Quantification of noise in bifunctionality-induced post-translational modification.

We present a generic analytical scheme for the quantification of fluctuations due to bifunctionality-induced signal transduction within the members of a bacterial two-component system. The proposed model takes into account post-translational modifications in terms of elementary phosphotransfer kinetics. Sources of fluctuations due to autophosphorylation, kinase, and phosphatase activity of the sensor kinase have been considered in the model via Langevin equations, which are then solved within the framework of linear noise approximation.

Quantum stochastic dynamics in the presence of a time-periodic rapidly oscillating potential: nonadiabatic escape rate.

Escape from a metastable state in the presence of a high-frequency field (where the driving becomes nonadiabatic) underlies a broad range of phenomena of physics and chemistry, and thus its understanding is of paramount importance. We study the problem of intermediate-to-high-damping escape from a metastable state of a dissipative system driven by a rapidly oscillating field, one of the most important classes of nonequilibrium systems, in a broad range of field driving frequencies (ω) and amplitudes (a). We construct a Langevin equation using quantum gauge transformation in the light of Floquet theorem and exploiting a systematic perturbative expansion in powers of 1/ω using "Kapitza-Landau time window".

Escape rate for a quantum particle moving in a time-periodic rapidly oscillating potential: a time-independent approach.

We explore, in the quantum regime, the stochastic dynamics of a time-periodic, rapidly oscillating potential (having a characteristic frequency of ω) within the framework of a time-dependent system-reservoir Hamiltonian. We invoke the idea of a quantum gauge transformation in light of the standard Floquet theorem in an attempt to construct a Langevin equation (bearing a time-independent effective potential) by employing a systematic perturbative expansion in powers of ω^{-1} using the natural time-scale separation. The time-independent effective potential (corrected to ω^{-2} in leading order) that acts on the slow motion of the driven particle can be employed for trapping.

Controlling activated processes of nonadiabatically, periodically driven dynamical systems: a multiple scale perturbation approach.

We arrive at the escape rate from a metastable state for a system of Brownian particles driven periodically by a space dependent, rapidly oscillating external perturbation (with frequency ω) in one dimension (one of the most important class of nonequilibrium system). Though the problem may seem to be time-dependent, and is poised on the extreme opposite side of adiabaticity, there exists a multiple scale perturbation theory ("Kapitza window") by means of which the dynamics can be treated in terms of an effective time-independent potential that is derived as an expansion in orders of 1/ω to the order ω(-3). The resulting time-independent equation is then used to calculate the escape rate of physical systems from a metastable state induced by external monochromatic field in the moderate-to-large damping limit and to investigate the effect of ω on the resulting rate in conjunction with the thermal energy.

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 Kapitza's pendulum (where the point of suspension is moved periodically) in the presence of friction.

Effective quantum Brownian dynamics in presence of a rapidly oscillating space-dependent time-periodic field.

We explore the Brownian dynamics in the quantum regime (by investigating the quantum Langevin and Smoluchowski equations) in terms of an effective time-independent Hamiltonian in the presence of a rapidly oscillating field. We achieve this by systematically expanding the time-dependent system-reservoir Hamiltonian in the inverse of driving frequency with a systematic time-scale separation and invoking a quantum gauge transformation within the framework of Floquet theorem.

Development of a semiclassical method to compute mobility and diffusion coefficient of a Brownian particle in a nonequilibrium environment.

We explore the issue of a quantum-noise-induced directed transport of an overdamped Brownian particle that is allowed to move in a spatially periodic potential. The established system-reservoir model has been employed here to study the quantum-noise-induced transport of a Brownian particle in a periodic potential, where the reservoir is being modulated externally by a Gaussian-colored noise. The mobility of the Brownian particle in the linear response regime has been calculated.

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.

External-noise-driven bath and the generalized semiclassical Kramers theory.

We address the issue of a system that has been tacitly made thermodynamically open by externally driving the associated heat bath in an attempt to gain better insight regarding many physical situations that are akin to this problem. This work embodies the study of the quantum effects in the rate of decay from a metastable state of a Brownian particle which is in contact with a correlated noise-driven bath. We do this by initiating from a suitable system-reservoir model to derive the operator-valued Langevin equation.

Realization of a Brownian engine to study transport phenomena: a semiclassical approach.

Brownian particles moving in a periodic potential with or without external load are often used as good theoretical models for the phenomenological studies of microscopic heat engines. The model that we propose here, assumes the particle to be moving in a nonequilibrium medium and we have obtained the exact expression for the stationary current density. We have restricted our consideration to the overdamped motion of the Brownian particle.

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.

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.

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.

Stochastic resonance in a generalized quantum Kubo oscillator.

We discuss stochastic resonance in a biased linear quantum system that is subject to multiplicative and additive noises. Starting from a microscopic system-reservoir Hamiltonian, we derive a c-number analogue of the generalized Langevin equation. The developed approach puts forth a quantum mechanical generalization of the "Kubo type" oscillator which is a linear system.

