Related papers: Statistical characterization of the standard map
We calculate the decay rate for a state prepared in a thermal density matrix centered on a metastable ground state. We find a rate that is intrinsically time {\it dependent}, as opposed to the {\it constant} rates of previous works. The…
From the analyticity properties of the equation governing infinitesimal perturbations, it is shown that all stability properties of spatially extended 1D systems can be derived from a single function that we call entropy potential since it…
We highlight a few recent results on the effect of the diffusion process in deterministic area preserving maps with noncompact phase space, namely the standard map. In more detail, we focus on the anomalous diffusion arising due to the…
A generalization of the entropy production rate is proposed $\Pi_q$ in non-equilibrium systems by extending the formalism of classical stochastic thermodynamics to regimes with non-Gaussian fluctuations. Through the R\'enyi entropy $S_q$ ,…
We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions $\rho(p,q)$. Of particular interest is $\lambda_2$, an exponent which quantifies the rate at which chaotically evolving…
The study of generic properties of quantum states has led to an abundance of insightful results. A meaningful set of states that can be efficiently prepared in experiments are ground states of gapped local Hamiltonians, which are well…
We investigate prethermalization by studying the statistical properties of the time-dependent largest Lyapunov exponent $\Lambda(t)$ for unitary-circuit maps upon approaching integrability. We follow the evolution of trajectories for…
We study the behaviour of the Standard map critical function in a neighbourhood of a fixed resonance, that is the scaling law at the fixed resonance. We prove that for the fundamental resonance the scaling law is linear. We show numerical…
Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed…
For an infinitely renormalizable negative Schwarzian unimodal map $f$ with non-flat critical point, we analyze statistical properties of periodic points as the periods tend to infinity. Introducing a weight function $\varphi$ which is a…
We consider random perturbations of discrete-time dynamical systems. We give sufficient conditions for the stochastic stability of certain classes of maps, in a strong sense. This improves the main result in J. F. Alves, V. Araujo, Random…
Transport properties of disordered electron system can be characterized by the conductance, Lyapunov exponent, or level spacing. Two additional parameters, $K_{11}$ and $\gamma $ were introduced recently which measure the non-homogeneity of…
It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of ${\fR}^2$. A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} in a computer-assisted…
In this paper we introduce a notion of expansiveness for a set valued map defined on a topological space different from that given by Richard Williams at \cite{Wi, Wi2} and prove that the topological entropy of an expansive set valued map…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
We consider skew tent maps $T_{{\alpha}, {\beta}}(x)$ such that $( {\alpha}, {\beta})\in[0,1]^{2}$ is the turning point of $T {_ { {\alpha}, {\beta}}}$, that is, $T_{{\alpha}, {\beta}}=\frac{{\beta}}{{\alpha}}x$ for $0\leq x \leq {\alpha}$…
We show that for the standard map family, for all values of the parameter, except one, the mapping has positive topological entropy. The main tool is the following result. Let $S$ be a compact connected orientable surface and $f:S…
We investigate the critical behavior of continuous phase transitions in the context of Ginzburg Landau models with a double well effective potential. In particular, we show that the recently proposed configurational entropy, a measure of…
The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a…
Using the diagonal entropy, we analyze the dynamical signatures of the Lipkin-Meshkov-Glick (LMG) model excited-state quantum phase transition (ESQPT). We first show that the time evolution of the diagonal entropy behaves as an efficient…