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Publications & Preprints

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Project B1: Hyperbolic dynamical systems, periodic orbits and quantum spectra


Spectral statistics of nearly unidirectional quantum graphs
M. Akila, B. Gutkin
J. Phys. A: Math. Theor. 48 (2015) 345101
Universality in spectral statistics of "open" quantum graphs
B. Gutkin, V. Al. Osipov
Phys. Rev. E91 (2015) 060901(R)/1-5
Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs
H.M. Huynh, M. Kunze
Nonlinearity 28 (2015) 593-623
Higher dimensional nonclassical eigenvalue asymptotics
N. Rautenberg, B. Camus
Journal of Mathematical Physics 56, 021506 (2015)
Self-averaging characteristics of spectral fluctuations
P. Braun, F. Haake
J. Phys. A 48 (2015) 135101
A review of sigma models for quantum chaotic dynamics
A. Altland, S. Gnutzmann, F. Haake, T. Micklitz

Rep. Prog. Phys. 78 (2015) 086001
Invariant tori and topological entropy in Tonelli Lagrangian systems on the 2-torus
J.P. Schröder

Ergodic Theory and Dynamical Systems, publ. online (2015), available on CJO2015; doi: 10.1017/etds.2014.137
Geodesic flows on S² and area-preserving homeomorphisms of the annulus
S. Klempnauer

Master thesis, Ruhr-Universität Bochum (01/2015)


Spectral Properties and Dynamical Tunneling in Constant-Width Billiards
B. Dietz, T. Guhr, B. Gutkin, M. Miski-Oglu, A. Richter
arXiv:1407.6630 [
Physical Review E 90, 052909 (2014)
Unconventional quantum criticality in the kicked rotor
J. Wang, C. Tian, A. Altland
Phys. Rev. B 89, 195105 (2014)
Topological entropy of minimal geodesics and volume growth on surfaces
E. Glasmachers, G. Knieper, C. Ogouyandjou, J.P. Schröder

Journal of Modern Dynamics 8 (2014) 75-91
Partner orbits and action differences on compact factors of the hyperbolic plane
H.M. Huynh

Dissertation, Universität zu Köln (2014)
Dynamik des geodätischen Flusses auf Mannigfaltigkeiten negativer Krümmung
B. Schulz

Master thesis, Ruhr-Universität Bochum (08/2014)
On Partner orbits in hyperbolic dynamics
K. Bieder

Dissertation, Ruhr-Universität Bochum (12/2014)
On spectral geometry of unbounded domains
N. Rautenberg

Dissertation, Ruhr-Universität Bochum (11/2014)


Path Integral Approach to Spreading in Many-Body-Systems
M. Akila

Master thesis, Universität Duisburg-Essen (04/2013)
Tonelli Lagrangians on the 2-torus: global minimizers, invariant tori and topological entropy
J.P. Schröder

Dissertation, Ruhr-Universität Bochum (12/2013)


Beyond the Heisenberg time: Semiclassical treatment of spectral correlations in chaotic systems with spin 1/2
P. Braun
J. Phys. A 45 (2012) 045102
Chaotic maps and flows: Exact Riemann-Siegel lookalike for spectral fluctuations
P. Braun, F. Haake
J. Phys. A 45 (2012) 425101
Spreading the Integrable and Non-Integrable Systems
J. Freese

Diplom thesis, Universität Duisburg-Essen (02/2012)


Spectral problem of block-rectangular hierarchical matrices
B. Gutkin, V.Al. Osipov
Journal of Statistical Physics Volume 143, Number 1, pp.72-87, 2011
Quantum phase transitions in the quasi-periodic kicked rotor
C. Tian, A. Altland, M. Garst
Phys. Rev. Lett. 107 (2011) 074101
Theory of Anderson Transition in the Quasiperiodic Kicked Rotor
C. Tian, A. Altland, M. Garst

