The Bistable Potential: An Archetype for Classical and Quantum Systems

Abstract

In this work we analyze the transient dynamics of three different classical and quantum systems. First, we consider a classical Brownian particle moving in an asymmetric bistable potential, subject to a multiplicative and additive noise source. We investigate the role of these two noise sources on the life time of the metastable state. A nonmonotonic behavior of the lifetime as a function of both additive and multiplicative noise intensities is found, revealing the phenomenon of noise enhanced stability. Afterward, by using a Lotka-Volterra model, the dynamics of two competing species in the presence of Lévy noise sources is analyzed. Quasiperiodic oscillations and stochastic resonance phenomenon in the dynamics of the competing species are found. Finally the dynamics of a quantum particle subject to an asymmetric bistable potential and interacting with a thermal reservoir is investigated. We use the Caldeira-Leggett model and the approach * Invited talk at the International Conference on Statistical Physics, 11-15 July 2011, Cyprus. 1241006-1 B. Spagnolo et al.of the Feynman-Vernon functional in discrete variable representation. We obtain the time evolution of the population distributions in energy eigenstates of the particle, for different values of the coupling strength with the thermal bath.

Quantum dissipative dynamics of a bistable system in the sub-Ohmic to super-Ohmic regime

“…This can be shown by considering the quantum Langevin equation for the system, as done in [3]. The magnitude of this mass renormalization due to the high frequency modes of the bath is shown in figure 3 as a function of the exponent s of the spectral density function (see equation (4)). This behavior involves uniquely the features of the thermal bath.…”

Dissipative dynamics in a quantum bistable system: Crossover from weak to strong damping

“…[8], a formally exact expression for the reduced density matrix of our multi-level system is derived in the localized basis given in Eq. (10). Approximations which go beyond the NIBA-like generalization to multi-level systems proposed in Ref.…”

Energy transport mechanism in the form of proton soliton in a one-dimensional hydrogen-bonded polypeptide chain

“…In general, the evolution of a quantum particle subjected to a time-dependent asymmetric bistable potential and affected by environmental noise has been analyzed by the Caldeira-Leggett model, which allows to derive a quantum mechanical analogue of the generalized Langevin equation [34][35][36].…”