Dissipation and transport dynamics in a ratchet coupled to a discrete bath

Abstract

We investigate a particle in a ratchet potential (the system) coupled to an harmonic bath of N=1-500 degrees of freedom (the discrete bath). The dynamics of the energy exchange between the system and the discrete bath is studied in the transition regime from low to high values of N . First manifestation of dissipation (energy lost by the system) appears for the bath composed of 10 less, similar N less, similar 20 oscillators, as expected. For low values of N , beside small dissipation effects, the system experiences the bath-induced particle transfer between different potential wells from the ratchet. We show that this effect decreases the mobility of particles along the ratchet. The hopping probability along the ratchet and the energy decay rates for the system are shown to obey the power law for late times, a behavior typical of discrete baths which for low and intermediate values of N always induce a non-Markovian process. The exponential decay is recovered for high bath frequencies distribution and for high values of N , where the Markovian limit is expected. Moreover, by including the external oscillating field with intensity F , we show that current reversal occurs in two situations: By increasing N and by switching from low to high frequencies distribution of the bath. The mobility of particles is shown to have a maximum at F=0.1 , which is N independent (for higher values of N ).

Quantum energy and coherence exchange with discrete baths

“…Differently from most of the previous studies, the environment here is composed by a finite number N of uncoupled HOs, as studied recently for classical continuous systems [25,26] and maps [27]. In such cases we say to have a discrete or structured bath.…”

Classical small systems coupled to finite baths

“…In the theory of open systems, the deterministic dynamics of particles in the system is replaced by the stochastic Langevin equation in the classical limit. The problem has been investigated with the use of various models in which a single particle (the system) is attached at the center (or edge) of a linear chain [2,3], or it is coupled to a bath consisting of a collection of harmonic oscillators [4]- [13]. Many studies have been made for open systems by using the Caldeira-Leggett (CL) model given by [4][5][6] …”

“…The CL model was originally introduced for infinite bath (N B → ∞). In recent years, the CL model has been employed for a study of properties of a small system coupled to a finite bath [9]- [13]. A thermalization of a particle (the system) coupled to a finite bath has been investigated [9,10].…”

“…The specific heat of a single oscillator (the system) coupled to finite bath has been studied with the use of two different evaluation methods [11,12]. The energy exchange between particles in a rachet potential (the system) and finite bath (N B = 1 − 500) has been investigated [13].…”

“…In existing models which have been proposed for open systems [5]- [13], the number of particles in a systems is taken to be unity (N S = 1) while a generic open system may contain any number of particles. It is necessary to develop an (N S + N B ) model including finite N S -body system (N S ≥ 1) coupled to N B -body bath, with which we may investigate the properties of generic small systems.…”