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Research

In page navigation: Mathematical Physics and Operator Algebras
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  • Prof. Dr. Andreas Knauf
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Research

Books

M. Klein, A. Knauf: Classical Planar Scattering by Coulombic Potentials.
Lecture Notes in Physics m 13. Berlin, Heidelberg, New York:
Springer; 1993

Ya. Sinai, A. Knauf: Classical Nonintegrability, Quantum Chaos.
DMV–Seminar Band 27. Basel: Birkhäuser 1997

A. Knauf: Mathematische Physik: Klassische Mechanik.
Springer Master Class. 640 pp., 2011. 2. Auflage 2017

A. Knauf: Mathematical Physics: Classical Mechanics. Springer, 683 pp., 2018

Peer-Reviewed Publications

2021

  • Fejoz J., Knauf A., Montgomery R.:
    Classical n-body scattering with long-range potentials
    In: Nonlinearity 34 (2021), p. 8017-8054
    ISSN: 0951-7715
    DOI: 10.1088/1361-6544/ac288d
    BibTeX: Download

2020

  • Amsharov K., Knauf A., Tomada J.:
    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
    BibTeX: Download
  • Knauf A., Martynchuk N.:
    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
    BibTeX: Download

2019

  • Fleischer S., Knauf A.:
    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
    BibTeX: Download

2018

  • Fleischer S., Knauf A.:
    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
    BibTeX: Download
  • Knauf A.:
    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
    BibTeX: Download

2017

  • Féjoz J., Knauf A., Montgomery R.:
    Lagrangian relations and linear point billiards
    In: Nonlinearity 30 (2017), p. 1326-1355
    ISSN: 0951-7715
    DOI: 10.1088/1361-6544/aa5b26
    BibTeX: Download
  • Knauf A., Seri M.:
    Symbolic Dynamics of Magnetic Bumps
    In: Regular & Chaotic Dynamics 22 (2017), p. 448-454
    ISSN: 1560-3547
    DOI: 10.1134/S1560354717040074
    BibTeX: Download

2016

  • Knauf A.:
    Stable Degeneracies for Ising Models
    In: Communications in Mathematical Physics (2016), p. 1432-0916
    ISSN: 0010-3616
    DOI: 10.1007/s00220-016-2579-x
    BibTeX: Download
  • Seri M., Knauf A., Degli Esposti M., Jecko T.:
    Resonances in the two-center Coulomb systems
    In: Reviews in Mathematical Physics 28 (2016)
    ISSN: 0129-055X
    DOI: 10.1142/S0129055X16500161
    BibTeX: Download

2015

  • Knauf A.:
    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
    BibTeX: Download
  • Knauf A., Weis S., Ay N., Zhao MJ.:
    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
    BibTeX: Download

2014

  • Knauf A., Schumacher C.:
    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
    BibTeX: Download

2013

  • Knauf A., Schulz F., Siburg KF.:
    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
    BibTeX: Download

2012

  • Knauf A., Weis S.:
    Entropy distance: New quantum phenomena
    In: Journal of Mathematical Physics 53 (2012), p. 102206, 25
    ISSN: 0022-2488
    DOI: 10.1063/1.4757652
    BibTeX: Download

2011

  • Knauf A.:
    Mathematische Physik: Klassische Mechanik
    Springer, 2011
    (Springer Masterclass)
    ISBN: 978-3642209772
    BibTeX: Download

2010

  • Knauf A., Krapf M.:
    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
    BibTeX: Download

2008

  • Knauf A., Castella F., Jecko T.:
    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
    BibTeX: Download
  • Knauf A., Krapf M.:
    The non-trapping degree of scattering
    In: Nonlinearity 21 (2008), p. 2023--2041
    ISSN: 0951-7715
    DOI: 10.1088/0951-7715/21/9/005
    BibTeX: Download

2007

  • Knauf A., Degli Esposti M., Isola S.:
    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
    BibTeX: Download

2006

  • Knauf A., Ay N.:
    Maximizing Multi-information
    In: Kybernetika 42 (2006), p. 517--538
    ISSN: 0023-5954
    BibTeX: Download
  • Knauf A., Oeckl S., Schön T., Louis AK.:
    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
    BibTeX: Download

2005

  • Knauf A., Taimanov IA.:
    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
    BibTeX: Download

