Quantum Smoluchowski equation: escape from a metastable state

Abstract

We develop a quantum Smoluchowski equation in terms of a true probability distribution function to describe quantum Brownian motion in configuration space in large friction limit at arbitrary temperature and derive the rate of barrier crossing and tunneling within an unified scheme. The present treatment is independent of path integral formalism and is based on canonical quantization procedure.

Quantum Smoluchowski equation for a spin bath

“…The effective spectral density which contains a temperature-dependent factor plays a significant role in the diffusion coefficient D f of the particle in a spin bath or the rate coefficient k. As the temperature rises there is an effective reduction of system-bath coupling due to thermal saturation. Thus the finite-temperature behavior of the spin bath is markedly different from that of the harmonic bath treated earlier by Ankerhold et al and others [24,25] in the context of overdamped quantum dynamics. The origin of this difference may be traced to two factors: First, while the harmonic bath reaches the well-known classical macroscopic limit, the spin bath, in a strict sense, does not.…”

Anharmonic quantum contribution to vibrational dephasing

“…[13][14][15][16][17][18][19]27, 28͒ therefore rests on quantum correction terms, ͗␦q n (t)͓͘ϭB n (t)͔, which are determined by solving the quantum correction equations as discussed in Sec. For example, the second order Q(t) is given by Q(t) ϭϪ 1 2 Vٞ(q)͗␦q 2 ͘.…”

Quantum phase-space function formulation of reactive flux theory

“…In Appendix A we have derived the equations for quantum corrections upto forth oder 39 . Under very special circumstances, it has been possible to include quantum effects to all orders 27,40 . The present theory thus takes into account of the anharmonicity as an integral part of the treatment.…”

“…The essential requirement for such a theory is obviously the quantum phase space distribution function. Very recently, based on a coherent state representation of quantum noise operator and an ensemble averaging procedure, we have developed 24,25,26,27 a c-number quantum generalized Langevin equation. The theory is valid for arbitrary temperature and noise correlation.…”