Kramers's escape rate problem within a non-Markovian description

Abstract

We compare the thermal escape rates of a Brownian particle, initially trapped into one of the two wells of an asymmetric double-well potential, for thermal Markovian and non-Markovian noise. The Markovian treatment of this problem goes originally back to the studies of Kramers in 1940 and is therefore often referred to as "Kramers's escape rate problem". We solve the generalized Langevin equation for the trajectories of the particles numerically and analytically for both limiting cases, Markovian and non-Markovian thermal noise. We compute the escape rate and work out the fundamental differences arising from finite correlation times of the thermal noise.

arXiv comment42 pages, 18 figures

References in corpus (16)

• Heavy-flavour and quarkonium production in the LHC era: from proton-proton to heavy-ion collisions
• Relativistic Brownian Motion
• Microphysical Approach to Nonequilibrium Dynamics of Quantum Fields
• Classical Fields Near Thermal Equilibrium
• Nonequilibrium chiral fluid dynamics including dissipation and noise
• Stochastic interpretation of Kadanoff-Baym equations and their relation to Langevin processes
• Chiral fluid dynamics with explicit propagation of the Polyakov loop
• Classical and quantum many-body description of bremsstrahlung in dense matter (Landau - Pomeranchuk - Migdal effect)
• Forming Disoriented Chiral Condensates through Fluctuations
• Stochastic dynamics of a Josephson junction threshold detector
• Stochastic Langevin equations: Markovian and non-Markovian dynamics
• Stochastic treatment of Disoriented Chiral Condensates within a Langevin description
• Causal Baryon Diffusion and Colored Noise
• Josephson junction detector of non-Gaussian noise
• Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect
• Thermal decay rate of a metastable state with two degrees of freedom: dynamical modeling versus approximate analytical formula

Cited by in corpus (6)

• Memory effects on energy loss and diffusion of heavy quarks in the quark-gluon plasma
• First-passage time theory of activated rate chemical processes in electronic molecular junctions
• Non-Markovian dynamics of black hole phase transition
• Persistent nonequilibrium effects in generalized Langevin dynamics of nonrelativistic and relativistic particles
• Experimental measurement of mean transition path velocities of colloidal particles surmounting energy barriers
• Quantifying Tipping Risks in Power Grids and beyond