arXiv subjects

Deb Shankar Ray

Publications and source records attributed to Deb Shankar Ray.

At least 37 records · Page 2Linked to original sources

arXiv2006

Stochastic Energetics of Quantum Transport

We examine the stochastic energetics of directed quantum transport due to rectification of non-equilibrium thermal fluctuations. We calculate the quantum efficiency of a ratchet device both in presence and absence of an external load to characterize two quantifiers of efficiency. It has been shown that the quantum current as well as efficiency in absence of load (Stokes efficiency) is higher as compared to classical current and efficiency, respectively, at low temperature. The conventional efficiency of the device in presence of load on the other hand is higher for a classical system in contrast to its classical counterpart. The maximum conventional efficiency being independent of the nature of the bath and the potential remains the same for classical and quantum systems.

cond-mat.soft↗

arXiv2005

Noise-induced transition in a quantum system

We examine the noise-induced transition in a fluctuating bistable potential of a driven quantum system in thermal equilibrium. Making use of a Wigner canonical thermal distribution for description of the statistical properties of the thermal bath, we explore the generic effects of quantization like vacuum field fluctuation and tunneling in the characteristic stationary probability distribution functions undergoing transition from unimodal to bimodal nature and in signal-to-noise ratio characterizing the co-operative effect among the noise processes and the weak periodic signal.

cond-mat.stat-mech↗

arXiv2005

Quantum state-dependent diffusion and multiplicative noise: a microscopic approach

The state-dependent diffusion, which concerns the Brownian motion of a particle in inhomogeneous media has been described phenomenologically in a number of ways. Based on a system-reservoir nonlinear coupling model we present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Markovian Langevin description and an associated Fokker-Planck equation in position space in the overdamped limit. We examine the thermodynamic consistency and explore the possibility of observing a quantum current, a generic quantum effect, as a consequence of this state-dependent diffusion similar to one proposed by Büttiker [Z. Phys. B {\bf 68}, 161 (1987)] in a classical context several years ago.

cond-mat.stat-mech↗

arXiv2005

Noise-induced quantum transport

We analyze the problem of directed quantum transport induced by external exponentially correlated telegraphic noise. In addition to quantum nature of the heat bath, nonlinearity of the periodic system potential brings in quantum contribution. We observe that quantization, in general, enhances classical current at low temperature, while the differences become insignificant at higher temperature. Interplay of quantum diffusion and quantum correction to system potential is analyzed for various ranges of temperature, correlation time and strength of external noise and asymmetry parameters. A possible experimental realization of the observed quantum effects in a superionic conductor placed in a random asymmetric dichotomous electric field has been suggested.

cond-mat.stat-mech↗

arXiv2004

Quantum Kramers turnover: a phase space function approach

The problem of Kramers' turnover is a central issue of dynamical theory of reaction rate. Since its classical solution in the Markovian limit in mid-eighties by Melnikov and Meshkov, the problem has been addressed by a number of groups in the last decade both in classical non-Markovian and quantum mechanical context. Based on a coherent state representation of noise operators and a positive definite Wigner canonical thermal distribution function we have recently developed a c-number quantum Langevin equation [Barik \textit{et al}, J. Chem. Phys. {\bf 119}, 680 (2003); Banerjee \textit{et al}, Phys. Rev. E {\bf 65}, 021109 (2002)]. We implement this scheme within Pollak's well known normal mode description to calculate the quantum transmission coefficient over an arbitrary range of friction, noise correlation and temperature. The theory generalizes the quantum correction to Grote-Hynes factor in the rate expression down to vacuum limit which reduces to well known high temperature quantum correction, \textit{i.e.}, the Wolynes term for quantum transmission and reflection for the barrier in the appropriate limit and also considers the quantum corrections due to nonlinearity of the system potential order by order which contributes to energy loss and dispersion due to coupling between unstable and stable normal modes near the barrier top and is valid for both above and below the activated tunneling regime. Our results have been compared with those obtained earlier for a model potential and found to be good agreement.

cond-mat.soft↗

arXiv2004

A generalization of Wolynes factor in activated processes

Kramers-Grote-Hynes factor is the key nonequilibrium contribution to rate constant of a reaction over and above the transition state theory rate in the spatial limited regime. Wolynes in eighties introduced a quantum correction to the overall rate coefficient. This is responsible for tunneling and quantum enhancement of rate at low temperature. However, its validity is restricted to activated tunneling region or above crossover temperature. Based on a quantum formulation of the normal mode analysis, we suggest a generalization of Wolynes factor and a consequent multidimensional transition state rate expression which are valid in the deep tunneling region down to zero degree Kelvin.

cond-mat.other↗

arXiv2004

Numerical simulation of transmission coefficient using c-number Langevin equation

We numerically implement the reactive flux formalism on the basis of a recently proposed c-number Langevin equation [Barik \textit{et al}, J. Chem. Phys. {\bf 119}, 680 (2003); Banerjee \textit{et al}, Phys. Rev. E {\bf 65}, 021109 (2002)] to calculate transmission coefficient. The Kramers' turnover, the $T^2$ enhancement of the rate at low temperatures and other related features of temporal behaviour of the transmission coefficient over a range of temperature down to absolute zero, noise correlation and friction are examined for a double well potential and compared with other known results. This simple method is based on canonical quantization and Wigner quasiclassical phase space function and takes care of quantum effects due to the system order by order.

