We consider an exactly soluble model of a set of coupled harmonic oscillators, which was presented in a previous work. We show numerical results for the time evolution of the main dynamical quantities and compare them with analytical results.

Brownian motion of a parametric oscillator with asymmetric square waves which take a spring constant during a given length of time and suddenly change to a different value with a different length of time-duration has been investigated analytically with a view to the Paul trap in contrast to...

An alternative method of how to characterize, at equilibrium, the diffusion process of a Brownian charged particle (heavy ion) in a fluid in presence of an electromagnetic field is presented. The theory is formulated via a Langevin equation associated with the ion's velocity vector, which is...

The Brownian motion of a particle in a double-well potential is considered and the position correlation function (excluding inertial effects) for the potential V(x)=ax2/2+bx4/4 is evaluated first by averaging the governing Langevin equation over its realizations. The exact solution is then...

A general stationary case of a Brownian particle with a time-dependent periodic potential proportional to the square of the position of the particle is treated. Even though the vigorous change of the time-dependent proportionality coefficient is applied, there are cases where the fluctuation of...

We derive a generalized Langevin Equation (GLE) for the evolution of an arbitrary phase variable in a classical fluid that is initially at equilibrium and is subsequently subjected to an external field and a thermostat of the type used in nonequilibrium molecular dynamics computer simulations....

We consider a charged Brownian gas under the influence of external, static and uniform electric and magnetic fields, immersed in a uniform bath temperature. We obtain the solution for the associated Langevin equation, and thereafter the evolution of the nonequilibrium temperature towards a...

In this work we derive a generalized Langevin equation that describes the translational Brownian motion of a tracer particle which interacts with other diffusing particles in the system. The direct interactions of the tracer with these other diffusing particles give rise to memory effects...

A many-particle Hamiltonian, where the interaction term conserves the number of particles, is considered. A master equation for the populations of the different levels is derived in an exact way. It results in a local equation with time-dependent coefficients, which can be identified with the...

Within the framework of the theory of hydrodynamic fluctuations the Brownian motion of a spherical particle in a compressible fluid has been considered taking into account the action of a harmonic potential. The general relations for the velocity autocorrelation function and mean square...