Analytical and numerical investigation of escape rate for a noise driven bath

Abstract

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.

Generalization of the escape rate from a metastable state driven by external cross-correlated noise processes

“…In the expression (48) in addition to T , D R /(γk B ) defines a new effective temperature due to external driving. In a different context where the heat bath is modulated by an external fluctuating field we have also encountered the appearance of the effective temperature [14,16].…”

“…We then numerically solve the Langevin equation (1) by employing stochastic Heun's algorithm [29,30]. The numerical rate has been defined as the inverse of mean first passage time [14,16,31] and has been calculated by averaging over 10,000 trajectories. In our simulation we have always used τ ǫ = τ π = τ = 1 such that the effective correlation time τ R is always equals to 1, independent of values of the other parameters.…”

“…In absence of FDR, such external input of energy makes the system open and in contrast to the closed system the equilibrium Boltzmann distribution gets replaced by a steady state distribution (SSD) in the long time limit. It may therefore be anticipated that the absence of FDR tends to make the SSD function dependent on the strength and correlation time of external noise as well as on the dissipation of the system [14,15,16]. It is pertinent to point out that though thermodynamically closed systems with homogeneous boundary conditions possess, in general, time-dependent solution, the driven open systems may settle down to complicated multiple steady states when one takes into account nonlinearity of the systems.…”

“…In nonequilibrium statistical mechanical terminology, such systems are referred to as closed system [12]. It may happen sometime that an additional source of energy in the form of fluctuations can be pumped from outside for * Electronic address: jprc˙8@yahoo.com † Electronic address: sudip˙chattopadhyay@rediffmail.com ‡ Electronic address: skbanik@phys.vt.edu which there is no counter balancing force like dissipation [13,14,15,16]. In absence of FDR, such external input of energy makes the system open and in contrast to the closed system the equilibrium Boltzmann distribution gets replaced by a steady state distribution (SSD) in the long time limit.…”

Quantum phase-space function formulation of reactive flux theory

“…Over the decades the field has grown in various new directions, e.g. , extension of Kramers results to non-Markovian regime 4,5,6 , generalizations to higher dimensions 7,8 , inclusion of complex potentials 9,10 , generalization to open systems 11,12,13 , analysis of semiclassical and quantum effects 14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29 , thermal ratchet 30 and molecular motors 31 etc. These developments have been the subject of several reviews and monographs.We refer to 15,16,17,22 .…”