 10.3934/dcds.2026027
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Regularisation by Hamiltonian extension
In: Nonlinearity 38 (2025), Article No.: 075033
ISSN: 0951-7715
DOI: 10.1088/1361-6544/adf0d8
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Mini-course: Classical mechanics and transport
In: Journal of Mathematical Physics 64 (2023), Article No.: 082903
ISSN: 0022-2488
DOI: 10.1063/5.0153118
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Compactification of the Energy Surfaces for NBodies
In: Regular & Chaotic Dynamics 28 (2023), p. 628-658
ISSN: 1560-3547
DOI: 10.1134/S1560354723040081
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Classical n-body scattering with long-range potentials
In: Nonlinearity 34 (2021), p. 8017-8054
ISSN: 0951-7715
DOI: 10.1088/1361-6544/ac288d
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Generating carbon nanotube caps of almost all chiralities, using six molecular segment types
In: Discrete Applied Mathematics 285 (2020), p. 55-60
ISSN: 0166-218X
DOI: 10.1016/j.dam.2020.05.031
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Topology change of level sets in Morse theory
In: Arkiv For Matematik 58 (2020), p. 333-356
ISSN: 0004-2080
DOI: 10.4310/ARKIV.2020.v58.n2.a6
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Improbability of Collisions in n-Body Systems.
In: Archive for Rational Mechanics and Analysis (2019)
ISSN: 0003-9527
DOI: 10.1007/s00205-019-01406-4
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Improbability of Wandering Orbits Passing Through a Sequence of Poincaré Surfaces of Decreasing Size
In: Archive for Rational Mechanics and Analysis 231 (2018), p. 1781–1800
ISSN: 0003-9527
DOI: 10.1007/s00205-018-1309-2
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Asymptotic velocity for four celestial bodies
In: Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences 376 (2018), Article No.: 20170426
ISSN: 1364-503X
DOI: 10.1098/rsta.2017.0426
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Lagrangian relations and linear point billiards
In: Nonlinearity 30 (2017), p. 1326-1355
ISSN: 0951-7715
DOI: 10.1088/1361-6544/aa5b26
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Symbolic Dynamics of Magnetic Bumps
In: Regular & Chaotic Dynamics 22 (2017), p. 448-454
ISSN: 1560-3547
DOI: 10.1134/S1560354717040074
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Stable Degeneracies for Ising Models
In: Communications in Mathematical Physics (2016), p. 1432-0916
ISSN: 0010-3616
DOI: 10.1007/s00220-016-2579-x
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Resonances in the two-center Coulomb systems
In: Reviews in Mathematical Physics 28 (2016)
ISSN: 0129-055X
DOI: 10.1142/S0129055X16500161
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The spectrum of an adelic Markov operator
In: Indiana University Mathematics Journal 64 (2015), p. 1465--1512
ISSN: 0022-2518
DOI: 10.1512/iumj.2015.64.5655
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Maximizing the divergence from a hierarchical model of quantum states
In: Open Systems & Information Dynamics 22 (2015), p. 1550006, 22
ISSN: 1230-1612
DOI: 10.1142/S1230161215500067
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Classical motion in random potentials
In: Ergodic Theory and Dynamical Systems 34 (2014), p. 557--593
ISSN: 0143-3857
DOI: 10.1017/etds.2012.141
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Positive topological entropy for multi-bump magnetic fields
In: Nonlinearity 26 (2013), p. 727--743
ISSN: 0951-7715
DOI: 10.1088/0951-7715/26/3/727
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Entropy distance: New quantum phenomena
In: Journal of Mathematical Physics 53 (2012), p. 102206, 25
ISSN: 0022-2488
DOI: 10.1063/1.4757652
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Mathematische Physik: Klassische Mechanik
