Multiplicative cross-correlated noise induced escape rate from a metastable state

Abstract

We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. By starting from a phenomenological stationary Langevin description with multiplicative noise processes, we have investigated the Kramers theory for activated rate processes in a nonequilibrium open system (one dimensional in nature) driven by two external cross-correlated noise processes which are Gaussian, stationary, and delta correlated. Based on the Fokker-Planck description in phase space, we then derive the escape rate from a metastable state in the moderate to large friction limit to study the effect of degree of correlation on the same. By employing numerical simulation in the presence of external cross-correlated additive and multiplicative noises, we check the validity of our analytical formalism for constant dissipation, which shows a satisfactory agreement between both the approaches for the specific choice of noise processes. It is evident both from analytical development and the corresponding numerical simulation that the enhancement of rate is possible by increasing the degree of correlation of the external fluctuations.

Memory effects in nanoparticle dynamics and transport

“…34 Alternative approaches to decrease the barrier crossing time have also been discussed in the context of modulating the host fluid to a non-equilibrium state, 42 or subjecting the nanoparticle to an external noise source of additive or multiplicative nature. 43,44 Thus, memory effects are important and should be included in the stochastic-simulation based multi-scale approaches used to study the dynamics and transport of fullerene-like nanoparticles in aqueous solution/biological environment.…”

Role of the interpretation of stochastic calculus in systems with cross-correlated Gaussian white noises

“…Cross-correlated noises can also arise if the action of the random environment affects the internal fluctuations of the system. The effect of cross correlations between noises has been studied in a variety of applications, e.g., in single-mode lasers [24][25][26], in bistable systems [27][28][29][30][31][32], in stochastic resonance [33][34][35][36][37][38][39], in anomalous diffusion [40], in noiseinduced transport [41,42], in tumor growth [9,[43][44][45][46][47][48], in vegetation models [49], in metapopulation models [50], in barrier crossing and transitions from metastable states [51][52][53][54][55][56][57][58][59], and in nonequilibrium phase transitions in spatially extended systems [60].…”

The mean first passage time of a three-level atomic optical bistable system subjected to noise

“…[31][32][33][34] On the level of a Langevin-or Fokker-Planck-type description of a dynamical system, the presence of correlations between two noises can change the dynamics of the system. [35,36] Correlated noise processes have made their presence felt in a wide range of applications, such as the statistical properties of a single mode laser, [37][38][39] bistable kinetics, [40,41] tumor cell growth, [42,43] barrier crossing dynamics, [44,45] stochastic resonance in linear systems, [46] and steady state entropy production. [47] In the present work, we study the transient properties of the transition between the different stable states in a three-level atomic optical bistable system in the presence of multiplicative and additive noises.…”