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Papers by Bidhan Chandra Bag

It seems that a stochastic system must be a nonlinear one to observe the phenomenon, noise induce... more 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 f...

The Journal of Chemical Physics, 2011

The Journal of Chemical Physics, 2007

Czechoslovak Journal of Physics, 2004

Journal of Statistical Mechanics: Theory and Experiment, 2016

In this paper we have presented the dynamics of a Brownian particle with time-delayed feedback. I... more In this paper we have presented the dynamics of a Brownian particle with time-delayed feedback. It clearly suggests that the delayed feedback may introduce a dissipation-like effect. As a result of this a breakdown of the fluctuation–dissipation relation occurs and the system behaves like an open one. Therefore, the stationary distribution deviates from the Boltzmann type. It depends on the damping strength. The probability at the barrier top increases with the enhancement of the damping strength. This is a sharp contrast to closed systems (which obey the fluctuation–dissipation relation) and the usual open systems, where the noise strength does not depend on the damping strength. This special feature motivated us to calculate Kramers' rate in the presence of the delayed feedback. Our calculation shows that the activation energy decreases with an increase in the damping strength. This peculiarity introduces a noticeable observation. Kramers' turnover behaviour appears even in the spatial diffusive regime. Thus its origin is quite different from the known Kramers' turnover, which is a result of an interplay of energy and spatial diffusive regimes. It should be mentioned here that all our theoretical results are well justified by the numerical experiments.

In this paper we have investigated the dynamics of a damped harmonic oscillator in the presence o... more 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 fi...

Physical review. E, 2020

In the present study we have developed an alternative formulation for the quantum stochastic ther... more In the present study we have developed an alternative formulation for the quantum stochastic thermodynamics based on the c-number Langevin equation for the system-reservoir model. This is analogous to the classical one. Here we have considered both Markovian and non-Markovian dynamics (NMD). Consideration of the NMD is an important issue at the current state of the stochastic thermodynamics. Applying the present formalism, we have carried out a comparative study on the heat absorbed and the change of entropy with time for a linear quantum system and its classical analog for both Markovian and NMD. Here the strength of the thermal noise and its correlation time for the respective cases are the leading quantities to explain any distinguishable feature which may appear with the equilibration kinetics. For another application, we have proposed a formulation with classical look for a quantum stochastic heat engine. Using it we have presented a comparative study on the efficiency and its ...

fluctuating magnetic field Shrabani Mondal, L. R. Rahul Biswas, and Bidhan Chandra Bag ∗ Departme... more fluctuating magnetic field Shrabani Mondal, L. R. Rahul Biswas, and Bidhan Chandra Bag ∗ Department of Chemistry, University of Massachusetts Boston, Boston, MA 02125 Department of Chemistry, Visva-Bharati, Santiniketan, India, 731235 Abstract It seems to us 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 fluctu...

Physical review. E, 2021

In a recent paper Das et al. [J. Chem. Phys. 147, 164102 (2017)JCPSA60021-960610.1063/1.4999408] ... more In a recent paper Das et al. [J. Chem. Phys. 147, 164102 (2017)JCPSA60021-960610.1063/1.4999408] proposed the Fokker-Planck equation (FPE) for the Brownian harmonic oscillator in the presence of a magnetic field and the non-Markovian thermal bath, respectively. This system has been studied very recently by Hidalgo-Gonzalez and Jiménez-Aquino [Phys. Rev. E 100, 062102 (2019)PREHBM2470-004510.1103/PhysRevE.100.062102] 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 et al. Then we reexamine our calculation and which is present in this comment. The revised calculation shows that both methods give the same result.

Using a shortcut way we have derived the Fokker-Planck equation for the Langevin dynamics with a ... more 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.

In this paper we have presented the mechanism of the barrier crossing dynamics of a Brownian part... more 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. PACS numbers: 05.40.Jc,05.20.-y,89.70.Cf ∗ Author for correspondence, e-mail:bidhanchandra.bag@visva-bharati.ac.in

Physica A: Statistical Mechanics and its Applications

Abstract Based on the entropy balance equation for a multidimensional linear Fokker–Planck equati... more Abstract Based on the entropy balance equation for a multidimensional linear Fokker–Planck equation we have developed connections between the several thermodynamically inspired quantities such as the total entropy production, the entropy production of the irreversible thermodynamics and the non-equilibrium temperature. Then we have calculated both upper and lower bounds of these properties with the help of the entropy balance equation and the Schwartz inequality which has been applied to the differential equation for the time evolution of the entropy. With these we have shown that there is a lower bound of time derivative of the entropy in addition to its upper limit. The present formalism has been applied for the coupling of a Brownian particle with the Markovian and the non-Markovian thermal baths, respectively.

