arXiv subjects

Deb Shankar Ray

Publications and source records attributed to Deb Shankar Ray.

50 records · Page 3Linked to original sources

arXiv2000

Chaos and information entropy production

We consider a general N-degree-of-freedom nonlinear Hamiltonian system which is chaotic and dissipative and show that the origin of chaotic diffusion lies in the correlation of fluctuation of 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 and an information entropy balance equation a relationship between chaotic diffusion and the thermodynamically-inspired quantities like entropy production and entropy flux is established. The theoretical propositions have been verified by numerical experiments.

chao-dyn↗

arXiv2000

Fluctuations and the existence of potential in dissipative semiclassical systems

We examine the weak noise limit of an overdamped dissipative system within a semiclassical description and show how quantization influences the growth and decay of fluctuations of the thermally equilibrated systems. We trace its origin in a semiclassical counterpart of the generalized potential for the dissipative system.

cond-mat.stat-mech↗

arXiv2000

Environment-induced dynamical chaos

We examine the interplay of nonlinearity of a dynamical system and thermal fluctuation of its environment in the ``physical limit'' of small damping and slow diffusion in a semiclassical context and show that the trajectories of c-number variables exhibit dynamical chaos due to the thermal fluctuations of the bath.

nlin.CD↗

arXiv2000

Fluctuation-dissipation relationship in chaotic dynamics

We consider a general N-degree-of-freedom dissipative system which admits of chaotic behaviour. Based on a Fokker-Planck description associated with the dynamics we establish that the drift and the diffusion coefficients can be related through a set of stochastic parameters which characterize the steady state of the dynamical system in a way similar to fluctuation-dissipation relation in non-equilibrium statistical mechanics. The proposed relationship is verified by numerical experiments on a driven double well system.

nlin.CD↗

arXiv2000

The generalized Kramers' theory for nonequilibrium open one-dimensional systems

The Kramers' theory of activated processes is generalized for nonequilibrium open one-dimensional systems. We consider both the internal noise due to thermal bath and the external noise which are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. We stress the role of a nonequilibrium stationary state distribution for this open system which is reminiscent of an equilibrium Boltzmann distribution in calculation of rate. The generalized rate expression we derive here reduces to the specific limiting cases pertaining to the closed and open systems for thermal and non-thermal steady state activation processes.

cond-mat.stat-mech↗

arXiv2000

The generalized Kramers' theory for an external noise driven bath

We consider a system-reservoir model where the reservoir is modulated by an external noise. Both the internal noise of the reservoir and the external noise are stationary, Gaussian and are characterized by arbitrary decaying correlation functions. Based on a relation between the dissipation of the system and the response function of the reservoir driven by external noise we derive the generalized Kramers' rate for this nonequilibrium open system.

cond-mat.stat-mech↗

arXiv1999

A simple semiclassical approach to Kramers' problem

We show that 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 temerature, Ohmic environment can be identified as a semiclassical version of Kramers' equation. Based on an expansion in powers of $\hbar$ we solve this equation to calculate the semiclassical correction to Kramers' rate.

cond-mat.stat-mech↗

arXiv1999

Quantum noise-induced chaotic oscillations

We examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxiliary Hamiltonian manifests itself as an additional fluctuational degree of freedom which may induce chaotic and regular oscillations in a nonlinear oscillator.

chao-dyn↗

arXiv1999

Barrier crossing induced by very slow external noise

We consider the motion of a particle in a force field subjected to adiabatic, fluctuations of external origin. We do not put the restriction on the type of stochastic process that the noise is Gaussian. Based on a method developed earlier by us [ J. Phys. A {\bf 31} (1998) 3937, 7301] we have derived the equation of motion for probability distribution function for the particle on a coarse-grained timescale $Δt$ assuming that it satisfies the separation of timescales; $|μ|^{-1} \ll Δt \ll τ_c$, where $τ_c$ is the correlation time of fluctuations. $|μ|^{-1}$ refers to the inverse of the damping rate (or, the largest of the eigenvalues of the unperturbed system) and sets the shortest timescale in the dynamics in contrast to the conventional theory of fast fluctuations. The equation includes a third order noise term. We solve the equation for a Kramers' type potential and show that although the system is thermodynamically open, appropriate boundary conditions allow the distinct steady states. Based on the exact solution of the third order equation for the linearized potential and the condition for attainment of the steady states we calculate the adiabatic noise-induced rate of escape of a particle confined in a well. A typical variation of the escape rate as a function of dissipation which is reminiscent of Kramers' turn-over problem, has been demonstrated.

cond-mat.stat-mech↗

arXiv1999

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.

cond-mat.stat-mech↗

arXiv1999

Notes on Brownian motion and related phenomena

In this article we explore the phenomena of nonequilibrium stochastic process starting from the phenomenological Brownian motion. The essential points are described in terms of Einstein's theory of Brownian motion and then the theory extended to Langevin and Fokker-Planck formalism. Then the theory is applied to barrier crossing dynamics, popularly known as Kramers' theory of activated rate processes. The various regimes are discussed extensively and Smoluchowski equation is derived as a special case. Then we discuss some of the aspects of Master equation and two of its applications.

physics.ed-ph↗

arXiv1999

A semiclassical theory of dissipative Henon-Heiles system

A semiclassical theory of dissipative Henon-Heiles system is proposed. Based on $\hbar$-scaling of an equation for evolution of Wigner quasiprobability distribution function in presence of dissipation and thermal diffusion, we derive a semiclassical equation for quantum fluctuations, governed by the dissipation and the curvature of the classical potential. We show how the initial quantum noise gets amplified by classical chaotic diffusion which is expressible in terms of correlation of stochastic fluctuations of the curvature of the potential due to classical chaos and ultimately settles down to equilibrium under the influence of dissipation. We also establish that there exists a critical limit to the expansion of phase space. The limit is set by chaotic diffusion and dissipation. Our semiclassical analysis is corroborated by numerical simulation of quantum operator master equation.

chao-dyn↗

arXiv1999

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.

physics.optics↗

arXiv1998

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.

cond-mat.stat-mech↗