Springer, 2011
(Springer Masterclass)
ISBN: 978-3642209772
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The escape rate of a molecule
In: Journal of Mathematical Physics Analysis Geometry 13 (2010), p. 159--189
ISSN: 1812-9471
DOI: 10.1007/s11040-010-9073-z
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Semiclassical resolvent estimates for Schrödinger operators with Coulomb singularities
In: Annales Henri Poincaré 9 (2008), p. 775--815
ISSN: 1424-0637
DOI: 10.1007/s00023-008-0372-x
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The non-trapping degree of scattering
In: Nonlinearity 21 (2008), p. 2023--2041
ISSN: 0951-7715
DOI: 10.1088/0951-7715/21/9/005
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Generalized Farey trees, transfer operators and phase transitions
In: Communications in Mathematical Physics 275 (2007), p. 297--329
ISSN: 0010-3616
DOI: 10.1007/s00220-007-0294-3
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- , :
Maximizing Multi-information
In: Kybernetika 42 (2006), p. 517--538
ISSN: 0023-5954
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Multiresolution 3D-Computerized Tomography and its Application to NDT
9th European Conference on Non-Destructive Testing (ECNDT) (Berlin)
In: Proceedings of the 9th European Conference on Non-Destructive Testing (ECNDT) 2006
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On the integrability of the n-centre problem
In: Mathematische Annalen 331 (2005), p. 631--649
ISSN: 0025-5831
DOI: 10.1007/s00208-004-0598-y
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Stochastically stable quenched measures
In: Journal of Statistical Physics 117 (2004), p. 831--844
ISSN: 0022-4715
DOI: 10.1007/s10955-004-5707-5
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On the Form Factor for the Unitary Group
In: Journal of Mathematical Physics 45 (2004), p. 4956--4979
ISSN: 0022-2488
DOI: 10.1063/1.1814419
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Integrability of the n-center problem at high energies
In: Doklady Mathematics 70 (2004)
ISSN: 1064-5624
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Introduction to Dynamical Systems
In: Mirko Degli Esposti, Sandro Graffi (ed.): The Mathematical Aspects of Quantum Maps, Heidelberg: Springer, 2003, p. 1-24 (Lecture Notes in Physics, Vol.618)
DOI: 10.1007/3-540-37045-5_1
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Does Quantum Chaos Exist?
In: Jean Bricmont, Giancarlo Ghirardi, Detlef Dürr, Francesco Petruccione, Maria Carla Galavotti, Nino Zanghi (ed.): Chance in Physics, Berlin, Heidelberg: Springer, 2001, p. 235-241 (Lecture Notes in Physics, Vol.547)
DOI: 10.1007/3-540-44966-3_17
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The n-Centre Problem of Celestial Mechanics
In: Journal of the European Mathematical Society 4 (2001), p. 1-114
ISSN: 1435-9855
DOI: 10.1007/s100970100037
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Quantum Transport on KAM Tori
In: Communications in Mathematical Physics 205 (1999), p. 113-128
ISSN: 0010-3616
DOI: 10.1007/s002200050670
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A Fully Magnetizing Phase Transition
In: Journal of Statistical Physics 97 (1999), p. 523-539
ISSN: 0022-4715
DOI: 10.1023/A:1004607107241
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Erratum: ``The number-theoretical spin chain and the Riemann zeros'' [Comm.\ Math.\ Phys. 6 (1998), no. 3, 703--731; {MR}1645212 (2000d:11108)]
In: Communications in Mathematical Physics 206 (1999), p. 491
ISSN: 0010-3616
DOI: 10.1007/s002200050715
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Number Theory, Dynamical Systems and Statistical Mechanics
In: Reviews in Mathematical Physics 11 (1999), p. 1027-1060
ISSN: 0129-055X
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Qualitative Aspects of Classical Potential Scattering
