Fluctuating magnetic field induced resonant activation.

In this paper, we have studied the properties of a Brownian particle at stationary state in the presence of a fluctuating magnetic field. Time dependence of the field makes the system thermodynamically open. As a signature of that the steady state distribution function becomes function of damping strength, intensity of fluctuations and constant parts of the applied magnetic field. It also depends on the correlation time of the fluctuating magnetic field. Our another observation is that the random magnetic field can induce the resonant activation phenomenon. Here correlation time is increased under the fixed variance of the fluctuating field. But if the correlation time (τ) increases under the fixed field strength then the mean first passage time rapidly grows at low τ and it almost converges at other limit. This is sharp contrast to the usual colored noise driven open system case where the mean first passage time diverges exponentially. We have also observed that a giant enhancement of barrier crossing rate occurs particularly at large strength of constant parts of the applied magnetic field even for very weak fluctuating magnetic field. Finally, break down of the Arrhenius result and disappearance of the Kramers' turn over phenomenon may occur in the presence of a fluctuating magnetic field.

Nonequilibrium entropic temperature and its lower bound for quantum stochastic processes.

In this paper, we have studied the Shannon "entropic" nonequilibrium temperature (NET) of quantum Brownian systems. The Brownian particle is attached to either a bosonic or fermionic bath. Based on the Fokker-Planck description of the c-number quantum Langevin equation, we have calculated entropy production, NET, and their bounds. Entropy production (EP), the upper bound of entropy production (UBEP), and the deviation of the UBEP from EP monotonically decrease as functions of time to equilibrium value for both of the thermal baths. The deviation decreases with increase of temperature of the bosonic thermal bath, but it becomes larger as the temperature of the fermionic bath grows. We also observe that nonequilibrium temperature and its lower bound monotonically increase to equilibrium value with the progression of time. But their difference as a function of time shows an optimum behavior in most cases. Finally, we have observed that at long time, the entropic temperature (for a bosonic thermal bath) first increases nonlinearly as a function of thermodynamic temperature (TT) and, if the TT is appreciably large, then it grows linearly. But for the fermionic thermal bath, the entropic temperature decreases monotonically as a nonlinear function of thermodynamic temperature to zero value.

Tuning of barrier crossing time of a particle by time dependent magnetic field.

We have studied the effect of time dependent magnetic field on the barrier crossing dynamics of a charged particle. An interplay of the magnetic field induced electric field and the applied field reveals several interesting features. For slowly oscillating field the barrier crossing rate increases remarkably particularly at large amplitude of the field. For appreciably large frequency a generically distinct phenomenon appears by virtue of parametric resonance manifested in multiple peaks appearing in the variation of the mean first passage time as a function of the amplitude. The parametric resonance is more robust against the variation of amplitude of the oscillating field compared to the case of variation of frequency. The barrier crossing time of a particle can be tuned para-metrically by appropriate choice of amplitude and frequency of the oscillating magnetic field.

Magnetic field induced dynamical chaos.

In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x-y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples.

Barrier crossing dynamics of a charged particle in the presence of a magnetic field: a new turnover phenomenon.

In this paper we have investigated the effect of a magnetic field on the barrier crossing rate of a charged particle. At the low friction regime we have observed a new turnover phenomenon for the variation of rate as a function of field strength. Thus although the force due to the magnetic field is not dissipative in nature, it plays a role in the steady state barrier crossing rate similar to that of a dissipative force in the weak damping regime. For appreciable damping strength, the rate monotonically decreases with the increase of field strength. We have demonstrated an interesting resonance effect due to the variation of frequency of the harmonic oscillator associated with the y-component motion at low damping and magnetic field strength.

Colored non-gaussian noise driven open systems: generalization of Kramers' theory with a unified approach.

In this paper we have calculated escape rate from a meta stable state in the presence of both colored internal thermal and external nonthermal noises. For the internal noise we have considered usual gaussian distribution but the external noise may be gaussian or non-gaussian in characteristic. The calculated rate is valid for low noise strength of non-gaussian noise such that an effective gaussian approximation of non-gaussian noise wherein the higher order even cumulants of order "4" and higher are neglected. The rate expression we derived here reduces to the known results of the literature, as well as for purely external noise driven activated rate process. The latter exhibits how the rate changes if one switches from non-gaussian to gaussian character of the external noise.

Magnetic-field-induced breakdown of equivalence of multidimensional motion.

In this paper, we have studied Brownian motion in multidimension phase space in presence of a magnetic field. The nonequilibrium behavior of thermodynamically inspired quantities along the individual component of motion has been studied in detail. Based on the Fokker-Planck description of the stochastic process and entropy balance equation, we have calculated information entropy production and entropy flux at nonequilibrium state. The dependence of these quantities on time, magnetic field, and thermal bath is studied. In this context, we have observed that there exists extremum behavior in the dynamics and the applied magnetic field breaks the equivalence in motion of the components in the nonequilibrium state.