Related papers: Long-time limit of correlation functions
This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…
We study certain properties of the function space of autocorrelation functions of Unit Continuous Time Markov Chains (CTMCs). It is shown that under particular conditions, the $L^p$ norm of the autocorrelation function of arbitrary finite…
In the mode coupling theory of the liquid to glass transition the long time structural relaxation follows from equations solely determined by equilibrium structural parameters. The present extension of these structural relaxation equations…
Regularized coherent-state functional integrals are derived for ensembles of identical bosons on a lattice, the regularization being a discretization of Euclidian time. Convergence of the time-continuum limit is shown for various…
Temporal correlations in the time series observed in various systems have been characterized by the autocorrelation function. Such correlations can be explained by heavy-tailed interevent time distributions as well as by correlations…
In order to investigate the reliability of the classical approximation for non-perturbative real time correlation functions at finite temperature we study the two-point correlator for the anharmonic oscillator. For moderately large times…
Near equilibrium, the symmetric part of the time-integrated steady-state covariance, i.e., the time integral of correlation functions, is governed by the fluctuation-dissipation theorem, while the antisymmetric part vanishes due to Onsager…
Bounds for the correlation functions of identical bosons are discussed for the general case of a Gaussian density matrix. In particular, for a purely chaotic system the two-particle correlation function must always be greater than one. On…
We discuss the approach to equilibrium of systems governed by the Fokker-Planck equation. In particular, we focus on problems involving barrier penetration and the associated Kramers' time. We also describe the connection between stochastic…
An investigation of two-time correlation functions is reported within the framework of (i) Stochastic Quantum Mechanics and (ii) conventional Heisenberg-Schr\"odinger Quantum Mechanics. The spectral functions associated with the two-time…
The time-dependent pair correlation functions for a degenerate ideal quantum gas of charged particles in a uniform magnetic field are studied on the basis of equilibrium statistics. In particular, the influence of a flat hard wall on the…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
For a class of tight-binding many-electron models on hyper-cubic lattices the equal-time correlation functions at non-zero temperature are proved to decay exponentially in the distance between the center of positions of the electrons and…
We discuss the dynamic behavior of a tagged particle close to a classical localization transition in the framework of the mode-coupling theory of the glass transition. Asymptotic results are derived for the order parameter as well as the…
In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the…
We establish the connection between the presence of a glass phase and the appearance of a Coulomb gap in disordered materials with strongly interacting electrons. Treating multiparticle correlations in a systematic way, we show that in the…
We discuss a novel approach, the point-to-set correlation functions, that allows to determine relevant static and dynamic length scales in glass-forming liquids. We find that static length scales increase monotonically when the temperature…
The grand potential $\Omega$ and the response $R = - \partial \Omega /\partial x$ of a phase-coherent confined noninteracting electron gas depend sensitively on chemical potential $\mu$ or external parameter $x$. We compute their…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
The correlation functions for a strongly correlated exactly solvable one-dimensional boson system on a finite chain as well as in the thermodynamic limit are calculated explicitly. This system which we call the phase model is the strong…