Phys. Rev. Lett. 107 (2011) 074101


Entropic bounds on semiclassical measures for quantized one-dimensional maps
B. Gutkin
abstract math-ph/0802.3400
Commun. Math. Phys. 294, 303-342 (2010)
Quantum kinetic Ising models
R. Augusiak, F. M. Cucchietti, F. Haake, M. Lewenstein
abstract cond-mat/0911.0624
New Journal of Physics 12, 025021 (2010)
Collective versus Single--Particle Motion in Quantum Many--Body Systems from the Perspective of an Integrable Model
J. Hammerling, B. Gutkin, T. Guhr
abstract quant-ph/0911.2724
J. Phys. A43, 265101–1-17 (2010)
Quantum Corrections to Fidelity Decay in Chaotic Systems
B. Gutkin, D. Waltner, M. Gutierrez, J. Kuipers, K. Richter
abstract cond-mat/0911.0823
Phys. Rev. E81.036222
Survival Probability of a Doorway State in regular and chaotic environments
H. Kohler, H. J. Sommers, S. Aberg
abstract cond-mat/0912.3174
J. Phys. A43, 215102– 1-16 (2010)
Exact Fidelity and Full Fidelity Statistics in Regular and Chaotic Surroundings
H.Kohler, H.J. Sommers, S. Aberg, T. Guhr
abstract cond-mat/0912.3180
Phys. Rev. E81, 050103(R)–1-4 (2010)
Observation of Periodic Orbits on Curved Two - dimensional Geometries
M. Avlund, C. Ellegaard, M. Oxborrow, T. Guhr, N. Sondergaard
abstract cond-mat/1004.4511
Phys. Rev. Lett. 104, 164101 (2010)
Coupling Coeffcient Distribution in the Doorway Mechanism
Heiner Kohler, Thomas Guhr, Sven Aberg
abstract quant-ph/1001.1420
New J. Phys. 12, 073026–1-20 (2010)
Level statistics in arithmetical and pseudo-arithmetical chaos
P. Braun, F. Haake
abstract cond-mat/1001.3339
J. Phys. A 43, 262001 (2010)
A New Approach To The Treatment Of Separatrix Chaos And Its Applications
S.M. Soskin, R. Mannella, O.M. Yevtushenko, I.A. Khovanov, P.V.E. McClintock
abstract nlin.CD/0906.3444
Chapter 2 in "Hamitonian Chaos Beyond the KAM Theory", edited by A.C.J. Luo and V. Afraimovich (Higher Education Press, Beijing; Springer, Heidelberg, 2010) 51-142
Characterization of geodesic flows on T^2 with and without positive topological entropy
E. Glasmachers, G. Knieper
abstract cond-mat/0707.0666
to appear in Geometric and Functional Analysis (GAFA) (2010)
Theory of localization and resonance phenomena in the quantum kicked rotor
C. Tian and A. Altland
abstract nlin.CD/1001.4322
New J. Phys. 12 043043 (2010)
Spectral Statistics of “Cellular” Billiards
B. Gutkin
abstract nlin.CD/1010.0276
submitted for publication in Nonlinearity
Collective versus Single--Particle Motion in Quantum Many--Body Systems: Spreading and its Semiclassical Interpretation
Jens Hammerling, Boris Gutkin, Thomas Guhr
abstract quant-ph/1012.3111
Kicked top
F. Haake and M. Kus
Scholarpedia, 5(11):10242 (2010)


Periodic-orbit theory of universal level correlations in quantum chaos
S. Müller, S. Heusler, A. Altland, P. Braun, F. Haake
abstract cond-mat/0906.1960
New J. Phys. 11, 103025 (2009)
The dephasing rate formula in the many body context
D. Cohen, J. von Delft, F. Marquardt, Y. Imry
abstract cond-mat/0909.1441
Phys. Rev. B 80, 245410 (2009)
Doorway Mechanism in Many–Body Systems and in Quantum Billiards
T. Guhr

Acta Physica Polonica A116, 741-748 (2009)
New results on noncompact harmonic manifolds
G. Knieper
abstract cond-mat/0910.3872
to appear in Commentarii Mathematici Helvetici (2009)
Microscopic Theory of the Andreev Gap
T. Micklitz and A. Altland
abstract nlin.CD/0901.3137
Phys. Rev. Lett. 103, 080403 (2009)
Semiclassical theory for universality in quantum chaos with symmetry crossover
K. Saito, T. Nagao, S. Müller, and P. Braun
abstract nlin.CD/0906.2033
J. Phys. A 42, 495101 (2009)
Note on Converse Quantum Ergodicity
B. Gutkin

Proc. Amer. Math. Soc. 137, 2795-2800 (2009)
Equicontinuous geodesic flows
C. Pries
abstract math.DS/0710.4016
Ergodic Theory and Dynamical Systems 29.6, 1951-1963 (2009)
Geodesics closed on a projective plane
C. Pries

Geometric and Functional Analysis 18.5, 1774-1785 (2009)


Anderson localization from classical trajectories
P. W. Brouwer, A. Altland
abstract cond-mat/0802.0976
Phys. Rev. B 78, 075304 (2008)
Ergodic properties of isoperimetric domains in spheres
G.Knieper, N.Peyerimhoff

J. of Modern Dynamics No. 2 (2008), 1-20
Superscars in billiards -- A model for doorway states in quantum spectra
S. Aberg, T. Guhr, M. Miski-Oglu and A. Richter
abstract nlin.CD/0805.2345
Phys. Rev. Lett. 100, 204101–1-4 (2008)
Families of Spherical Caps: Spectra and Ray Limit
N. Søndergaard and T. Guhr
abstract nlin.CD/0802.0140
J. Phys. A 41 075309 (2008)
Semiclassical spectral correlator in quasi one-dimensional systems
P. Braun, S. Müller, and F. Haake
abstract nlin.CD/0806.2066
J. Phys. A 41, 395101 (2008)
Near action-degenerate periodic-orbit bunches: A skeleton of chaos
D. A. Altland, P. Braun, F. Haake, S. Heusler, G. Knieper, and S. Müller
abstract nlin.CD/0906.4930
Path Integrals New Trends and Perspectives: Proc. 9th Int Conf (Dresden), 40-47, ed W. Janke and A. Pelster (Singapore, World Scientific, 2008)
Fundamental solutions for a class of non-elliptic homogeneous differential operators
B. Camus
abstract math.AP/0704.0801
Bulletin des Sciences Mathématiques 132.6, 486-499 (2008)
Semiclassical spectral estimates for Schrödinger operators at a critical energy level. Case of a degenerate minimum of the potential
B. Camus