In: Regular & Chaotic Dynamics 4 (1999), p. 1-20
ISSN: 1560-3547
DOI: 10.1.1.56.8620
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Motion in periodic potentials
In: Nonlinearity 11 (1998), p. 175--200
ISSN: 0951-7715
DOI: 10.1088/0951-7715/11/1/011
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Quantum chaos and dynamical entropy
In: Communications in Mathematical Physics 198 (1998), p. 607--688
ISSN: 0010-3616
DOI: 10.1007/s002200050489
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Free energy and correlations of the number-theoretical spin chain
In: Journal of Mathematical Physics 39 (1998), p. 3188--3202
ISSN: 0022-2488
DOI: 10.1063/1.532247
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The Number-Theoretical Spin Chain and the Riemann Zeroes
In: Communications in Mathematical Physics 196 (1998), p. 703-731
ISSN: 0010-3616
DOI: 10.1007/s002200050441
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The size of the shadow boundary projection
In: Manuscripta Mathematica 95 (1998), p. 519--527
ISSN: 0025-2611
DOI: 10.1007/s002290050045
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The phase transition of the number-theoretical spin chain
In: Forum Mathematicum 9 (1997), p. 547--567
ISSN: 0933-7741
DOI: 10.1515/form.1997.9.547
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Velocity and entropy of motion in periodic potentials
In: Séminaire sur les Équations aux Dérivées Partielles, 1996--1997, École Polytech., Palaiseau, 1997, p. 1-11
URL: http://eudml.org/doc/10921
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Classical nonintegrability, quantum chaos. With a contribution by Viviane Baladi
Birkhäuser Verlag, Basel, 1997
(DMV Seminar, Vol.27)
ISBN: 3-7643-5708-8
DOI: 10.1007/978-3-0348-8932-2
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The low activity phase of some Dirichlet series
In: Journal of Mathematical Physics 37 (1996), p. 5458--5475
ISSN: 0022-2488
DOI: 10.1063/1.531717
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Irregular scattering, number theory, and statistical mechanics
In: Wojciech Cegła, Zbigniew Haba, Lech Jakóbczyk (ed.): Stochasticity and quantum chaos (Sobótka Castle, 1993), Kluwer Acad. Publ., Dordrecht, 1995, p. 137--148 (Mathematics and its Applications, Vol.317)
DOI: 10.1007/978-94-011-0169-1_13
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On a ferromagnetic spin chain. {II}. Thermodynamic limit
In: Journal of Mathematical Physics 35 (1994), p. 228--236
ISSN: 0022-2488
DOI: 10.1063/1.530769
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Classical Planar Scattering by Coulombic Potentials
Berlin, Heidelberg, New York: Springer, 1993
(Lecture Notes in Physics, Vol.13)
DOI: 10.1007/978-3-540-47336-7
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Inverse KAM-Theorie
In: Seiler Ruedi, Enss Volker, Müller Werner (ed.): Geometrie und Physik, Berlin, New York: De Gruyter, 1993 (Akademie der Wissenschaften zu Berlin, Forschungsberichte, Vol.8)
ISBN: 978-3-11-013944-0
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On a ferromagnetic spin chain
In: Communications in Mathematical Physics 153 (1993), p. 77--115
ISSN: 0010-3616
DOI: 10.1007/BF02099041
URL: http://projecteuclid.org/euclid.cmp/1104252597
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Phases of the Number-Theoretic Spin Chain
In: Journal of Statistical Physics 73 (1993), p. 423--431
ISSN: 0022-4715
DOI: 10.1007/BF01052771
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On the absence of a first order correction for the number of bound states of a Schrödinger operator with Coulomb singularity
In: Communications in Partial Differential Equations 17 (1992), p. 615--639
ISSN: 0360-5302
DOI: 10.1080/03605309208820856
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Chaotic motion in Coulombic potentials
