title: Kramers theory in the relaxation dynamics of a tilted asymmetric periodic potential.
abstract: We investigate the low-temperature relaxation dynamics toward a nonequilibrium steady state in a tilted asymmetric periodic potential based on the WKB analysis and the numerical diagonalization of the Fokker-Planck operator. Due to the tilting, the Fokker-Planck operator, and thus the Schrödinger operator associated with it, are non-Hermitian. Therefore, we evaluate the decay rate based on the WKB analysis both for real- and complex-valued eigenvalues. In the tilting range where the double-humped barrier exists, the decay rate is shown to obey a law which is a subtle nonequilibrium extension of the so-called Kramers escape rate. The decay rate for the single-humped barrier case is analyzed as well. The large tilting regime where the barriers no longer exist is also investigated.
authors.affiliation: Department of Applied Physics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.
authors.forename: Takaaki
authors.initials: T
authors.lastname: Monnai
authors.forename: Ayumu
authors.initials: A
authors.lastname: Sugita
authors.forename: Katsuhiro
authors.initials: K
authors.lastname: Nakamura