Escape from a metastable state

Abstract

Many important processes in science involve the escape of a particle over a barrier. In this review, we report, extend, and interpret various theories of noiseactivated escape. We discuss the connection between many-body transition state theory and Kramers' original diffusive Brownian motion approach (both in oneand multidimensional potential fields) and emphasize the physical situation inherent in Kramers' rate for weak friction. A rate theory accounting for memory friction is presented together with a set of criteria which test its validity. The complications and peculiarities of noise-activated escape in driven systems exhibiting multiple, locally stable stationary nonequilibrium states are identified and illustrated. At lower temperatures, quantum tunneling effects begin to play an increasingly important role. Early approaches and more recent developments of the quantum version of Kramers approach are discussed, thereby providing a description for dissipative escape at all temperatures.

Nanoparticles at liquid interfaces: Rotational dynamics and angular locking

“…MD simulations show the presence of long-lived metastable states where the particle remains "locked" at angular orientations where certain localized features lie at the interface. The observed lifetime of these metastable states compares well with predictions from Kramers' escape theory 12,13 . In Sec.…”

“…The prefactor C k = 2πξ/ F min |F max | in Eq. 8 is determined by the rotational viscous damping ξ of the particle and the local curvature of the free energyF ≡ ∂ 2 F/∂θ 2 at the minima and neighboring maxima for each metastable state 11,13 . Hence, one can obtain the ratio of the expected lifetimes as…”

Kramers problem for a dimer: Effect of noise correlations

“…The theory of Brownian motion provides one of the most elegant approaches to study the problem by identifying the additional degrees of freedom as noise and friction [1]. This approach towards the escape problem was grounded in the seminal work of Kramers [2,3], who provided theoretical estimates for the rate of escape for a particle trapped in a metastable state in the limits of low and high friction.…”

The diffusion in the quantum Smoluchowski equation

“…This scheme models the phenomenon of Brownian motion, a phenomenon that has been described theoretically by the two ''grandfathers'' of Brownian motion: Albert Einstein and Marian von Smoluchowski [3,4]. For a classical Brownian particle moving in an external field, the statistical properties are described by the Klein-Kramers equation in the phase space of position and momentum degree of freedom [1,2,5]. In the strong friction limit it reduces to the so-called Smoluchowski equation in position space alone [6].…”

“…Different approaches have been proposed in the recent years that are seemingly not wholly consistent with each other [10]. Here, we follow the scheme that is rigorously based on a path integral formulation of the (reduced) quantum Brownian motion [5,7].…”