physics.chem-ph↗

arXiv2004

Anharmonic quantum contribution to vibrational dephasing

Based on a quantum Langevin equation and its corresponding Hamiltonian within a c-number formalism we calculate the vibrational dephasing rate of a cubic oscillator. It is shown that leading order quantum correction due to anharmonicity of the potential makes a significant contribution to the rate and the frequency shift. We compare our theoretical estimates with those obtained from experiments for small diatomics $N_2$, $O_2$ and $CO$.

physics.chem-ph↗

arXiv2003

Quantum phase space function formulation of reactive flux theory

On the basis of a coherent state representation of quantum noise operator and an ensemble averaging procedure a scheme for quantum Brownian motion has been proposed recently [Banerjee {\it et al}, Phys. Rev. E {\bf65}, 021109 (2002); {\bf66}, 051105 (2002)]. We extend this approach to formulate reactive flux theory in terms of quantum phase space distribution functions and to derive a time dependent quantum transmission coefficient - a quantum analogue of classical Kramers'-Grote-Hynes coefficient in the spirit of Kohen and Tannor's classical formulation. The theory is valid for arbitrary noise correlation and temperature. The specific forms of this coefficient in the Markovian as well as in the non-Markovian limits have been worked out in detail for intermediate to strong damping regime with an analysis of quantum effects. While the classical transmission coefficient is independent of temperature, its quantum counterpart has significant temperature dependence particularly in the low temperature regime.

cond-mat.stat-mech↗

arXiv2003

A numerical method for generation of quantum noise and solution of generalized c-number quantum Langevin equation

Based on a coherent state representation of noise operator and an ensemble averaging procedure we have recently developed [Phys. Rev. E {\bf 65}, 021109 (2002); {\it ibid.} 051106 (2002)] a scheme for quantum Brownian motion to derive the equations for time evolution of {\it true} probability distribution functions in $c$-number phase space. We extend the treatment to develop a numerical method for generation of $c$-number noise with arbitrary correlation and strength at any temperature, along with the solution of the associated generalized quantum Langevin equation. The method is illustrated with the help of a calculation of quantum mean first passage time in a cubic potential to demonstrate quantum Kramers turnover and quantum Arrhenius plot.

cond-mat.stat-mech↗

arXiv2002

Solutions of Fisher and Burger's equations with finite transport memory

The Fisher and Burgers' equations with finite memory transport, describing reaction-diffusion and convection-diffusion processes, respectively have recently attracted a lot of attention in the context of chemical kinetics, mathematical biology and turbulence. We show here that they admit exact solutions. While the speed of the traveling wavefront is dependent on the relaxation time in Fisher equation, memory effects significantly smoothen out the shock wave nature of Burgers' solution, without making any influence on the corresponding wave speed. We numerically analyze the ansatz for the exact solution and show that for the reaction-diffusion system the strength of the reaction term must be moderate enough not to exceed a critical limit to allow travelling wave solution to exist for appreciable finite memory effect.

nlin.PS↗

arXiv2002

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.

cond-mat.stat-mech↗

arXiv2002

Quantum Smoluchowski equation: Escape from a metastable state

We develop a quantum Smoluchowski equation in terms of a true probability distribution function to describe quantum Brownian motion in configuration space in large friction limit at arbitrary temperature and derive the rate of barrier crossing and tunneling within an unified scheme. The present treatment is independent of path integral formalism and is based on canonical quantization procedure.

cond-mat↗

arXiv2002

Class of self-limiting growth models in the presence of nonlinear diffusion

The source term in a reaction-diffusion system, in general, does not involve explicit time dependence. A class of self-limiting growth models dealing with animal and tumor growth and bacterial population in a culture, on the other hand are described by kinetics with explicit functions of time. We analyze a reaction-diffusion system to study the propagation of spatial front for these models.

physics.bio-ph↗

arXiv2002

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

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability 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 {\it 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 co-ordinates 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 the Smoluchowski equations are the {\it exact} quantum analogues of their classical counterparts. The present work is {\it 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 (Smoluchowski equation being considered in the overdamped limit).

quant-ph↗

arXiv2001

Approach to Quantum Kramers' Equation and Barrier Crossing Dynamics

We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum mechanical mean values of their co-ordinates and momenta we have derived a $c$-number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers' equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers' rate of barrier crossing and analyze its variation as a function of temperature and friction. While almost all the earlier theories rest on quasi-probability distribution functions (like Wigner function) and path integral methods, the present work is based on {\it true probability distribution functions} and is independent of path integral techniques. The theory is a natural extension of the classical theory to quantum domain and provides a unified description of thermal activated processes and tunneling.

quant-ph↗

arXiv2001

The 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.

cond-mat.stat-mech↗

arXiv2001

Analytical and numerical investigation of escape rate for a 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 numerically examine the model using a full bistable potential to show that one can recover the turn-over features of the usual Kramers' dynamics when the external noise modulates the reservoir rather than the system directly. We derive the generalized Kramers' rate for this nonequilibrium open system. The theoretical results are verified by numerical simulation.

cond-mat.stat-mech↗