Related papers: A Statistical Mechanical Approximation for the Cal…
A theoretical framework for analyzing stochastic data from single-particle tracking in complex or viscoelastic materials and under the influence of a trapping potential is presented. Starting from a generalized Langevin equation we found…
We define a correlation function that quantifies the spatial correlation of single-particle displacements in liquids and amorphous materials. We show for an equilibrium liquid that this function is related to fluctuations in a bulk…
As an indicator of cooperative motion in a system of Brownian particles that models two-dimensional colloidal liquids, displacement correlation tensor is calculated analytically and compared with numerical results. The key idea for the…
Many natural phenomena exhibit a stochastic nature that one attempts at modeling by using stochastic processes of different types. In this context, often one is interested in investigating the memory properties of the natural phenomenon at…
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…
The calculation of quantum canonical time correlation functions is considered in this paper. Transport properties, such as diffusion and reaction rate coefficients, can be determined from time integrals of these correlation functions.…
The concept of time correlation functions is a very convenient theoretical tool in describing relaxation processes in multiparticle systems because, on one hand, correlation functions are directly related to experimentally measured…
Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction (diameter sigma) is studied with a liquid-theoretical approach. The mean square displacement, the two-particle displacement correlation, and…
The mean square displacement and instantaneous diffusion coefficient for different configurations of charged particles in stochastic motion are calculated by numerically solving the associated equations of motion. The method is suitable for…
Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the…
It is shown that the solution of generalized Langevin equation can be obtained on the basis of simple comparison of the time scale for the velocity autocorrelation function of a particle (atom, molecule) and of the time scale for the…
The relation between the Lyapunov modes (delocalized Lyapunov vectors) and the momentum autocorrelation function is discussed in two-dimensional hard-disk systems. We show numerical evidence that the smallest time-oscillating period of the…
We present a new time-dependent Density Functional approach to study the relaxational dynamics of an assembly of interacting particles subject to thermal noise. Starting from the Langevin stochastic equations of motion for the velocities of…
We investigate the usage of a recently introduced noise-cancellation algorithm for Brownian simulations to enhance the precision of measuring transport properties such as the mean-square displacement or the velocity-autocorrelation…
The behavior of spins undergoing Lamor precession in the presence of time varying fields is of interest to many research fields. The frequency shifts and relaxation resulting from these fields are related to their power spectrum and can be…
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…
Within the framework of probability distributions on projective Hilbert space a scheme for the calculation of multitime correlation functions is developed. The starting point is the Markovian stochastic wave function description of an open…
Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc.…
Analysis of three-particle correlations is performed on the basis of simulation data of atomic dynamics in liquid and amorphous aluminium. A three-particle correlation function is introduced to characterize the relative positions of various…
The problem of calculating real-time correlation functions is formulated in terms of an imaginary-time partial differential equation. The latter is solved analytically for the perturbed harmonic oscillator and compared with the known exact…