Anindita Shit

Microscopic realization of cross-correlated noise processes

We present a microscopic theory of cross-correlated noise processes, starting from a Hamiltonian system-reservoir description. In the proposed model, the system is nonlinearly coupled to a reservoir composed of harmonic oscillators, which in turn is driven by an external fluctuating force. We show that the resultant Langevin equation derived from the composite system (system+reservoir+external modulation) contains the essential features of cross-correlated noise processes.

A semiclassical approach to explore the bistable kinetics of a Brownian particle in a nonequilibrium environment

We explore the noise-induced barrier crossing dynamics of a Brownian particle in the high temperature quantum regime under large damping. We assume the associated heat bath not to be in thermal equilibrium; it is rather driven by an externally applied random force which exposes the system particles to a nonequilibrium environment. We propose a system + reservoir model to study the stochastic Langevin dynamics. We also construct the corresponding Fokker–Planck equation in the said regime and solve it to explore the bistable kinetics. We investigate the role of different parameters in shaping the nature of such a bistable kinetics in detail and hence allowing one to get some insight into the very complicated dynamics of quantum dissipative system(s). Finally, we analyze the semiclassical rate vis-a-vis the classical analog.

A microscopic model for noise induced transport: Heat-bath nonlinearly driven by external white noise

This work explores the observation that, even in the absence of a net externally applied bias, a symmetric homogeneous system coupled linearly to two heat baths is capable of producing unidirectional motion simply by nonlinearly driving one of the heat baths by an external Gaussian white noise. This is quite contrary to the traditional observation that, in order to obtain a net drift current, a state-dependent dissipation, which is a consequence of nonlinear system-bath coupling, is ubiquitous.

Escape of a driven particle from a metastable state: A semiclassical approach

In this article we explore the dynamics of escape of a particle in the semiclassical regime by driving the particle externally. We demonstrate that under suitable approximations the semiclassical escape rate essentially assumes the structure of classical Kramers rate. Both internal (due to thermal bath) as well as external noises (due to driving) are being considered. The noises are stationary, Gaussian, and are characterized by arbitrary decaying memory kernel. Finally, we subject our formulation to rigorous numerical test under variedly changing conditions of the parameters.

Time-independent description of rapidly driven systems in the presence of friction: Multiple scale perturbation approach

The dynamics of a classical system driven by a rapidly oscillating field (with frequency ω) in the presence of friction has been investigated using the multiple scale perturbation theory (MSPT). By exploiting the idea of separation of time scales, the slow motion has been computed in a systematic expansion in the inverse of ω to the order ω(-3). This perturbation series can be viewed as a generalization of the calculation presented by Landau and Lifshitz for Kapitzas pendulum (where the point of suspension is moved periodically) in the presence of friction. The radiation induced dynamics of the system is found to be described by an effective time-independent potential with friction that controls the slow motion. The explicit appearance of friction in our computed effective potential is a manifestation of the dynamical effect due to the fast motion. The present study demonstrates that MSPT can be used to understand and predict the classical dynamics of a driven system in the presence of friction.

Kramers turnover in class of thermodynamically open systems: Effect of interplay of nonlinearity and noises

Abstract A system–reservoir nonlinear coupling model has been proposed for a situation where the reservoir is nonlinearly driven by an external Gaussian stationary noise which exposes the system particles to a nonequilibrium environment. Apart from the internal thermal noise, the thermodynamically open system encounters two other noises that are multiplicative in nature. Langevin equation derived from the resulting composite system contains the essential features of the interplay between these noise processes. Based on the numerical simulation of the full model potential, we show that one can recover the turnover features of the Kramers dynamics even when the reservoir is modulated nonlinearly by an external noise.

Generalized Einstein relation in tilted periodic potential: a semiclassical approach.

This paper concerns the investigation of the quantum motion of a system in a dissipative Ohmic heat bath in the presence of an external field using the traditional system-reservoir model. Using physically motivated initial conditions, we then obtain the c-number of the generalized quantum Langevin equation by which we calculate the quantum correction terms using a perturbation technique. As a result of this, one can apply a classical differential equation-based approach to consider quantum diffusion in a tilted periodic potential, and thus our approach is easy to use. We use our expression to calculate the Einstein relation for the quantum Brownian particle in a ratchet-type potential in a very simple closed analytical form using a suitable and convenient approximation. It is found that the diffusion rate is independent of the detailed form of the potential both in quantum and classical regimes, which is the main essence of this work.

High-frequency behavior of periodically modulated stochastic quantum system: activated escape

We explore the dynamics of a quantum dissipative system subjected to a space dependent, rapidly oscillating periodical force in semiclassical regime. Starting from a time dependent quantum system-reservoir Hamiltonian, we arrive at an effective time independent c-number generalized Langevin equation at leading order using multiple scale perturbation theory which rules the dynamics of the system. The motion for the slow part has been calculated perturbatively in powers of the frequency (ω) of the applied force to the order . We have employed our derived time-independent results to study the escape rate of the modulated system by numerical simulations. To illustrate the impact of driving on the resulting rate in conjunction with the thermal noise, we provide the results without driving and results of the corresponding classical analogue. The escape rate is larger in the presence of driving due to the intricate interplay of spatially periodic gradients, periodic modulation and thermal noise.