Journal of Mathematical Analysis and Applications 341.2, 1170-1180 (2008)
Rigidity of cylinders without conjugate points
H. Koehler

Asian Journal of Mathematics 12.1, 35-45 (2008)


Semiclassical Approach to Chaotic Quantum Transport
S. Müller, S. Heusler, P. Braun, F. Haake
abstract cond-mat/0610560
New J. Phys. 9 (2007) 12
Universal spectral correlations from the ballistic sigma model
J. Müller, T. Micklitz, A. Altland
abstract nlin.CD/0707.2274
Phys. Rev. E 76, 056204 (2007)
Semiclassical Limits for the QCD Dirac Operator
T. Guhr and S. Keppeler
abstract cond-mat/0601065
Ann. Phys. (NY) 322 (2007) 287-314
Asymptotically harmonic spaces in dimension 3
G. Knieper, J. Heber, and H.M. Shah

Proceedings of the American Mathematical Society 135.3, 845-849 (2007)
Periodic-Orbit Theory of Level Correlations
S. Heusler, S. Müller, A. Altland, P. Braun, and F. Haake
abstract nlin.CD/0610053
Phys. Rev. Lett. 98, 044103 (2007)
Semiclassical Theory for Parametric Correlation of Energy Levels
T. Nagao, P. Braun, S. Müller, Keiji Saito, S. Heusler, and F. Haake
abstract nlin.CD/0607070
J. Phys. A 40, 47 (2007)


Semi-classical spectral estimates for Schrödinger operators at a critical level. Case of a degenerate maximum of the potential
B. Camus
abstract math.SP/0502568
Journal of Differential Equations 226 (2006) 295-322
Semiclassical Theory of Chaotic Conductors
S. Heusler, S. Müller, P. Braun, F. Haake
abstract cond-mat/0509598
Phys. Rev. Lett 96, 066804 (2006)
Semiclassical Prediction for Shot Noise in Chaotic Cavities
P. Braun, S. Heusler, S. Müller, F. Haake
abstract cond-mat/0511292
J. Phys. A 39 (2006) L159-L165
Equilibrium and eigenfunctions estimates in the semi-classical regime
B. Camus
abstract math.AP/0605637
Convolutions of semi-classical spectral distributions and periodic-orbit theory
B. Camus

To appear in Journal of Functional analysis


Spectral correlations of individual quantum graphs
S. Gnutzmann, A. Altland
abstract nlin.CD/0508009
Phys. Rev. E 72 056215 (2005) 1-14
Periodic-Orbit Approach to Universality in Quantum Chaos
S. Müller
abstract nlin.CD/0512058
The uniqueness of the maximal measure for geodesic flows on symmetric spaces of higher rank
G. Knieper
Israel Journal of Mathematics 149 (2005) 171-183.
Spectral fluctuations of Schrödinger operators generated by critical points of the potential
B. Camus
abstract math-ph/0504073
J. of State. Phys. 123 (2006) 1-9
Spectral estimates for degenerate critical levels
B. Camus
Journal of Fourier Analysis and Applications, Volume 12, Number 5 / October 2006, 495-515
Asymptotic approximation of degenerate fiber integrals
B. Camus
abstract math.GM/0503505
Journal of Mathematical Analysis and Applications 320/2 pp. 528-542
Periodic-Orbit Theory of Universality in Quantum Chaos
S. Müller, S. Heusler, P. Braun, F. Haake, A. Altland
abstract nlin.CD/0503052
Phys. Rev. E 72, 046207 (2005)
Semiclassical form factor for spectral and matrix element fluctuations of multi-dimensional chaotic systems
M. Turek, D. Spehner, S. Müller, and K. Richter
abstract nlin.CD/0409012
Phys. Rev. E 71, 016210 (2005)


Universal spectral form factor for chaotic dynamics
S. Heusler, S. Müller, P. Braun, F. Haake
Nonlinear Sciences, abstract nlin.CD/0309022
J. Phys. A: Math. Gen. 37, L31 (2004)
Semiclassical Foundation of Universality in Quantum Chaos
S. Müller, S. Heusler, P. Braun, F. Haake, A. Altland
abstract nlin.CD/0401021
Phys.Rev.Lett. 93 (2004) 014103
Semiclassical spectral estimates for Schrödinger operators at a critical energy level
B. Camus
abstract math-ph/0406058
Journal of Differential Equations 226/1 pp. 295-322
Universal spectral statistics in quantum graphs
S. Gnutzmann, A. Altland
abstract nlin.CD/0402029
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