Physical review. E, 2018

A one-dimensional linear autonomous system coupled to a generic stationary nonequilibrium fluctua... more A one-dimensional linear autonomous system coupled to a generic stationary nonequilibrium fluctuating bath can exhibit resonant response when its damped oscillation period matches some characteristic bath's relaxation time. This condition justifies invoking the stochastic resonance paradigm, even if it can be achieved more easily by tuning the system to the bath and not vice versa, as is usually the case. The simple nature of the mechanism numerically investigated here suggests a number of interesting applications for instance in the context of (1) energy harvesting from random ambient vibrations, (2) activated barrier crossing through a saddle point, or (3) an unstable limit cycle.

Polymer Degradation and Stability

The European Physical Journal B, 2016

Abstract In this paper we have demonstrated how the conversion of the ambient energy into the ele... more Abstract In this paper we have demonstrated how the conversion of the ambient energy into the electrical energy depends on the properties of the ambient energy and the mechanical oscillator. We have observed that the conversion of the vibration energy into the electrical energy may be good if the voltage can follow closely the evolution of of the amplitude of the oscillator. Thus if the voltage and the position fluctuate in a correlated manner then the conversion of the ambient energy into the electrical energy is good. Our another observation is that for a given capacitance, the power transferred (PT) from the oscillator to the transducer may be maximum in the variation of PT with increase in resistance, R. In other words, the power transferred changes with a maximum as the capacitance, C grows for a fixed value of the resistance. Along with these we have investigated how the other relevant quantities such as the efficiency of the energy transferred process depends on the characteristics of the oscillating systems, the environment and the piezoelectric dynamics.

Physical Review E, 2015

In this paper we have presented the heat exchange between the two fermionic thermal reservoirs wh... more In this paper we have presented the heat exchange between the two fermionic thermal reservoirs which are connected by a fermionic system. We have calculated the heat flux using solution of the c-number Langevin equation for the system. Assuming small temperature difference between the baths we have defined the thermal conductivity for the process. It first increases as a nonlinear function of average temperature of the baths to a critical value then decreases to a very low value such that the heat flux almost becomes zero. There is a critical temperature for the fermionic case at which the thermal conductivity is maximum for the given coupling strength and the width of the frequency distribution of bath modes. The critical temperature grows if these quantities become larger. It is a sharp contrast to the Bosonic case where the thermal conductivity monotonically increases to the limiting value. The change of the conductivity with increase in width of the frequency distribution of the bath modes is significant at the low temperature regime for the fermionic case. It is highly contrasting to the Bosonic case where the signature of the enhancement is very prominent at high temperature limit. We have also observed that thermal conductivity monotonically increases as a function of damping strength to the limiting value at the asymptotic limit. There is a crossover between the high and the low temperature results in the variation of the thermal conductivity as a function of the damping strength for the fermionic case. Thus it is apparent here that even at relatively high temperature, the fermionic bath may be an effective one for the strong coupling between system and reservoir. Another interesting observation is that at the low temperature limit, the temperature dependence of the heat flux is the same as the Stefan-Boltzmann law. This is similar to the bosonic case.

The Journal of Chemical Physics, 2015

In this article, we have explored the resonance behavior of a particle in the presence of a time ... more In this article, we have explored the resonance behavior of a particle in the presence of a time dependent magnetic field (TDMF). The particle is bound in a harmonic potential well. Based on the Hamiltonian description of the system in terms of action and angle variables, we have derived the resonance condition for the applied TDMF along z-direction which is valid for arbitrary frequencies along x and y directions of the two dimensional harmonic oscillator. We have also derived resonance condition for the applied magnetic field which is lying in a plane. Finally, we have explored resonance condition for the isotropic magnetic field. To check the validity of the theoretical calculation, we have solved equations of motion numerically for the parameter sets which satisfy the derived resonance condition. The numerical experiment fully agrees with the theoretically derived resonance conditions.