Adiabatic noise-induced escape rate for nonequilibrium open systems

We consider the motion of an overdamped particle in a force field in presence of an external, adiabatic noise, without the restriction that the noise process is Gaussian or the stochastic process is Markovian. We examine the condition for attainment of steady state for this nonequilibrium open system and calculate the adiabatic noise-induced rate of escape of the particle over a barrier.Comment: 6 pages, 3 figure

Theory of non-stationary activated rate processes : nonexponential relaxation kinetics

We have explored a simple microscopic model to simulate a thermally activated rate process where the associated bath which comprises a set of relaxing modes is not in an equilibrium state. The model captures some of the essential features of non-Markovian Langevin dynamics with a fluctuating barrier. Making use of the Fokker-Planck description we calculate the barrier dynamics in the steady state and non-stationary regimes. The Kramers-Grote-Hynes reactive frequency has been computed in closed form in the steady state to illustrate the strong dependence of the dynamic coupling of the system with the relaxing modes. The influence of nonequilibrium excitation of the bath modes and its relaxation on the kinetics of activation of the system mode is demonstrated. We derive the dressed time-dependent Kramers rate in the nonstationary regime in closed analytical form which exhibits strong non-exponential relaxation kinetics of the reaction co-ordinate. The feature can be identified as a typical non-Markovian dynamical effect.Comment: Plain Latex, no figure, 31 pages, to appear in J. Chem. Phy

Modified Bloch equations in presence of a nonstationary bath

Based on the system-reservoir description we propose a simple solvable microscopic model for a nonequilibrium bath. This captures the essential features of a nonstationary quantum Markov process. We establish an appropriate generalization of the fluctuation-dissipation relation pertaining to this process and explore the essential modifications of the Bloch equations to reveal the nonexponential decay of the Bloch vector components and transient spectral broadening in resonance fluorescence. We discuss a simple experimental scheme to verify the theoretical results.Comment: Revtex, 27 pages, 2 ps figures. To appear in European Physical Journal

A simple semiclassical approach to the Kramers' problem

We show that the Wigner-Leggett-Caldeira equation for Wigner phase space distribution function which describes the quantum Brownian motion of a particle in a force field in a high temperature, ohmic environment can be identified as a semiclassical version of Kramers' equation. Based on an expansion in powers of ℏ, we solve this equation to calculate the semiclassical correction to Kramers' rat

Chaos and information entropy production

We consider a general N-degrees-of-freedom nonlinear system which is chaotic and dissipative, and show that the nature of chaotic diffusion is reflected in the correlation of fluctuation of the linear stability matrix for the equation of motion of the dynamical system whose phase space variables behave as stochastic variables in the chaotic regime. Based on a Fokker-Planck description of the system in the associated tangent space and an information entropy balance equation, a relationship between chaotic diffusion and the thermodynamically inspired quantities such as entropy production and entropy flux is established. The theoretical propositions have been verified by numerical experiments

Simple model for transport phenomena : Microscopic construction of Maxwell Demon like engine

We present a microscopic Hamiltonian framework to develop Maxwell demon like engine. Our model consists of a equilibrium thermal bath and a non-equilibrium bath; latter generated by driving with an external stationary, Gaussian noise. The engine we develop, can be considered as a device to extract work by modifying internal fluctuations. Our theoretical analysis focusses on finding the essential ingredients necessary for generating fluctuation induced transport under non-equilibrium condition. An important outcome of our model is that the net motion occurs when the non-linear bath is modulated by the external noise, creating the non-zero effective temperature even when the temperature of both the baths are same.Comment: 6 pages, RevTex