Publications Arnd Bäcker
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Partial barriers to chaotic transport in 4D symplectic maps
M. Firmbach, A. Bäcker, R. Ketzmerick
arXiv:2210.09863v1 [nlin.CD] - Quantum coherence controls the nature of equilibration in coupled chaotic systems
J. J. Pulikkottil, A. Lakshminarayan, S. C. L. Srivastava, M. F. I. Kieler, A. Bäcker, and S. Tomsovic
arXiv:2204.07561 [quant-ph] - Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations
Roland Ketzmerick, Konstantin Clauß, Felix Fritzsch, Arnd Bäcker, 2022Phys. Rev. Lett. 129, 193901 (2022), arXiv:2203.09752v1 [physics.optics]
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Creating triple-NOON states with ultracold atoms via chaos-assisted tunnelling
G. Vanhaele, A. Bäcker, R. Ketzmerick, P. Schlagheck
Phys. Rev. A 106, L011301 (2022), arXiv:2202.05589v1 [cond-mat.quant-gas] -
Universal intensity statistics of multifractal resonance states
K. Clauß, F. Kunzmann, A. Bäcker & R. Ketzmerick
Phys. Rev. E 103, 042204 (2021), arXiv:2012.02541 [nlin.CD] -
Geometry of complex instability and escape in four-dimensional symplectic maps
J. Stöber and A. Bäcker
Phys. Rev. E 103, 042208 (2021), arXiv:2009.00970 [nlin.CD], Videos -
Linear and logarithmic entanglement production in an interacting chaotic system
S. Paul and A. Bäcker
Phys. Rev. E 102, 050102(R) (2020), 6 pages (Open Access) , arXiv:2007.13604 [quant-ph] -
Entanglement production by interaction quenches of quantum chaotic subsystems
J. J. Pulikkottil, A. Lakshminarayan, S. C. L. Srivastava, A. Bäcker, and S. Tomsovic
Phys. Rev. E 101, 032212 (2020), arXiv:1909.04733 [quant-ph] -
Power-law trapping in the volume-preserving Arnold-Beltrami-Childress map
S. Das and A. Bäcker
Phys. Rev. E 101, 032201 (2020), arXiv 1911.08207 [nlin.CD] -
Entanglement in coupled kicked tops with chaotic dynamics
T. Herrmann, M. F. I. Kieler, F. Fritzsch, and A. Bäcker
Phys. Rev. E 101, 022221 (2020), arXiv 1910.13447 [quant-ph] -
Structure of resonance eigenfunctions for chaotic systems with partial escape
K. Clauß, E. G. Altmann A. Bäcker, R. Ketzmerick -
Resonance-assisted tunneling in deformed optical microdisks with a mixed phase space
F. Fritzsch, R. Ketzmerick, and A. Bäcker
Phys. Rev. E 100, 042219 (2019), arXiv:1907.06900 [physics.optics] -
Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems
A. Bäcker, M. Haque, and I. M. Khaymovich
Phys. Rev. E 100, 032117 (2019), arXiv:1905.03099 [cond-mat.stat-mech] -
Elliptic Bubbles in Moser's 4D Quadratic Map: the Quadfurcation
A. Bäcker, J. D. Meiss
SIAM J. Appl. Dyn. Syst. 19, 442-479 (2020), arXiv:1807.06074 [nlin.CD], Videos -
Resonance-Assisted Tunneling in 4D Normal-Form Hamiltonians
M. Firmbach, F. Fritzsch, R. Ketzmerick, and A. Bäcker -
Ordered level spacing probability densities
S. C. L. Srivastava, A. Lakshminarayan, S. Tomsovic, and A. Bäcker
J. Phys. A 52, 025101 (2019), arXiv:1810.01569 [nlin.CD] -
Moser's quadratic, symplectic map
A. Bäcker, J. D. Meiss
Regul. Chaotic Dyn. 23, 654-664 (2018), arXiv:1808.07229 [nlin.CD] Videos -
Eigenstate entanglement between quantum chaotic subsystems: Universal transitions and power laws in the entanglement spectrum
S. Tomsovic, A. Lakshminarayan, S. C. L. Srivastava and A. Bäcker -
Elliptic Bubbles in Moser's 4D Quadratic Map: the Quadfurcation
A. Bäcker, J. D. Meiss -
Three-dimensional billiards: Visualization of regular structures and trapping of chaotic trajectories
