arXiv subjects

Bidhan Chandra Bag

Publications and source records attributed to Bidhan Chandra Bag.

At least 19 recordsLinked to original sources

arXiv2025

Effect of an electromagnetic field on the barrier crossing rate

We investigate the spectrum for the rate constant of an electric field-driven charged Brownian particle in the presence of a magnetic field (MF). For the cross fields with low or high values of the cyclotron frequency, an asymmetric splitting of the spectrum occurs with two peaks. Anharmonicity-induced additional splitting may appear around the lower resonating frequency at the intermediate strength of the applied MF. Another observation is that if the magnetic field is tilted from the z-direction, an additional peak appears between the two peaks. The position of the middle peak may be independent of the strength of the applied MF. In some cases, only one peak appears even in the presence of a magnetic field. We explain these observations considering the dynamics around the stable fixed point and determine the position of the peak in the spectrum for the rate constant as a function of the strength of the applied magnetic field. Thus the present study may find applications for tuning the conductivity of a solid electrolyte, which is very important in recent technology. Other applications may be in areas such as electromagnetic field-induced modulation of (a) thermally activated tunneling ionization, (b) thermally stimulated ionization, etc.

cond-mat.stat-mech↗

arXiv2025

The correspondence between the Adam-Gibbs and the Rosenfield relations

In this paper, we derive both the Adam-Gibbs and the Rosenfield relations from the microscopic point of view and compare them with the numerical calculation for one and two dimensional systems. The comparison shows there is an excellent agreement between theoretical and numerical calculations for their valid zones (in terms of the thermodynamic temperature) as suggested by experiments. It implies that there may be a transition temperature at which the two relations correspond to each other. We derive a relation to calculate it. Then, we generalize the Rosenfield relation for configurational thermodynamic entropy like quantity(TELQ) and time-dependent Shanon information entropy. At the same time, using a description with a fictitious Hamiltonian, we show that time-dependent configurational Shanon information entropy for a thermodynamic system (of Brownian particles) which is characterized by the absolute temperature, can not be recognized as thermodynamic entropy. At best, it can be identified as a thermodynamic entropy-like quantity. Furthermore, the description based on the fictitious Hamiltonian may lead to the conclusion that the correspondence between the Shanon information entropy and thermodynamic entropy is not a singular feature at equilibrium. It may be a continuation of the correspondence between the information entropy and the thermodynamic entropy-like quantity. Thus, the present study appears to offer important justification for the postulate that the Shannon entropy at steady state may be regarded as a thermodynamic entropy. This postulate holds significant importance in the framework of stochastic thermodynamics.

cond-mat.stat-mech↗

arXiv2022

A shortcut way to the Fokker-Planck equation for the non-Markovian dynamics

Using a shortcut way we have derived the Fokker-Planck equation for the Langevin dynamics with a generalized frictional memory kernel and time-dependent force field. Then we have shown that this method is applicable for the non-Markovian dynamics with additional force from harmonic potential or magnetic field or both of them. The simplicity of the method in these complex cases is highly noticeable and it is applicable to derive the Fokker-Planck equation for any kind of linear Langevin equation of motion which describes additive colored noise driven non Markovian dynamics with or without frictional memory kernel. For example, one may apply the method even for the linear system with an additional colored Gaussian noise which is not related to the damping strength. With these the present study may get strong attention in the field of stochastic thermodynamics which is now at early stage to consider the non-Markovian dynamics.

cond-mat.stat-mech↗

arXiv2022

Magnetic field induced anomalous distribution of particles

It seems that a stochastic system must be a nonlinear one to observe the phenomenon, noise induced transition. But in the present paper, we have demonstrated that the phenomenon may be observed even in a linear stochastic process where both deterministic and stochastic parts are linear functions of the relevant phase space variables. The shape of the stationary distribution of particles (which are confined in a harmonic potential) may change on increasing the strength of the applied fluctuating magnetic field. The probability density may vary non monotonically with an increase in the coordinate of a Brownian particle. Thus the distribution of particles may deviate strongly from the Boltzmann one and it is a unique signature of the fluctuating magnetic field. Then we are motivated strongly to study the distribution of particles in a nonlinear stochastic system where the Brownian particles are confined in a bi-stable potential energy field in the presence of the fluctuating magnetic field. With a relatively large strength of the fluctuating field, the distribution of particles may be a strange one where many islands may appear which are not expected from the given potential energy field. It may offer an explanation to describe the phenomenon, the reduction of the current in a semiconductor in the presence of a time dependent magnetic field.

cond-mat.stat-mech↗

arXiv2021

Magnetic field induced asymmetric splitting of the output signal

In this paper we have investigated the dynamics of a damped harmonic oscillator in the presence of an electromagnetic field. The transients for the two dimensional harmonic oscillator imply about the modulation of the frequency of the oscillator by the velocity dependent non conservative force from an applied magnetic field. Except a special condition, the motion is in general quasi periodic nature even in the absence of damping. Another interesting finding is that the magnetic field may induce an asymmetric splitting of the spectrum of the output signal with two peaks in the case of a driven damped two dimensional harmonic oscillator. One more additional peak may appear for the three dimensional case. In some cases the spectrum may have similarity with the Normal Zeeman Effect. At the same time one may observe to appear the anti resonance phenomenon even for the driven damped cyclotron motion where the system with the purely non conservative force fields is driven by an electric field. Finally, our calculation exhibits how the magnetic field can modulate the phase difference (between input and output signals) and the efficiency like quantity of the energy storing process. Thus the present study might be applicable in the areas related to the refractive index, the barrier crossing dynamics and autonomous stochastic resonance, respectively.

physics.class-ph↗

arXiv2021

Comment on "Non-Markovian harmonic oscillator across a magnetic field and time dependent force fields"

