Bidhan Chandra Bag

Noise properties of stochastic processes and entropy production

Based on a Fokker-Planck description of external Ornstein-Uhlenbeck noise and cross-correlated noise processes driving a dynamical system we examine the interplay of the properties of noise processes and the dissipative characteristic of the dynamical system in the steady state entropy production and flux. Our analysis is illustrated with appropriate examples.

The effect of interference of coloured additive and multiplicative white noises on escape rate

In this paper we have calculated the escape rate from a meta stable state for coloured and correlated noise driven open systems based on the Fokker–Planck description of the stochastic process. We consider the effect of two correlation times due to the additive coloured noise and the correlation between additive coloured and multiplicative white noises. The effect of the noise correlation strength on the rate has also been investigated.

Upper bound for the time derivative of entropy for nonequilibrium stochastic processes

We have shown how the intrinsic properties of a noise process can set an upper bound for the time derivative of entropy in a nonequilibrium system. The interplay of dissipation and the properties of noise processes driving the dynamical systems in presence and absence of external forces, reveals some interesting extremal nature of the upper bound.

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

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’ rate.

Effect of time delay on the onset of synchronization of the stochastic Kuramoto model

We consider the Kuramoto model of globally coupled phase oscillators with time-delayed interactions, that is subject to Ornstein–Uhlenbeck (Gaussian) colored or non-Gaussian colored noise. We investigate numerically the interplay between the influences of the finite correlation time of noise τ and the time delay τd on the onset of the synchronization process. The cases for identical and nonidentical oscillators have both been considered. Among the obtained results for identical oscillators is a large increase of the synchronization threshold as a function of time delay for the colored non-Gaussian noise compared to the case of the colored Gaussian noise at low noise correlation time τ. However, the difference reduces remarkably for large noise correlation times. For the case of nonidentical oscillators, the incoherent state may become unstable around the maximum value of the threshold (as a function of time delay) even at lower coupling strength values in the presence of colored noise as compared to the noiseless case. We have studied the dependence of the critical value of the coupling strength (the threshold of synchronization) on given parameters of the stochastic Kuramoto model in great detail and presented results for possible cases of colored Gaussian and non-Gaussian noises.

Quantum escape kinetics over a fluctuating barrier

The escape rate of a particle over a fluctuating barrier in a double-well potential exhibits resonance at an optimum value of correlation time of fluctuation. This has been shown to be important in several variants of kinetic model of chemical reactions. We extend the analysis of this phenomenon of resonant activation to quantum domain to show how quantization significantly enhances resonant activation at low temperature due to tunneling.

Quantum Kramers equation for energy diffusion and barrier crossing dynamics in the low-friction regime

Based on a true phase space probability distribution function and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)] a non-Markovian quantum Kramers equation to derive the quantum rate coefficient for barrier crossing due to thermal activation and tunneling in the intermediate to strong friction regime. We complement and extend this approach to weak friction regime to derive quantum Kramers equation in energy space and the rate of decay from a metastable well. The theory is valid for arbitrary temperature and noise correlation. We show that depending on the nature of the potential there may be a net reduction of the total quantum rate below its corresponding classical value, which is in conformity with earlier observation. The method is independent of path integral approaches and takes care of quantum effects to all orders.

Nonequilibrium stochastic processes: time dependence of entropy flux and entropy production.

Based on the Fokker-Planck and the entropy balance equations we have studied the relaxation of a dissipative dynamical system driven by external Ornstein-Uhlenbeck noise processes in the absence and presence of nonequilibrium constraint in terms of the thermodynamically inspired quantities such as entropy flux and entropy production. The interplay of nonequilibrium constraint, dissipation, and noise reveals some interesting extremal nature in the time dependence of entropy flux and entropy production.

Study of non-Markovian dynamics of a charged particle in presence of a magnetic field in a simple way

In this paper, we have investigated the dynamics of a Brownian particle in the presence of a magnetic field. The present investigation is generalized considering different kinds of force fields, magnetic field, and non-Markovian thermal bath. The properties of the Brownian particle have been calculated based on the multi-dimensional Fokker-Planck description of stochastic processes. It leads to the study of non-Markovian dynamics of a Brownian particle in the presence of a magnetic field in a simple way. Using the present simple method, we have identified several important signatures of magnetic field and non-Markovian thermal bath in the dynamics.