Related papers: Autocorrelation function of eigenstates in chaotic…
Physical systems are often neither completely closed nor completely open, but instead they are best described by dynamical systems with partial escape or absorption. In this paper we introduce classical measures that explain the main…
We point out that by the ``smoothness means fast decay'' principle in Fourier analysis, it is possible to infer the smoothness (or nonsmoothness) of the autocorrelation function from a mere glimpse of the initial state. Specifically, for a…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's…
Time-dependent response and correlation functions are studied in random quantum systems composed of infinitely many parts without mutual interaction and defined with statistically independent random matrices. The latter are taken within the…
We study entanglement in two coupled quartic oscillators. It is shown that the entanglement, as measured by the von Neumann entropy, increases with the classical chaos parameter for generic chaotic eigenstates. We consider certain isolated…
We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent…
The observed preponderance of ground states with angular momentum L=0 in many-body quantum systems with random two-body interactions is analyzed in terms of correlation coefficients (covariances) among different eigenstates. It is shown…
We prove spatial decay estimates on disorder-averaged position-momentum correlations in a gapless class of random oscillator models. First, we prove a decay estimate on dynamic correlations for general eigenstates with a bound that depends…
We study autocorrelation times of physical observables in lattice QCD as a function of the molecular dynamics trajectory length in the hybrid Monte-Carlo algorithm. In an interval of trajectory lengths where energy and reversibility…
One of the most important quantities characterizing the microscopic properties of quantum systems are dynamical correlation functions. These correlations are obtained by time-evolving a perturbation of an eigenstate of the system, typically…
We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of…
Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty…
This paper considers the problem of estimating the time auto-correlation function for a quantity that is defined in configuration space, given a knowledge of the mean-square displacement as function of time in configuration space. The…
The autocorrelation function $C_{\varphi,\eps}(\Delta\varphi,\,\Delta \eps)=$ $\langle \delta g(\varphi,\,\eps)\, \delta g(\varphi+\Delta\varphi,\,\eps+\Delta \eps)\rangle$ ($\varphi$ and $\eps$ are rescaled magnetic flux and energy) for…
Motions of fluctuating Brownian particles in an incompressible viscous fluid have been studied by coupled simulations of Brownian particles and host fluid. We calculated the velocity autocorrelation functions of Brownian particles and…
We show that the time-dependence of correlation functions in an extended quantum system in d dimensions, which is prepared in the ground state of some hamiltonian and then evolves without dissipation according to some other hamiltonian, may…
Many dynamical systems, including power systems, recover from perturbations more slowly as they approach critical transitions---a phenomenon known as critical slowing down. If the system is stochastically forced, autocorrelation and…
We study the eigenstates of open maps whose classical dynamics is pseudointegrable and for which the corresponding closed quantum system has multifractal properties. Adapting the existing general framework developed for open chaotic quantum…
Particle-particle correlation functions in ionic systems control many of their macroscopic properties. In this work, we use stochastic density functional theory to compute these correlations, and then we analyze their long-range behavior.…