2004

  • Knauf A., Contucci P., Bianchi A.:
    Stochastically stable quenched measures
    In: Journal of Statistical Physics 117 (2004), p. 831--844
    ISSN: 0022-4715
    DOI: 10.1007/s10955-004-5707-5
    BibTeX: Download
  • Knauf A., Degli Esposti M.:
    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
    BibTeX: Download
  • Knauf A., Taimanov IA.:
    Integrability of the n-center problem at high energies
    In: Doklady Mathematics 70 (2004)
    ISSN: 1064-5624
    BibTeX: Download

2003

  • Knauf A.:
    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
    BibTeX: Download

2001

  • Knauf A.:
    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
    BibTeX: Download
  • Knauf A.:
    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
    BibTeX: Download

1999

  • Asch J., Knauf A.:
    Quantum Transport on KAM Tori
    In: Communications in Mathematical Physics 205 (1999), p. 113-128
    ISSN: 0010-3616
    DOI: 10.1007/s002200050670
    BibTeX: Download
  • Contucci P., Kleban P., Knauf A.:
    A Fully Magnetizing Phase Transition
    In: Journal of Statistical Physics 97 (1999), p. 523-539
    ISSN: 0022-4715
    DOI: 10.1023/A:1004607107241
    BibTeX: Download
  • Knauf A.:
    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
    BibTeX: Download
  • Knauf A.:
    Number Theory, Dynamical Systems and Statistical Mechanics
    In: Reviews in Mathematical Physics 11 (1999), p. 1027-1060
    ISSN: 0129-055X
    BibTeX: Download
  • Knauf A.:
    Qualitative Aspects of Classical Potential Scattering
    In: Regular & Chaotic Dynamics 4 (1999), p. 1-20
    ISSN: 1560-3547
    DOI: 10.1.1.56.8620
    BibTeX: Download

1998

  • Asch J., Knauf A.:
    Motion in periodic potentials
    In: Nonlinearity 11 (1998), p. 175--200
    ISSN: 0951-7715
    DOI: 10.1088/0951-7715/11/1/011
    BibTeX: Download
  • Benatti F., Hudetz T., Knauf A.:
    Quantum chaos and dynamical entropy
    In: Communications in Mathematical Physics 198 (1998), p. 607--688
    ISSN: 0010-3616
    DOI: 10.1007/s002200050489
    BibTeX: Download
  • Guerra F., Knauf A.:
    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
    BibTeX: Download
  • Knauf A.:
    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
    BibTeX: Download
  • Knauf A.:
    The size of the shadow boundary projection
    In: Manuscripta Mathematica 95 (1998), p. 519--527
    ISSN: 0025-2611
    DOI: 10.1007/s002290050045
    BibTeX: Download

1997

  • Contucci P., Knauf A.:
    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
    BibTeX: Download
  • Knauf A.:
    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
    BibTeX: Download
  • Sinai YG., Knauf A.:
    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
    BibTeX: Download

1996

  • Contucci P., Knauf A.:
    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
    BibTeX: Download

1995

  • Knauf A.:
    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
    BibTeX: Download

1994

  • Knauf A.:
    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
    BibTeX: Download

1993

  • Klein M., Knauf A.:
    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
    BibTeX: Download
  • Knauf A.:
    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

    BibTeX: Download
  • Knauf A.:
    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
    BibTeX: Download
  • Knauf A.:
    Phases of the Number-Theoretic Spin Chain
    In: Journal of Statistical Physics 73 (1993), p. 423--431
    ISSN: 0022-4715
    DOI: 10.1007/BF01052771
    BibTeX: Download

1992

  • Helffer B., Knauf A., Siedentop H., Weikard R.:
    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
    BibTeX: Download
  • Klein M., Knauf A.:
    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
    BibTeX: Download

1991

  • Gérard C., Knauf A.:
    Collisions for the quantum Coulomb Hamiltonian
    In: Communications in Mathematical Physics 143 (1991), p. 17-26
    ISSN: 0010-3616
    DOI: 10.1007/BF02100283
    BibTeX: Download

1990

  • Golin S., Knauf A., Marmi S.:
    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
    BibTeX: Download
  • Knauf A.:
    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
    BibTeX: Download

1989

  • Golin S., Knauf A., Marmi S.:
    Hannay angles: existence and geometrical interpretation
    In: Nonlinear dynamics (Bologna, 1988), World Sci. Publ., Teaneck, NJ, 1989, p. 200--209
    BibTeX: Download
  • Golin S., Knauf A., Marmi S.:
    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
    BibTeX: Download
  • Knauf A.:
    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
    BibTeX: Download
  • Knauf A.:
    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
    BibTeX: Download

1987

  • Knauf A.:
    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
    BibTeX: Download
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