# 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 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.

## Publications

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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