Related papers: Measuring the Lyapunov exponent using quantum mech…
The agenda of Dissipative Quantum Chaos is to create a toolbox which would allow us to categorize open quantum systems into "chaotic" and "regular" ones. Two approaches to this categorization have been proposed recently. One of them is…
This paper is concerned with the large time behavior of solutions to the Euler-Fourier system with damping in $\mathbb{R}^{d}~(d\geq1)$. A time-weighted energy argument has been developed within the $L^2$ framework to derive the optimal…
In this study, we explore how a fermion-antifermion ($f\overline{f}$) pair interacts via an exponentially decaying potential. Using a covariant one-time two-body Dirac equation, we examine their relative motion in a three-dimensional flat…
We consider a general class of maps of the interval having Lyapunov subexponential instability $|\delta x_{t}|\sim|\delta x_{0}|\exp[\Lambda_{t}(x_{0})\zeta(t)]$, where $\zeta(t)$ grows sublinearly as $t\rightarrow\infty$. We outline here a…
We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various…
We investigate trend to equilibrium for the damped wave equation with a confining potential in the Euclidean space. We provide with necessary and sufficient geometric conditions for the energy to decay exponentially uniformly. The proofs…
We study the largest Lyapunov exponent $\lambda$ and the finite size effects of a system of N fully-coupled classical particles, which shows a second order phase transition. Slightly below the critical energy density $U_c$, $\lambda$ shows…
We discuss the behavior of fidelity for a classically chaotic quantum system in the metallic regime. We show the existence of a critical value of the perturbation below which the exponential decay of fidelity is determined by the width of…
We discuss the connection between the out-of-time-ordered correlator and the number of harmonics of the phase-space Wigner distribution function. In particular, we show that both quantities grow exponentially for chaotic dynamics, with a…
We consider multitype Markovian branching processes evolving in a Markovian random environment. To determine whether or not the branching process becomes extinct almost surely is akin to computing the maximal Lyapunov exponent of a sequence…
We describe some salient features as well as some recent developments concerning short-time deviations from the exponential decay law in the context of Quantum Mechanics by using the Lee Hamiltonian approach and Quantum Field Theory by…
We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions are written in terms of the parameters and are explicit for the case of…
Lyapunov exponents, a purely classical quantity, play an important role in the evolution of quantum chaotic systems in the semiclassical limit. We conjecture the existence of an upper bound on the Lyapunov exponents that contribute to the…
From a kinematical point of view, the geometrical information of hamiltonian chaos is given by the (un)stable directions, while the dynamical information is given by the Lyapunov exponents. The finite time Lyapunov exponents are of…
We exploit the presence of approximate (broken) symmetries to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Specifically, we consider a two-frequency forcing function and trace the…
Statistical behavior of a classical $\phi ^{4}$ Hamiltonian lattice is investigated from microscopic dynamics. The largest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system. It is…
We study the stability of one-dimensional linear hyperbolic systems with non-symmetric relaxation. Introducing a new frequency-dependent Kalman stability condition, we prove an abstract decay result underpinning a form of inhomogeneous…
We introduce a `proper time' formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field theoretical problem to a quantum-mechanical…
Nonlinear classical dissipative systems present a rich phenomenology in their "route to chaos", including period-doubling, i.e. the system evolves with a period which is twice that of the driving. However, typically the attractor of a…
We study in detail the time behavior of classical fidelity for chaotic systems. We show in particular that the asymptotic decay, depending on system dynamical properties, can be either exponential, with a rate determined by the gap in the…