Related papers: Long-time limit of correlation functions
We derive the statistical limit of the spectral autocorrelation function and of the survival probability for the indirect photodissociation of molecules in the regime of non-overlapping resonances. The results are derived in the framework…
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…
Temporal correlations in the harmonically trapped finite temperature Bose gas are studied through the calculation of appropriate phase correlation functions. A wide parameter regime is covered to ascertain the role that temperature…
We investigate the properties of a class of mode-coupling equations for the glass transition where the density mode decays into multiple relaxation channels. We prove the existence and uniqueness of the solutions for Newtonian as well as…
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes. The central limit theorem and functional central limit theorem are obtained for martingale like random variables under…
We study a classical lattice dipole gas with low activity in dimension $d \geq 3$. We investigate long distance properties by a renormalization group analysis. We prove that various correlation functions have an infinite volume limit. We…
There is a widespread recent interest in using ideas from statistical physics to model certain types of problems in economics and finance. The main idea is to derive the macroscopic behavior of the market from the random local interactions…
By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating…
We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and…
We give a version of the Borel-Cantelli lemma. As an application, we prove an almost sure local central limit theorem. As another application, we prove a dynamical Borel-Cantelli lemma for systems with sufficiently fast decay of…
A multi-time extension of a density correlation function is introduced to reveal temporal information about dynamical heterogeneity in glass-forming liquids. We utilize a multi-time correlation function that is analogous to the higher-order…
We calculate the ideal-glass-transition line for adhesive hard spheres in the temperature-volume-fraction plane within the framework of the mode-coupling theory. We find two intersecting lines, controlled by the hard-core and the adhesive…
The long time asymptotics of multi-time correlation functions of relaxing quantum mechanical systems can be conveniently studied by means of free-products of suitable C*-algebras and of states on these free products given by multiple…
The time-dependent structure of the Lyapunov vectors corresponding to the steps of Lyapunov spectra and their basis set representation are discussed for a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is observed…
Within the mode-coupling theory for the evolution of structural relaxation in glass-forming systems, it is shown that the correlation functions for density fluctuations for states at A_3- and A_4-glass-transition singularities can be…
In the setting of intermittent Pomeau-Manneville maps with time dependent parameters, we show a functional correlation bound widely useful for the analysis of the statistical properties of the model. We give two applications of this result,…
In this paper, we develop necessary and sufficient conditions for the validity of a martingale approximation for the partial sums of a stationary process in terms of the maximum of consecutive errors. Such an approximation is useful for…
The received wisdom in statistical mechanics is that isolated systems, when left to themselves, approach equilibrium. But under what circumstances does an equilibrium state exist and an approach to equilibrium take place? In this paper we…
In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…
We prove a limit theorem for an integral functional of a Markov process. The Markovian dynamics is characterized by a linear Boltzmann equation modeling a one-dimensional test particle of mass $\lambda^{-1}\gg 1$ in an external periodic…