Related papers: Semiclassical approach to fidelity amplitude
Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time -- the most clear example being the Solar System -- but the situation for their quantum counterparts is less well understood. As a…
We propose a formalism which defines chaos in both quantum and classical systems in an equivalent manner by means of \textit{adiabatic transformations}. The complexity of adiabatic transformations which preserve classical time-averaged…
We study stochastic perturbations of ODE with stable limit cycles -- referred to as stochastic oscillators -- and investigate the response of the asymptotic (in time) frequency of oscillations to changing noise amplitude. Unlike previous…
We discuss the fluctuation properties of diagonal matrix elements in the semiclassical limit in chaotic systems. For extended observables, covering a phase space area of many times Planck's constant, both classical and quantal distributions…
A test on the numerical accuracy of the semiclassical approximation as a function of the principal quantum number has been performed for the Pullen--Edmonds model, a two--dimensional, non--integrable, scaling invariant perturbation of the…
Experimentally, certain degrees of freedom may appear classical because their quantum fluctuations are smaller than the experimental error associated with measuring them. An approximation to a fully quantum theory is described in which the…
We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and…
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…
We study, analytically and numerically, the stability of quantum motion for a classically chaotic system. We show the existence of different regimes of fidelity decay which deviate from Fermi Golden rule and Lyapunov decay.
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
A hypothesis about the average phase-space distribution of resonance eigenfunctions in chaotic systems with escape through an opening is proposed. Eigenfunctions with decay rate $\gamma$ are described by a classical measure that $(i)$ is…
We present a refined semiclassical approach to the Landauer conductance and Kubo conductivity of clean chaotic mesoscopic systems. We demonstrate for systems with uniformly hyperbolic dynamics that including off-diagonal contributions to…
We present several recent results concerning the transition between quantum and classical mechanics, in the situation where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be…
We deal with a system comprising a nonlinear (Kerr-like) oscillator excited by a series of ultra-short external pulses. We introduce the fidelity-based entropic parameter that can be used as an indicator of quantum chaos. Moreover, we…
We propose to study echo dynamics in a random matrix framework, where we assume that the perturbation is time independent, random and orthogonally invariant. This allows to use a basis in which the unperturbed Hamiltonian is diagonal and…
The short-time behavior of quantum decay of an unstable state initially located within an interaction region of finite range is investigated using a resonant expansion of the survival amplitude. It is shown that in general the short-time…
We study the response of the quasi-energy levels in the context of quantized chaotic systems through the level velocity variance and relate them to classical diffusion coefficients using detailed semiclassical analysis. The systematic…
We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some…
The validity of the semiclassical approximation is investigated during the preheating phase in models of chaotic inflation using a modification of a criterion previously proposed for semiclassical gravity. If the modified criterion is…
Non-Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems.…