Quantum Chaos

1. Complex Single-Particle Dynamics

The quantum-classical correspondence has been a hot topic since the very beginning of quantum mechanics. Under which conditions do quantum systems behave classically, and how can we infer from the eigenvalues and eigenstates of a quantum system on the characteristic properties of its classical limit? Toy models, such as the quantum kicked rotor, allow us simple numerical computation which can be compared to theoretical predictions on the system's properties. The kicked rotor is experimentally implemented by kicking cold or ultracold atomic gases by optical lattices, and experimental data has nicely confirmed some of our research results (e.g. on quantum resonant motion, dissipative quantum ratchets, and decoherence-induced diffusion). Also one-electron Rydberg states under intense microwave driving exhibit a transition from classically regular to classically chaotic dynamics. Once the last invariant torus is destroyed by the driving field, unbounded chaotic diffusion leads to chaotic ionisation of the Rydberg electron, possibly amended by quantum localisation phenomena. Hot issues under debate are the (experimentally observable) signatures of typical structures of mixed phase space, such as cantori and elliptic islands.
Fractal fluctuations
Fractal conductance fluctuations in the open kicked rotor in the 2D parameter plane of quasi-momentum and kicking period.

2. Complex Many-Body Dynamics

Quantum chaos is intrinsically present in many-particle systems with strong interaction, which typically lead to strongly correlated many-body dynamics. An ideal playground for the study of many-body systems are ultracold atoms prepared in periodic potentials (optical lattices). Unsolved issues are, for instance, the transition from an effective one-particle (mean-field) to a true many-body description. We are studying the crossover between various dynamical regimes for bosons and fermions in static and possibly time-dependent external fields. The evolution of correlations and many-body entanglement are hot theoretical topics, in view of the unprecedented experimental control on ultracold quantum matter and future technical applications.


  • C. A. Parra-Murillo, J. Madronero, and S. Wimberger
    Quantum diffusion and thermalization at resonant tunneling, Phys. Rev. A 89, 053610 (2014)
  • C. A. Parra-Murillo and S. Wimberger
    Manifold approach for a many-body Wannier-Stark system: localization and chaos in energy space, Acta Phys. Pol. A 124, 1091 (2013)
  • C. A. Parra-Murillo, J. Madronero, and S. Wimberger
    A two-band Bose-Hubbard model for many-body resonant tunneling in the Wannier-Stark system, Phys. Rev. A 88, 032119 (2013)
  • P. Plötz, M. Lubasch, and S. Wimberger
    Detection of avoided crossings by fidelity, Physica A 390, 1363-1369 (2011)
  • P. Buonsante and S. Wimberger
    Engineering many-body quantum dynamics by disorder, Phys. Rev. A 77, 041606(R) (2008)
  • A. Tomadin, R. Mannella, and S. Wimberger
    Many-body Landau-Zener tunneling in the Bose-Hubbard model, Phys. Rev. A 77, 013606 (2008)
  • A. Tomadin, R. Mannella, and S. Wimberger
    Many-body interband tunneling as a witness for complex dynamics in the Bose-Hubbard model, Phys. Rev. Lett. 98, 130402 (2007)
  • A. Facchini, S. Wimberger, and A. Tomadin
    Multifractal fluctuations in the survival probability of an open quantum system, Physica A 376, 266-274 (2007)
  • E. Persson, S. Fuhrthauer, S. Wimberger, and J. Burgdörfer
    Transient localization in the kicked Rydberg atom , Phys. Rev. A 74, 053417 (2006)
  • G. Carlo, G. Benenti, G. Casati, S. Wimberger, O. Morsch, R. Mannella, and E. Arimondo
    Chaotic ratchet dynamics with cold atoms in a pair of pulsed optical lattices, Phys. Rev. A 74, 033617 (2006)
  • S. Wimberger, P. Schlagheck, Ch. Eltschka, and A. Buchleitner
    Resonance-Assisted Decay of Nondispersive Wave Packets, Phys. Rev. Lett. 97, 043001 (2006)
  • J. Madronero, A. Ponomarev, A.R.R. Carvalho, S. Wimberger, C. Viviescas, A.R. Kolovsky, K. Hornberger, P. Schlagheck, A. Krug, and A. Buchleitner
    Quantum chaos, transport, and control - in quantum optics, in: M. Scully and G. Rempe (Eds.), Adv. At. Mol. Opt. Phys. 53, 33, Elsevier, Amsterdam 2006
  • S. Wimberger and A. Buchleitner
    Saturation of fidelity in the atom-optics kicked rotor, J. Phys. B: At. Mol. Opt. Phys. 39, L145-L151 (2006)
  • A. Tomadin, R. Mannella, and S. Wimberger
    Can quantum fractal fluctuations be observed in an atom-optics kicked rotor experiment?, J. Phys. A: Math. Gen. 39, 2477-2491 (2006)

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