Related papers: Kramers's escape rate problem within a non-Markovi…
We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation $\partial_t \rho = \partial_x[\partial_x U\rho] + D\partial^2_x \rho^\nu$, where the potential of the drift, $U(x)$, presents a…
Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape…
We present an approximate analytical expression for the escape rate of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is…
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…
We consider the motion of a particle in a force field subjected to adiabatic, fluctuations of external origin. We do not put the restriction on the type of stochastic process that the noise is Gaussian. Based on a method developed earlier…
Kramers' rate theory forms a cornerstone for thermally activated barrier crossing. However, its reliance on equilibrium quantities excludes analysis of nonequilibrium dynamics at early times. Most works have thus focused on obtaining rates…
The properties of the thermal force driving micron particles in incompressible fluids are studied within the hydrodynamic theory of the Brownian motion. It is shown that the assumption used for the hydrodynamic Langevin equation in its…
A dynamics between Newton and Langevin formalisms is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding a vanishing zero-frequency friction the corresponding non-Markovian Brownian dynamics…
This paper considers the two-dimensional narrow escape problem in a domain which is composed of a relatively big head and several thin necks. The narrow escape problem is to compute the mean first passage time(MFPT) of a Brownian particle…
We introduce a generalized Langevin model system for different non-Markovian effects in the well and barrier regions of a potential, and use it to numerically study the dependence of the barrier-crossing time. In the appropriate limits, our…
We study the dynamics of an active Brownian particle with a nonlinear friction function located in a spatial cubic potential. For strong but finite damping, the escape rate of the particle over the spatial potential barrier shows a…
Using a time-averaging technique we obtain exactly the probability distribution for position and velocity of a Brownian particle under the influence of two heat baths at different temperatures. These baths are expressed by a white noise…
Kramers' theory frames chemical reaction rates in solution as reactants overcoming a barrier in the presence of friction and noise. For weak coupling to the solution, the reaction rate is limited by the rate at which the solution can…
The original perturbative Kramers' method (starting from the phase space coordinates) (Kramers, 1940) of determining the energy-controlled-diffusion equation for Newtonian particles with separable and additive Hamiltonians is generalized to…
The influence of the environment in the thermal equilibrium properties of a bipartite continuous variable quantum system is studied. The problem is treated within a system-plus-reservoir approach. The considered model reproduces the…
The expanding application of classical thermodynamic methods to black hole physics has yielded significant advances in characterizing phase transition behavior. Among these approaches, thermodynamic analysis -- particularly kinetic…
The reactive process of barrier escaping from the metastable potential well is studied together with the extension of Kramers' rate formula to the fractional case. Characteristic quantities are computed for an thimbleful of insight into the…
The time-dependent barrier passage of an anomalous system-reservoir coupling non-equilibrium open environment is studied where the heat bath is modulated by an external noise. The time-dependent barrier passing probability is obtained…
We consider a charged Brownian gas under the influence of external and non uniform electric, magnetic and mechanical fields, immersed in a non uniform bath temperature. With the collision time as an expansion parameter, we study the…
Owing to the Chapman-Kolmogorov equation for Markovian dynamics,any equilibrium trajectory of a Brownian particle in a solvent fluid can be viewed as the superposition of an uncountable number of non-equilibrium states. This property…