Quantum transport in a periodic symmetric potential of a driven quantum system.

A system-reservoir nonlinear coupling model has been proposed to the situation when the system is driven externally by a random force and the associated bath is kept in thermal equilibrium, in an attempt to put forth a microscopic approach to quantum state-dependent diffusion and multiplicative noises in terms of a quantum Langevin equation in the overdamped limit (quantum Smoluchowski equation). We then obtain the analytical expression for phase induced quantum current in a periodic potential when the external noise has finite correlation time and explore the dependence of the current on various parameters related to the external noise, for example, the noise strength.

Harmonic oscillator in presence of nonequilibrium environment.

Based on a microscopic Hamiltonian picture where the system is coupled with the nonequilibrium environment, comprising of a set of harmonic oscillators, the Langevin equation with proper microscopic specification of Langevin force is formulated analytically. In our case, the reservoir is perturbed by an external force, either executing rapid or showing periodic fluctuations, hence the reservoir is not in thermal equilibrium. In the presence of external fluctuating force, using Shapiro-Loginov procedure, we arrive at the linear coupled first order differential equations for the two-time correlations and examine the time evolution of the same considering the system as a simple harmonic oscillator.

Phase induced current in presence of nonequilibrium bath: A quantum approach.

Based on a system-reservoir nonlinear coupling model, where the associated bath is externally driven by a fluctuating force, we present a microscopic approach to quantum state-dependent diffusion and multiplicative noises in terms of a quantum (Markovian) Langevin equation in overdamped limit when the associated bath is in nonequilibrium state. We then explore the possibility of observing a quantum current when the bath is modulated by white noise, the phenomena which is absent in the classical regime.

Directed motion in a periodic potential of a quantum system coupled to a heat bath driven by a colored noise.

A system-reservoir nonlinear coupling model is proposed for a quantum system when the associated bath is not in thermal equilibrium but is modulated by an external colored noise, to present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Langevin description. Consequently, the Fokker-Planck equation in position space, valid in the overdamped limit, for multiplicative colored noise is constructed to explore the possibility of observing a quantum current and dependence of the current on various parameters of external noise is examined.

Effect of correlated noises on directed motion.

The Langevin equation for a Brownian particle, in contact with a heat bath which offers state dependent friction, is considered to study the directed motion in presence of two external correlated noises. The effects of correlation on transport of the Brownian particle in a symmetric periodic potential is studied and it has been found that the steady state current increases with increase in the degree of correlation. This property suggests that by controlling the degree of correlation one can enhance the current in a properly designed experiment.

Multiplicative cross-correlated noise induced escape rate from a metastable state.

We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. By starting from a phenomenological stationary Langevin description with multiplicative noise processes, we have investigated the Kramers theory for activated rate processes in a nonequilibrium open system (one dimensional in nature) driven by two external cross-correlated noise processes which are Gaussian, stationary, and delta correlated. Based on the Fokker-Planck description in phase space, we then derive the escape rate from a metastable state in the moderate to large friction limit to study the effect of degree of correlation on the same.

Simple model for transport phenomena: microscopic construction of Maxwell demonlike engine.

We present a microscopic Hamiltonian framework to develop Maxwell demonlike engine. Our model consists of an equilibrium thermal bath and a nonequilibrium 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.

Generalization of the escape rate from a metastable state driven by external cross-correlated noise processes.

We propose generalization of the escape rate from a metastable state for externally driven correlated noise processes in one dimension. In addition to the internal non-Markovian thermal fluctuations, the external correlated noise processes we consider are Gaussian, stationary in nature and are of Ornstein-Uhlenbeck type. Based on a Fokker-Planck description of the effective noise processes with finite memory we derive the generalized escape rate from a metastable state in the moderate-to-large damping limit and investigate the effect of degree of correlation on the resulting rate.

Dynamics of a metastable state nonlinearly coupled to a heat bath driven by external noise.

Based on a system-reservoir model, where the system is nonlinearly coupled to a heat bath and the heat bath is modulated by an external stationary Gaussian noise, we derive the generalized Langevin equation with space-dependent friction and multiplicative noise and construct the corresponding Fokker-Planck equation, valid for short correlation time, with space-dependent diffusion coefficient to study the escape rate from a metastable state in the moderate- to large-damping regime. By considering the dynamics in a model cubic potential we analyze the results numerically which are in good agreement with theoretical predictions. It has been shown numerically that enhancement of the rate is possible by properly tuning the correlation time of the external noise.

Escape rate from a metastable state weakly interacting with a heat bath driven by external noise.

Based on a system-reservoir model, where the reservoir is driven by an external stationary, Gaussian noise with arbitrary decaying correlation function, we study the escape rate from a metastable state in the energy diffusion regime. For the open system we derive the Fokker-Planck equation in the energy space and subsequently calculate the generalized non-Markovian escape rate from a metastable well in the energy diffusion domain. By considering the dynamics in a model cubic potential we show that the results obtained from numerical simulation are in good agreement with the theoretical prediction.