M. Firmbach, S. Lange, R. Ketzmerick, and A. Bäcker
- Resonance eigenfunction hypothesis for chaotic systems
Konstantin Clauß, Martin J. Körber, Arnd Bäcker, and Roland Ketzmerick
Phys. Rev. Lett. 121, 074101 (2018), arXiv:1803.02631 [nlin.CD] - Statistical Properties of Eigenstate Amplitudes in Complex Quantum Systems
W. Beugeling, A. Bäcker, R. Moessner, and M. Haque
Phys. Rev. E 98, 022204 (2018), [arXiv:1710.11433 [cond-mat.stat-mech]] - Homoclinic points of 2D and 4D maps via the parametrization method
S. Anastassiou, T. Bountis, and A. Bäcker
Nonlinearity 30 (2017) 3799-3820, arXiv:1605.05521 [nlin.DS] Videos -
Complex-path prediction of resonance-assisted tunneling in mixed systems
F. Fritzsch, A. Bäcker, R. Ketzmerick, and N. MertigPhys. Rev. E 95, 020202(R) (2017), 6 pages,arXiv:1609.09276 [nlin.CD]
- Perturbation-free prediction of resonance-assisted tunneling in mixed regular--chaotic systems
N. Mertig, J. Kullig, C. Löbner, A. Bäcker, and R. Ketzmerick
Phys. Rev. E 94, 062220 (2016), 18 pages, arXiv:1607.06477 [nlin.CD] - What is the mechanism of power-law distributed Poincaré recurrences in higher-dimensional systems?
S. Lange, A. Bäcker, and R. Ketzmerick
EPL 116, 30002 (2016), 6 pages, editor's choice, arXiv:1609.07977 [nlin.CD] Videos - Bifurcations of families of 1D-tori in 4D symplectic maps
F. Onken, S. Lange, R. Ketzmerick, and A. Bäcker
Chaos 26, 063124 (2016), 14 pages arXiv:1602.04658 [nlin.CD] Videos - Entanglement and localization transitions in eigenstates of interacting chaotic systems
A. Lakshminarayan, S. C. L. Srivastava, R. Ketzmerick, A. Bäcker, and S. Tomsovic
Phys. Rev. E 94, 010205(R) (2016), 5 pages arXiv:1601.07061 [quant-ph] - Universal scaling of spectral fluctuation transitions for interacting chaotic systems
S. C. L. Srivastava, S. Tomsovic, A. Lakshminarayan, R. Ketzmerick, and A. Bäcker
Phys. Rev. Lett. 116, 054101 (2016), 6 pages arXiv:1509.02329 [nlin.CD] - Localization of Chaotic Resonance States due to a Partial Transport Barrier
M. J. Körber, A. Bäcker, and R. Ketzmerick
Phys. Rev. Lett. 115, 254101 (2015), 6 pages arXiv:1509.00665 [nlin.CD] - Experimental Observation of Resonance-Assisted Tunneling
S. Gehler, S. Löck, S. Shinohara, A. Bäcker, R. Ketzmerick , U. Kuhl, and H.-J. Stöckmann
Phys. Rev. Lett. 115, 104101 (2015), 5 pages arXiv:1502.04263 [cond-mat] - Integrable approximation of regular regions with a nonlinear resonance chain
J. Kullig, C. Löbner, N. Mertig, A. Bäcker, and R. Ketzmerick
Phys. Rev. E 90, 052906 (2014), 9 pages arXiv:1407.2513 [nlin.CD] - Temporal flooding of regular islands by chaotic wave packets
L. Bittrich, A. Bäcker, and R. Ketzmerick
Phys. Rev. E 89, 032922 (2014), 11 pages arXiv:1401.5923 [nlin.CD] - Global structure of regular tori in a generic 4D symplectic map
S. Lange, M. Richter, F. Onken, A. Bäcker, and R. Ketzmerick
Chaos 24, 024409 (2014), 11 pages arXiv:1311.7632 [nlin.CD] Videos
Editors' pick, Featured article, and Cover image (pdf) (Chaos, June 2014, volume 24, number 2) - Visualization and comparison of classical structures and quantum states of 4D maps
M. Richter, S. Lange, A. Bäcker, and R. Ketzmerick
Phys. Rev. E 89, 022902 (2014), 12 pages arXiv:1307.6109 [nlin.CD] Videos - Integrable approximation of regular islands: The iterative canonical transformation method
C. Löbner, S. Löck, A. Bäcker, and R. Ketzmerick
Phys. Rev. E 88, 062901 (2013), 12 pages arXiv:1308.1561 [nlin.CD] - Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems
