Kramers theory in the relaxation dynamics of a tilted asymmetric periodic potential.
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.
Monnai
Takaaki
T
Department of Applied Physics, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan.
Sugita
Ayumu
A
Nakamura
Katsuhiro
K