arXiv subjects

Debashis Barik

Publications and source records attributed to Debashis Barik.

15 recordsLinked to original sources

arXiv2018

Temperature dependent divergence of thermal conductivity in momentum conserving 1D lattice with asymmetric potential

In this study we used nonequilibrium simulation method to investigate the temperature dependent divergence of thermal conductivity in one dimensional momentum conserving system with asymmetric double well nearest-neighbor interaction potential. We show that the value of divergence exponent ($\alpha$) in the power law divergence of thermal conductivity depends on the temperature of the system. At low and high temperatures $\alpha$ reaches close to $\sim0.5$ and $\sim0.33$ respectively. Whereas in the intermediate temperature the divergence of thermal conductivity with the chain length saturates with $\alpha\sim0.07$. Subsequent analysis showed that the predicted value of $\alpha$ in the intermediate temperature may not have reached its thermodynamic limit. Further calculations of local $\alpha$ revealed that its approach towards the thermodynamic limit crucially dependent on the temperature of the system. At low and high temperatures local $\alpha$ reaches its thermodynamic limits in shorter chain lengths. On the contrary in case of intermediate temperature it's progress towards the asymptotic limit is nonmonotonous.

cond-mat.stat-mech↗

arXiv2007

Directed motion generated by heat bath nonlinearly driven by external noise

Based on the system heat bath approach where the bath is nonlinearly modulated by an external Gaussian random force, we propose a new microscopic model to study directed motion in the overdamped limit for a nonequilibrium open system. Making use of the coupling between the heat bath and the external modulation as a small perturbation we construct a Langevin equation with multiplicative noise and space dependent dissipation and the corresponding Fokker-Planck-Smoluchowski equation in the overdamped limit. We examine the thermodynamic consistency condition and explore the possibility of observing a phase induced current as a consequence of state dependent diffusion and, necessarily, nonlinear driving of the heat bath by the external noise.

cond-mat.stat-mech↗

arXiv2006

Dynamics of a metastable state nonlinearly coupled to a heat bath driven by an 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 result numerically which are in good agreement with the theoretical prediction. It has been shown numerically that the enhancement of rate is possible by properly tuning the correlation time of the external noise.

cond-mat.stat-mech↗

arXiv2006

Inhomogeneous quantum diffusion and decay of a meta-stable state

We consider the quantum stochastic dynamics of a system whose interaction with the reservoir is considered to be linear in bath co-ordinates but nonlinear in system co-ordinates. The role of the space-dependent friction and diffusion has been examined in the decay rate of a particle from a meta-stable well. We show how the decay rate can be hindered by inhomogeneous dissipation due nonlinear system-bath coupling strength.

cond-mat.stat-mech↗

arXiv2006

Escape rate from a metastable state weakly interacting with a heat bath driven by an 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. It has been also shown numerically that the well known turnover feature can be restored from our model.

physics.chem-ph↗

arXiv2006

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.

cond-mat.stat-mech↗

arXiv2006

Langevin dynamics with dichotomous noise; direct simulation and applications

We consider the motion of a Brownian particle moving in a potential field and driven by dichotomous noise with exponential correlation. Traditionally, the analytic as well as the numerical treatments of the problem, in general, rely on Fokker-Planck description. We present a method for direct numerical simulation of dichotomous noise to solve the Langevin equation. The method is applied to calculate nonequilibrium fluctuation induced current in a symmetric periodic potential using asymmetric dichotomous noise and compared to Fokker-Planck-Master equation based algorithm for a range of parameter values. Our second application concerns the study of resonant activation over a fluctuating barrier.

cond-mat.stat-mech↗

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↗