Wiener–Khinchin theorem

About: Wiener–Khinchin theorem is a research topic. Over the lifetime, 172 publications have been published within this topic receiving 6575 citations.

The fluctuation-dissipation theorem

Abstract: The linear response theory has given a general proof of the fluctuation-dissipation theorem which states that the linear response of a given system to an external perturbation is expressed in terms of fluctuation properties of the system in thermal equilibrium. This theorem may be represented by a stochastic equation describing the fluctuation, which is a generalization of the familiar Langevin equation in the classical theory of Brownian motion. In this generalized equation the friction force becomes retarded or frequency-dependent and the random force is no more white. They are related to each other by a generalized Nyquist theorem which is in fact another expression of the fluctuation-dissipation theorem. This point of view can be applied to a wide class of irreversible process including collective modes in many-particle systems as has already been shown by Mori. As an illustrative example, the density response problem is briefly discussed.

Introduction to the theory of coverage processes

Abstract: Examples, concepts and tools random line segments, queues and counters vacancy counting and clumping elements of inference. Appendices: direct Radon-Nikodym theorem central limit theorem, Poisson limit theorem, ergodic theorem and law of large numbers Shepp's coverage theorem mean content and mean square content of cells formed by Poisson field of random planes multitype branching processes lattice percolation.

On the Calculation of Autocorrelation Functions of Dynamical Variables

Abstract: In this paper we develop a formalism for calculating the autocorrelation function of a dynamical variable in terms of a well‐defined memory function. Guided by simple physical arguments, an ansatz is adopted for the functional form of the memory function. This ansatz asserts that the memory of dynamical coherence decays exponentially. It is found that:(a) Despite the monotonic exponential decay of the memory function, the autocorrelation function deduced can display negative regions in some circumstances and decay monotonically in other circumstances.(b) The form of the autocorrelation function deduced is identical with that obtained from two other very different analyses, suggesting that the major properties of the function are of general validity.(c) The computed linear momentum autocorrelation function and power spectrum for liquid Ar are in good agreement with the computer experiments of Rahman.(d) The computed dipolar autocorrelation function reproduces all the features of the experimentally determin...

Aging and nonergodicity beyond the Khinchin theorem.

Abstract: The Khinchin theorem provides the condition that a stationary process is ergodic, in terms of the behavior of the corresponding correlation function. Many physical systems are governed by nonstationary processes in which correlation functions exhibit aging. We classify the ergodic behavior of such systems and suggest a possible generalization of Khinchin’s theorem. Our work also quantifies deviations from ergodicity in terms of aging correlation functions. Using the framework of the fractional Fokker-Planck equation, we obtain a simple analytical expression for the two-time correlation function of the particle displacement in a general binding potential, revealing universality in the sense that the binding potential only enters into the prefactor through the first two moments of the corresponding Boltzmann distribution. We discuss applications to experimental data from systems exhibiting anomalous dynamics.