title: Generalized Einstein relation in tilted periodic potential: a semiclassical approach.
abstract: This paper concerns the investigation of the quantum motion of a system in a dissipative Ohmic heat bath in the presence of an external field using the traditional system-reservoir model. Using physically motivated initial conditions, we then obtain the c-number of the generalized quantum Langevin equation by which we calculate the quantum correction terms using a perturbation technique. As a result of this, one can apply a classical differential equation-based approach to consider quantum diffusion in a tilted periodic potential, and thus our approach is easy to use. We use our expression to calculate the Einstein relation for the quantum Brownian particle in a ratchet-type potential in a very simple closed analytical form using a suitable and convenient approximation. It is found that the diffusion rate is independent of the detailed form of the potential both in quantum and classical regimes, which is the main essence of this work.
authors.affiliation: Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India.
authors.forename: Anindita
authors.initials: A
authors.lastname: Shit
authors.forename: Sudip
authors.initials: S
authors.lastname: Chattopadhyay
authors.forename: Suman Kumar
authors.initials: SK
authors.lastname: Banik
authors.forename: Jyotipratim Ray
authors.initials: JR
authors.lastname: Chaudhuri