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
2023
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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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2021
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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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2020
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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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2019
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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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2018
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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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2017
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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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2016
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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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2015
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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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2014
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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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2013
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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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2012
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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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2011
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Mathematische Physik: Klassische Mechanik
Springer, 2011
(Springer Masterclass)
ISBN: 978-3642209772
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2010
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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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2008
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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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2007
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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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2006
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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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2005
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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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2004
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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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2003
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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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2001
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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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1999
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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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1998
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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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1997
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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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1996
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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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1995
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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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1994
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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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1993
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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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1992
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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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1991
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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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1990
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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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1989
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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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1987
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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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