Quantum State-Dependent Diffusion and Multiplicative Noise: A Microscopic Approach

Abstract

The state-dependent diffusion, which concerns the Brownian motion of a particle in inhomogeneous media has been described phenomenologically in a number of ways. Based on a systemreservoir nonlinear coupling model we present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Markovian Langevin description and an associated Fokker-Planck equation in position space in the overdamped limit. We examine the thermodynamic consistency and explore the possibility of observing a quantum current, a generic quantum effect, as a consequence of this state-dependent diffusion similar to one proposed by Büttiker [Z. Phys. B 68, 161 (1987)] in a classical context several years ago.

Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach

“…It has been shown that the stationary probability distribution function (PDF) is independent of magnitudes of additive and multiplicative noises and of the relaxation time of colored noise [20][21][22]29], although the response to applied input depends on noise parameters [29]. This is in contrast with previous studies [30][31][32] which show that the stationary PDF of the Langevin model for the harmonic potential is Gaussian or non-Gaussian, depending on magnitudes of additive and multiplicative noises.…”

“…where the bracket · 0 stands for the average over initial states of q n (0) and p n (0) [18][19][20].…”

“…This is in contrast with previous studies [30][31][32] which show that the stationary PDF of the Langevin model for the harmonic potential is Gaussian or non-Gaussian, depending on magnitudes of additive and multiplicative noises. We expect that when the generalized CL model with a nonlinear coupling [20][21][22]29] is applied to a bistable system, properties of the calculated SR may be rather different from those having been derived by the phenomenological Langevin models [4,[6][7][8][9][10][11][12][13][14]. It is the purpose of the present paper to make a detailed study on SR of an open bistable system described by the microscopic, generalized CL model with nonlinear nonlocal dissipation and state-dependent diffusion [29].…”

“…In Sec. II, we briefly summarize the non-Markovian Langevin equation derived from the generalized CL model with OU colored noise [20][21][22]29].…”

Inhomogeneous quantum diffusion and decay of a meta-stable state

“…This in turn relates the additive noise of the thermal bath with linear dissipation of the system through fluctuationdissipation relation. However when coupling between the reservoir is linear in bath co-ordinates but nonlinear in system coordinates, one encounters multiplicative noise [8,9,10,11,12,13,14,15,16,17] and nonlinear dissipation in the form of co-ordinate dependent friction. The role of the space-dependent friction in classical context has been explored in several issues, e. g., charge transfer reaction in a polar medium and activated rate processes in the overdamped regime [18,19,20,21,22], fluctuationinduced transport [23,24], stochastic resonance [26,27], noise-induced transition [28,29], etc.…”