Escape of a driven particle from a metastable state: A semiclassical approach

Abstract

In this article we explore the dynamics of escape of a particle in the semiclassical regime by driving the particle externally. We demonstrate that under suitable approximations the semiclassical escape rate essentially assumes the structure of classical Kramers rate. Both internal (due to thermal bath) as well as external noises (due to driving) are being considered. The noises are stationary, Gaussian, and are characterized by arbitrary decaying memory kernel. Finally, we subject our formulation to rigorous numerical test under variedly changing conditions of the parameters.

Effect of Self-Oscillation on Escape Dynamics of Classical and Quantum Open Systems

“…In the quantum regime, the total system-bath Hamiltonian can be written as [ 25 , 26 , 30 ] where and are the coordinate and momentum operators of the system, respectively, and are the set of coordinate and momentum operators of the bath oscillators. The coordinate and the momentum operators follow the commutation relation and .…”

“…Moreover, the time-dependent escape rate during the interval is given by [ 37 ] Initially, in the classical regime, the velocity and coordinate obey a Gaussian distribution with zero-mean and variance, and . In the quantum regime, the velocity and coordinate obey a Gaussian distribution with zero-mean and variance [ 25 ], and .…”

“…One systematic approach is based on the Zwanzig–Mori projection operator formalism, which leads to a generalized Langevin equation (GLE) for classical open systems. Based on an initial coherent state representations of bath oscillators and an equilibrium canonical distribution of quantum mechanical mean values of their coordinates and momenta, a quantum generalized Langevin equation (QGLE) in c numbers can also be derived for quantum open systems [ 14 , 25 , 26 ]. We employ the memory kernel expressed by Zwanzig [ 27 ], i.e., , where is a cut-off frequency and constant, which is originated from the Debye cut-off for the frequency of oscillators in a heat bath.…”

Sequential nonideal measurements of quantum oscillators: Statistical characterization with and without environmental coupling

“…As discussed in the previous section, there are sequential quantum measurements schemes where the quantum particle tends to escape from a stable state, and the observed tracks tend, sooner or later, to cross the ground state barrier. On the other hand, it is well known that the observed (random) tracks of a classical oscillator driven by an external noise force are escaping tracks, and recent studies have considered the same problem with reference to the semiclassical regime [28]. It is thus of interest to understand to what extent the intrinsic quantum randomness might be confused with the randomness induced by an external source of noise in a classical system.…”

“…In order to determine a meaningful shape for the coupling coefficients, we shall focus on a widely used model that is sometimes referred to as the ohmic model [28,32]. For such a model, the spectral density depends linearly upon the frequency within a given bandwidth:…”