相关论文: Universal level-spacing distribution in quantum sy…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
The quantum-classical correspondence for dynamics of the nonlinear classically chaotic systems is analysed. The problem of quantum chaos consists of two parts: the quasiclassical quantisation of the chaotic systems and attempts to…
For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom…
We study quantum chaos in a non-KAM system, i.e. a kicked particle in a one-dimensional infinite square potential well. Within the perturbative regime the classical phase space displays stochastic web structures, and the diffusion…
The emergence of quantum chaos for interacting Fermi systems is investigated by numerical calculation of the level spacing distribution $P(s)$ as function of interaction strength $U$ and the excitation energy $\epsilon$ above the Fermi…
The character of motion (regular or chaotic) on the quantum level manifests itself in the statistics of the set of the system's energy levels. The completely regular case generates the sequence of the levels with exponential (Poisson) level…
Quantum chaos is linked to Brownian diffusion of the underlying quantum energy level-spacing sequences. The level-spacings viewed as functions of their order execute random walks which imply uncorrelated random increments of the…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
Using the remarkable mathematical construct of Eugene Wigner to visualize quantum trajectories in phase space, quantum processes can be described in terms of a quasi-probability distribution analogous to the phase space probability…
Mesoscopic devices, with system sizes in the range of several to several dozens wavelengths, represent paradigmatic model systems for the observation of quantum chaotic behaviour based on semiclassical concepts. Those electronic and…
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with…
We discover numerically that a moving wave packet in a quantum chaotic billiard will always evolve into a quantum state, whose density probability distribution is exponential. This exponential distribution is found to be universal for…
A widely accepted definition of ``quantum chaos'' is ``the behavior of a quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical…
Complex quantum systems consisting of large numbers of strongly coupled states exhibit characteristic level repulsion, leading to a non-Poisson spacing distribution which can be described by Random Matrix Theory. Scattering resonances…
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well…
In the large-$N$, classical limit, the Bose-Hubbard dimer undergoes a transition to chaos when its tunnelling rate is modulated in time. We use exact and approximate numerical simulations to determine the features of the dynamically…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…