Related papers: Fractal Weyl laws for chaotic open systems
Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify…
We prove quantum-classical correspondence for bound conservative classically chaotic Hamiltonian systems. In particular, quantum Liouville spectral projection operators and spectral densities, and hence classical dynamics, are shown to…
States supported by chaotic open quantum systems fall into two categories: a majority showing instantaneous ballistic decay, and a set of quantum resonances of classically vanishing support in phase space. We present a theory describing…
We consider quantum maps induced by periodically-kicked scattering systems and discuss the computation of their resonance spectra in terms of complex scaling and sufficiently weak absorbing potentials. We also show that strong absorptive…
We prove a Weyl upper bound on the number of scattering resonances in strips for manifolds with Euclidean infinite ends. In contrast with previous results, we do not make any strong structural assumptions on the geodesic flow on the trapped…
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We…
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…
We outline formal and physical similarities between the quantum dynamics of open systems, and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, that,…
Atmospheric flows exhibit selfsimilar fractal spacetime fluctuations manifested as the fractal geometry to global cloud cover pattern and inverse power law form for power spectra of meteorological parameters such as windspeed, temperature,…
We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show that the spectrum is characterized by the fractal Weyl law recently established…
In this third of a series of four articles, we continue the study of the representations of the hamiltonian dynamical transformations of systems of correlated quantized oscillators. By our use of generalized wave function solutions to…
New fluctuation properties arise in problems where both spatial integration and energy summation are necessary ingredients. The quintessential example is given by the short-range approximation to the first order ground state contribution of…
Using examples we test formulae previously conjectured to give the fractal information dimension of chaotic repellors and their stable and unstable manifolds in ``typical'' dynamical systems in terms of the Lyapunov exponents and the…
Systems with the power-law quasiparticle dispersion $\epsilon_{\bf k}\propto k^\alpha$ exhibit non-Anderson disorder-driven transitions in dimensions $d>2\alpha$, as exemplified by Weyl semimetals, 1D and 2D arrays of ultracold ions with…
For a class of quantized open chaotic systems satisfying a natural dynamical assumption, we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is…
We study the relationship between the spectral properties of diffusive open quantum maps and the classical spectrum of Ruelle-Pollicott resonances. The leading resonances determine the asymptotic time regime for several quantities of…
We consider the continuity equation for open chaotic quantum systems in the semiclassical limit. First we explicitly calculate a semiclassical expansion for the probability current density using an expression based on classical…
A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the…
Resonance states of the 3-disk scattering system are presented for the first Casati wave number $k \approx 912$ and the second Casati wave number $k \approx 91242$. They show multifractal structure in phase space, similar to the pioneering…
We generalize the Moyal equation, which describes the dynamics of quantum observables in phase space, to quantum systems coupled to a reservoir. It is shown that phase space observables become functionals of fluctuating noise forces…