In: Konrad Schmüdgen (ed.): Mathematical physics, X (Leipzig, 1991), Springer, Berlin, 1992, p. 308--312
DOI: 10.1007/978-3-642-77303-7_27
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Collisions for the quantum Coulomb Hamiltonian
In: Communications in Mathematical Physics 143 (1991), p. 17-26
ISSN: 0010-3616
DOI: 10.1007/BF02100283
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The Hannay Angles and Classical Perturbation Theory
In: Jean-Marc Luck, Pierre Moussa, Michel Waldschmidt (ed.): Number Theory and Physics, Springer, 1990, p. 216-222 (Proceedings in Physics, Vol.47)
DOI: 10.1007/978-3-642-75405-0_23
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Closed orbits and converse KAM theory
In: Nonlinearity 3 (1990), p. 961--973
ISSN: 0951-7715
DOI: 10.1088/0951-7715/3/3/019
URL: http://stacks.iop.org/0951-7715/3/961
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Hannay angles: existence and geometrical interpretation
In: Nonlinear dynamics (Bologna, 1988), World Sci. Publ., Teaneck, NJ, 1989, p. 200--209
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The Hannay Angles: Geometry, Adiabaticity, and an Example
In: Communications in Mathematical Physics 123 (1989), p. 95--122
ISSN: 0010-3616
DOI: 10.1007/BF01244019
URL: http://projecteuclid.org/euclid.cmp/1104178683
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Coulombic periodic potentials: The Quantum Case
In: Annals of Physics 191 (1989), p. 205--240
ISSN: 0003-4916
DOI: 10.1016/0003-4916(89)90315-1
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On Soft Billiard Systems
In: Physica D-Nonlinear Phenomena 36 (1989), p. 259-262
ISSN: 0167-2789
DOI: 10.1016/0167-2789(89)90084-5
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Ergodic and topological properties of Coulombic periodic potentials
In: Communications in Mathematical Physics 110 (1987), p. 89--112
ISSN: 0010-3616
DOI: 10.1007/BF01209018
URL: http://projecteuclid.org/euclid.cmp/1104159170
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Planung der Lehre in Funktionalanalysis, mathematischer Physik, Operatoralgebren in den nächsten Semestern
Zur Information von allen Studierenden, die sich näher mit Funktionalanalysis, Operatoralgebren und/oder mathematischer Quantenphysik (QM/QFT) befassen möchten, gibt es hier eine Übersicht über geplante Lehrveranstaltungen in diese Richtung. Der typische Einstieg in diese Forschungsrichtung verläuft über die aufeinander aufbauenden Vorlesungen
- Funktionalanalysis 1 (Sommersemester)
Basis für alle weiterführenden Vorlesungen an diesem und anderen Lehrstühlen. Kann direkt nach den Grundvorlesungen in Analysis/Lineare Algebra belegt werden. Themen: Normierte und andere topologische Vektorräume (Banachräume, Hilberträume), Operatoren auf diesen Räumen, Grundprinzipien der Funktionalanalysis. - Funktionalanalysis 2 (Wintersemester)
Baut auf Funktionalanalysis 1 auf und führt sie fort. Themen: Spektraltheorie, ggf. Einführung in Operatoralgebren. - Mathematische Quantentheorie (Wintersemester)
Baut auf den Funktionalanalysis-Kursen auf und präsentiert die mathematische Struktur der nichtrelativistischen Quantenphysik. Keine Vorkenntnisse in Physik erforderlich.
Weitere sehr empfehlenswerte Vorlesungen sind Topologie, Funktionentheorie, und (unitäre) Darstellungstheorie. Anschließend können spezialisiertere Vorlesungen und Seminare besucht werden, zB zu Vielteilchenquantensystemen, Quantenfeldtheorie, von Neumann Algebren, etc.Anschließend können spezialisiertere Vorlesungen und Seminar besucht werden, zB zu Vielteilchenquantensystemen, Quantenfeldtheorie, von Neumann Algebren, etc.
Die folgende Liste enthält die grobe Lehrplanung für die nächsten Semester. Einerseits enthält sie nicht alle Vorlesungen, die vom Lehrstuhl Mathematische Physik angeboten werden, und andererseits enthält sie auch thematisch passende Veranstaltungen von anderen Lehrstühlen.