In a recent paper Das {\it et al.} [J. Chem. Phys. {\bf 147}, 164102 (2017)] proposed the Fokker-Planck equation (FPE) for the Brownian harmonic oscillator in the presence of magnetic field and the non-Markovian thermal bath, respectively. This system has been studied very recently by J. C. Hidalgo-Gonzalez and J. I. Jiménez-Aquino [Phys. Rev. E {\bf{100}}, 062102 (2019)] and the Fokker-Planck equation was derived using the characteristic function. It includes a few extra terms in the FPE and the authors conclude that their method is accurate compared to the calculation by Das {\it et al.}. Then we reexamine our calculation and which is present in this comment. The revised calculation shows that both the methods give the same result.

cond-mat.stat-mech↗

arXiv2021

Mechanism of barrier crossing dynamics in the presence of both time dependent and independent magnetic fields

In this paper we have presented the mechanism of the barrier crossing dynamics of a Brownian particle which is coupled to a thermal bath in the presence of both time independent and fluctuating magnetic fields. Here the following three aspects are important in addition to the role of the thermal bath on the barrier crossing dynamics. Magnetic field induced coupling may introduce a resonance like effect. Another role of the field is that enhancement of its strength reduces the frequency factor of the barrier crossing rate constant. Finally, the fluctuating magnetic field introduces an induced electric field which activates the Brownian particle to cross the energy barrier. As a result of interplay among these aspects versatile non-monotonic behavior may appear in the variation of the rate constant as a function of the strength of the time independent magnetic field.

cond-mat.stat-mech↗

arXiv2012

Noise correlation-induced splitting of Kramers' escape rate from a metastable state

A correlation between two noise processes driving the thermally activated particles in a symmetric triple well potential, may cause a symmetry breaking and a difference in relative stability of the two side wells with respect to the middle one. This leads to an asymmetric localization of population and splitting of Kramers' rate of escape from the middle well, ensuring a preferential distribution of the products in the course of a parallel reaction.

physics.chem-ph↗

arXiv2012

Interference of stochastic resonances: Splitting of Kramers' rate

We consider the escape of particles located in the middle well of a symmetric triple well potential driven sinusoidally by two forces such that the potential wells roll as in stochastic resonance and the height of the potential barrier oscillates symmetrically about a mean as in resonant activation. It has been shown that depending on their phase difference the application of these two synchronized signals may lead to a splitting of time averaged Kramers' escape rate and a preferential product distribution in a parallel chemical reaction in the steady state.

physics.chem-ph↗

arXiv2012

Kinetics of self-induced aggregation of Brownian particles: non-Markovian and non-Gaussian features

In this paper we have studied a model for self-induced aggregation in Brownian particle incorporating the non-Markovian and non-Gaussian character of the associated random noise process. In this model the time evolution of each individual is guided by an over-damped Langevin equation of motion with a non-local drift resulting from the local unbalance distributions of the other individuals. Our simulation result shows that colored nose can induce the cluster formation even at large noise strength. Another observation is that critical noise strength grows very rapidly with increase of noise correlation time for Gaussian noise than non Gaussian one. However, at long time limit the cluster number in aggregation process decreases with time following a power law. The exponent in the power law increases remarkable for switching from Markovian to non Markovian noise process.

physics.chem-ph↗

arXiv2012

Periodic force induced stabilization or destabilization of the denatured state of a protein

We have studied the effects of an external sinusoidal force in protein folding kinetics. The externally applied force field acts on the each amino acid residues of polypeptide chains. Our simulation results show that mean protein folding time first increases with driving frequency and then decreases passing through a maximum. With further increase of the driving frequency the mean folding time starts increasing as the noise-induced hoping event (from the denatured state to the native state) begins to experience many oscillations over the mean barrier crossing time period. Thus unlike one-dimensional barrier crossing problems, the external oscillating force field induces both \emph{stabilization or destabilization of the denatured state} of a protein. We have also studied the parametric dependence of the folding dynamics on temperature, viscosity, non-Markovian character of bath in presence of the external field.

physics.chem-ph↗

arXiv2010

Effect of time delay on the onset of synchronization of the stochastic Kuramoto model

We consider the Kuramoto model of globally coupled phase oscillators with time-delayed interactions, that is subject to the Ornstein-Uhlenbeck (Gaussian) colored or the non-Gaussian colored noise. We investigate numerically the interplay between the influences of the finite correlation time of noise $τ$ and the time delay $τ_{d}$ on the onset of the synchronization process. Both cases for identical and nonidentical oscillators had been considered. Among the obtained results for identical oscillators is a large increase of the synchronization threshold as a function of time delay for the colored non-Gaussian noise compared to the case of the colored Gaussian noise at low noise correlation time $τ$. However, the difference reduces remarkably for large noise correlation times. For the case of nonidentical oscillators, the incoherent state may become unstable around the maximum value of the threshold (as a function of time delay) even at lower coupling strength values in the presence of colored noise as compared to the noiseless case. We had studied the dependence of the critical value of the coupling strength (the threshold of synchronization) on given parameters of the stochastic Kuramoto model in great details and presented results for possible cases of colored Gaussian and non-Gaussian noises.

cond-mat.stat-mech↗

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↗

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↗

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

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

Nonequilibrium stochastic processes: Time dependence of entropy flux and entropy production

Based on the Fokker-Planck and the entropy balance equations we have studied the relaxation of a dissipative dynamical system driven by external Ornstein-Uhlenbeck noise processes in absence and presence of nonequilibrium constraint in terms of the thermodynamically inspired quantities like entropy flux and entropy production. The interplay of nonequilibrium constraint, dissipation and noise reveals some interesting extremal nature in the time dependence of entropy flux and entropy production.

cond-mat.stat-mech↗