M. J. Körber, M. Michler, A. Bäcker, and R. Ketzmerick
Phys. Rev. Lett. 111, 114102 (2013), 5 pages arXiv:1304.2662 [nlin.CD] - Complex paths for regular-to-chaotic tunnelling rates
N. Mertig, S. Löck, A. Bäcker, R. Ketzmerick, and A. Shudo
Europhys. Lett. 102, 10005 (2013), 6 pages arXiv:1207.0985 [nlin.CD] - Universal Quantum Localizing Transition of a Partial Barrier in a Chaotic Sea
M. Michler, A. Bäcker, R. Ketzmerick, H.-J. Stöckmann, and S. Tomsovic
Phys. Rev. Lett. 109, 234101 (2012), 5 pages arXiv:1206.3118 [nlin.CD] - Consequences of Flooding on Spectral Statistics
T. Rudolf, N. Mertig, S. Löck, and A. Bäcker
Phys. Rev. E 85, 036213 (2012), 8 pages arXiv:1201.4288 [nlin.CD] - Coupling of bouncing-ball modes to the chaotic sea and their counting function
S. Löck, A. Bäcker, and R. Ketzmerick
Phys. Rev. E 85, 016210 (2012), 9 pages arXiv:1110.6307v1 [nlin.CD] - Partial Weyl Law for Billiards
A. Bäcker, R. Ketzmerick, S. Löck, and H. Schanz
Europhys. Lett. 94, 30004 (2011), 5 pages arXiv:1010.5093v2 [nlin.CD] - Fractional Power-Law Level-Statistics due to Dynamical Tunneling
A. Bäcker, R. Ketzmerick, S. Löck, and N. Mertig
Phys. Rev. Lett. 106, 024101 (2011), 4 pages arXiv:1007.4130v1 [nlin.CD] - Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach
A. Bäcker, R. Ketzmerick, and S. Löck
Phys. Rev. E 82, 056208 (2010), 24 pages arXiv:1009.0418v1 [nlin.CD] - Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime
S. Löck, A. Bäcker, R. Ketzmerick, and P. Schlagheck
Phys. Rev. Lett. 104, 114101 (2010), 4 pages arXiv:0906.4893 [nlin.CD] - Friedel oscillations in microwave billiards
A. Bäcker, B. Dietz, T. Friedrich, M. Miski-Oglu, A. Richter, F. Schäfer, and S. Tomsovic
Phys. Rev. E 80, 066210 (2009), 5 pages arXiv:0910.2855[nlin.CD] - Quality factors and dynamical tunneling in annular microcavities
A. Bäcker, R. Ketzmerick, S. Löck, J. Wiersig, and M. Hentschel
Phys. Rev. A 79, 063804 (2009), 6 pages arXiv:0903.0974 [nlin.CD] - Nano-wires with surface disorder: Giant localization lengths and dynamical tunneling in the presence of directed chaos
J. Feist, A. Bäcker, R. Ketzmerick, J. Burgdörfer, and S. Rotter
Phys. Rev. B 80, 245322 (2009), 14 pages arXiv:0908.3278 [cond-mat.mes-hall] - Semiclassical theory of nonlocal statistical measures: Residual Coulomb interactions
D. Ullmo, S. Tomsovic, and A. Bäcker
Phys. Rev. E 79, 056217 (2009), 20 pages - Dynamical tunneling in mushroom billiards
A. Bäcker, R. Ketzmerick, S. Löck, M. Robnik, G. Vidmar, R. Höhmann, U. Kuhl, and H.-J. Stöckmann
Phys. Rev. Lett. 100, 174103 (2008), 4 pages arXiv:0801.2833 [nlin.CD] - Residual Coulomb interaction fluctuations in chaotic systems: the boundary, random plane waves, and semiclassical theory
S. Tomsovic, D. Ullmo, and A. Bäcker
Phys. Rev. Lett. 100, 164101 (2008), 4 pages arXiv:0712.0225 [cond-mat.mes-hall] - Regular-to-chaotic tunneling rates using a fictitious integrable system
A. Bäcker, R. Ketzmerick, S. Löck, and L. Schilling
Phys. Rev. Lett. 100, 104101 (2008), 4 pages arXiv:0707.0217v1 [nlin.CD] - Universality in the flooding of regular islands by chaotic states
A. Bäcker, R. Ketzmerick, and A. Monastra
Phys. Rev. E 75, 066204 (2007), 11 pages nlin.CD/701032 - Nano-wires with surface disorder: Giant localization lengths and quantum-to-classical crossover
J. Feist, A. Bäcker, R. Ketzmerick, S. Rotter, B. Huckestein, and J. Burgdörfer
