Related papers: Dynamical Universal Behavior in Quantum Chaotic Sy…
In standard (mathematical) billiards a point particle moves uniformly in a billiard table with elastic reflections off the boundary. We show that in transition from mathematical billiards to physical billiards, where a finite size hard…
Wavefunctions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wavefunctions display universal density distributions and density auto-correlations in agreement with…
At lower energies, the resonances in scattering experiments are often isolated. In quantum chaotic many-body, disordered or generically stochastic systems, the resonances overlap at larger energies. Eventually, the Ericson regime is reached…
Chaotic systems exhibit rich quantum dynamical behaviors ranging from dynamical localization to normal diffusion to ballistic motion. Dynamical localization and normal diffusion simulate electron motion in an impure crystal with a vanishing…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
Many disordered systems show a superdiffusive dynamics, intermediate between the diffusive one, typical of a classical stochastic process, and the so called ballistic behaviour, which is generally expected for the spreading in a quantum…
In generic Hamiltonian systems with a mixed phase space chaotic transport may be directed and ballistic rather than diffusive. We investigate one particular model showing this behaviour, namely a spatially periodic billiard chain in which…
The geometry of a billiard boundary fundamentally governs its dynamics, ranging from integrable to mixed and fully chaotic regimes. Bean- and peanut-shaped billiards have varying curvature with both focusing and defocusing walls without a…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…
In the context of the mixing dynamical systems we present a derivation of the Gaussian ensembles distributions from mixing quantum systems having a classical analog that is mixing. We find that mixing factorization property is satisfied for…
Time dependent dynamics of the chaotic quantum-mechanical system has been studied. Irreversibility of the dynamics is shown. It is shown, that being in the initial moment in pure quantum-mechanical state, system makes irreversible…
Quantum ergodicity of classically chaotic systems has been studied extensively both theoretically and experimentally, in mathematics, and in physics. Despite this long tradition we are able to present a new rigorous result using only…
We study classical and quantum scattering properties in the ballistic regime of particles in two-dimensional chaotic billiards that are models of electron- or micro- waveguides. To this end we construct the purely classical counterparts of…
Quantum walks are at present an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior.…
Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo like fidelity plays a central role and…
An exponential behavior at all times is derived for a solvable dynamical model in the weak-coupling, macroscopic limit. Some implications for the quantum measurement problem are discussed, in particular in connection with dissipation.
We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations.…
We study the quantum behaviour of the stadium billiard. We discuss how the interplay between quantum localization and the rich structure of the classical phase space influences the quantum dynamics. The analysis of this model leads to new…
We show that an arbitrary probability distribution can be represented in exponential form. In physical contexts, this implies that the equilibrium distribution of any classical or quantum dynamical system is expressible in grand canonical…