Related papers: Phase-space correlations of chaotic eigenstates
We present a comprehensive account of directed transport in one-dimensional Hamiltonian systems with spatial and temporal periodicity. They can be considered as Hamiltonian ratchets in the sense that ensembles of particles can show directed…
The fundamental correspondence between quantum chaotic single-particle systems and random matrix theory is well-understood via periodic orbit theory. In contrast, we show that many-body systems with explicit subsystem structure possess…
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic…
The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…
Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…
This chapter gives an overview of transport problems where chaotic dynamics of the system plays a crucial role. We begin with single-particle transport problems and then come to conservative and then dissipative systems of identical…
The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and…
Unique set of coherent states for the anharmonic oscillator is obtained by requiring i. under the quantum mechanical time evolution a coherent state evolves into another, governed by trajectory in the classical phase space (of a related…
In the context of dissipative systems, we show that for any quantum chaotic attractor a corre- sponding classical chaotic attractor can always be found. We provide with a general way to locate them, rooted in the structure of the parameter…
The main goal of the present paper is to convince that it is feasible to construct a `periodic orbit theory' of localization by extending the idea of classical action correlations. This possibility had been questioned by many researchers in…
Interrelations between dynamical and statistical laws in physics, on the one hand, and between the classical and quantum mechanics, on the other hand, are discussed with emphasis on the new phenomenon of dynamical chaos. The principal…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
Using a new time-dependent measure, we demonstrate for the first time that each defect in a representative defect-mediated spatiotemporally chaotic system is associated with one to two degrees of dynamical freedom. Furthermore, we show that…
We discuss the appearance of chaos in time-periodic perturbations of reversible vector fields in the plane. We use the normal forms of codimension~$1$ reversible vector fields and discuss the ways a time-dependent periodic forcing term of…
Effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a…
We develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of…
We show that, in periodically perturbed chaotic systems, Phase Synchronization appears, associated to a special type of stroboscopic map, in which not only averages quantities are equal to invariants of the perturbation, the angular…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
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…