Phys. Rev. Lett. 97, 116804 (2006), 4 pages cond-mat/0606586 - Flooding of Chaotic Eigenstates into Regular Phase Space Islands
A. Bäcker, R. Ketzmerick, and A. Monastra
Phys. Rev. Lett. 94, 054102 (2005), 4 pages nlin.CD/0409029 - Poincaré Husimi representation of eigenstates in quantum billiards
A. Bäcker, S. Fürstberger, R. Schubert
Phys. Rev. E 70, 036204 (2004), 10 pages nlin.CD/0307035 - Numerical aspects of eigenvalue and eigenfunction computations for chaotic quantum systems
A. Bäcker
In The Mathematical Aspects of Quantum Maps, M. Degli Esposti and S. Graffi (Eds.) Springer Lecture Notes in Physics 618, 91-144 (2003) nlin.CD/0204061, Ulm report ULM-TP/02-4
For the Python programs see here. - Behaviour of boundary functions for quantum billiards
A. Bäcker, S. Fürstberger, R. Schubert and F. Steiner
J. Phys. A 35, 10293-10310 (2002) nlin.CD/0207034 - Isolated resonances in conductance fluctuations and hierarchical states
A. Bäcker, A. Manze, B. Huckestein, and R. Ketzmerick
Phys. Rev. E 66, 016211 (2002), 8 pages nlin.CD/0201057 - Orbit bifurcations and wavefunction autocorrelations
A. Bäcker, J. P. Keating and S. Prado
Nonlinearity 15, 1417-1433 (2002) nlin.CD/0204006 - Autocorrelation function of eigenstates in chaotic and mixed systems
A. Bäcker and R. Schubert
J. Phys. A 35, 539-564 (2002) nlin.CD/0106018 - Amplitude distribution of eigenfunctions in mixed systems
A. Bäcker and R. Schubert
J. Phys. A 35, 527-538 (2002) nlin.CD/0106017 - About ergodicity in the family of limaçon billiards
H. R. Dullin and A. Bäcker
Nonlinearity 14 (2001) 1673-1687 - Quantum chaos and quantum ergodicity
A. Bäcker and F. Steiner
In Ergodic Theory, Analysis and Efficient Simulation of Dynamical Systems, B. Fiedler (ed.), 717-752, Springer-Verlag Berlin/Heidelberg (2001) - Maximum norms of chaotic quantum eigenstates and random waves
R. Aurich, A. Bäcker, R. Schubert and M. Taglieber
In: Equadiff 99, Proceedings of the International Conference on Differential Equations, Berlin, B. Fiedler, K. Gröger and J. Sprekels (eds.) 1461-1463, World Scientific Singapore (2000) - Spectral statistics for quantized skew translations on the torus
A. Bäcker and G. Haag
J. Phys. A 32 (1999) L393-L398 - Chaotic eigenfunctions in momentum space
A. Bäcker and R. Schubert
J. Phys. A 32 (1999) 4795-4815 - Maximum norms of chaotic quantum eigenstates and random waves
R. Aurich, A. Bäcker, R. Schubert and M. Taglieber
Physica D 129 (1999) 1-14 - Mode fluctuation distribution for spectra of superconducting microwave billiards
Alt, A. Bäcker, C. Dembowski, H.-D. Gräf, R. Hofferbert, H. Rehfeld and A. Richter
Phys. Rev. E 58 (1998) 1737-1742 - Rate of quantum ergodicity in Euclidean billiards
A. Bäcker, R. Schubert and P. Stifter
Phys. Rev. E 57 (1998) 5425-5447, erratum Phys. Rev. E 58 (1998) 5192 - On the number of bouncing ball modes in billiards
A. Bäcker, R. Schubert and P. Stifter
J. Phys. A 30 (1997) 6783-6795 - Generating partitions for two-dimensional hyperbolic maps
A. Bäcker and N. Chernov
Nonlinearity 11 (1998) 79-87 - Mode fluctuations as fingerprints of chaotic and non-chaotic systems
R. Aurich, A. Bäcker and F. Steiner
Int. J. Mod. Phys. B 11 (1997) 805-849 - Symbolic dynamics and periodic orbits for the cardioid billiard
A. Bäcker and H.R. Dullin
J. Phys. A 30 (1997) 1991-2020 - Spectral statistics in the quantized cardioid billiard
A. Bäcker, F. Steiner and P. Stifter
Phys. Rev. E 52 (1995) 2463-2472