Informationen zu weiteren nicht-spezialisierten Veranstaltungen am Lehrstuhl, Vorlesungsskripten, und vergangenen Veranstaltungen finden sich auf den Seiten der einzelnen Dozenten.
Winter 26/27
- Vorlesung Funktionalanalysis 2. 4+2 Stunden, 10 ECTS (Lechner/Große)
Spektraltheorie und Operatoralgebren. - Seminar Spektraltheorie. 2 Stunden, 5 ECTS (Schulz-Baldes)
- Querschnittsmodulseminar Funktionalanalysis. 2 Stunden, 5 ECTS (Lechner)
Dieses Seminar vertieft und erweitert die Inhalte von Funktionalanalysis 1 in Vorträgen der TeilnehmerInnen. - Seminar Matrixalgebren und Quanteninformationstheorie. 2 Stunden, 5 ECTS (Fröb)
Kann direkt nach den Grundvorlesungen Analysis/Lineare Algebra im Bachelor belegt werden. - Seminar Dispersive PDEs, 2 Stunden, 5 ECTS (Boßmann/Wiedemann)
Sommer 27 (noch unvollständig)
- Vorlesung Mathematische Quantentheorie. 4+2 Stunden, 10 ECTS (Schulz-Baldes)
- Vorlesung Funktionalanalysis 1. 4+2 Stunden, 10 ECTS (Boßmann)
- Vorlesung Nets of Operator Algebras. 4+2 Stunden, 10 ECTS (Lechner)
- Seminar Spektraltheorie. 2 Stunden, 5 ECTS (Schulz-Baldes)
Winter 27/28 (noch unvollständig)
- Vorlesung Funktionalanalysis 2. 4+2 Stunden, 10 ECTS (Boßmann)
- Vorlesung Operatoralgebren. 4+2 Stunden, 10 ECTS (Schulz-Baldes)
- Querschnittsmodulseminar Funktionalanalysis. 2 Stunden, 5 ECTS (Boßmann)
- Seminar Spektraltheorie. 2 Stunden, 5 ECTS (Schulz-Baldes)
Sommer 28 (noch unvollständig)
- Vorlesung Mathematische Quantentheorie. 4+2 Stunden, 10 ECTS (Boßmann)
- Vorlesung Funktionalanalysis 1. 4+2 Stunden, 10 ECTS (Schulz-Baldes)
- Seminar Spektraltheorie. 2 Stunden, 5 ECTS (Schulz-Baldes)
Winter 27/28 (noch unvollständig)
- Vorlesung Funktionalanalysis 2. 4+2 Stunden, 10 ECTS (Schulz-Baldes)
- Seminar Spektraltheorie. 2 Stunden, 5 ECTS (Schulz-Baldes)
Frühere Semester (seit Sommer 2026)
Sommer 26
- Vorlesung Mathematische Quantentheorie. 4+2. (Lechner)
- Seminar Entropie. 2+0. (Lechner)
- Vorlesung Fourieranalysis. 4+2. (Fröb)
Research seminar Mathematical Physics
The research seminar on mathematical physics meets on Thursday 4pm ct in Übung 1 during term times, and is jointly run by
If you want to be kept up to date with seminar announcements, you can write to one of us and we will put you on our mailing list.
Winter 2026/27
- 12Nov4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
- 10Dec4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
Sommer 2026
- 12Nov4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
- 10Dec4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
Winter 2025/26
- 12Nov4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
- 10Dec4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
Sommer 2025
- 12Nov4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
- 10Dec4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
Winter 2024/25
- 12Nov4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
- 10Dec4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
Sommer 2024
- 12Nov4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
- 10Dec4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
Winter 2023/24
- 12Nov4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
- 10Dec4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
Sommer 2023
- 12Nov4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
- 10Dec4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
Winter 2022/23
- 12Nov4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
- 10Dec4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
Sommer 2022
- 12Nov4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
- 10Dec4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
Winter 2021/22
- 12Nov4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen
- 10Dec4:15 PM – 6:00 PMÜbung 1 / 01.250-128, Erlangen