Brownian motion and finite-temperature effects in the discrete nonlinear Schrödinger equation: Analytic results for the nonadiabatic dimer

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Abstract
The system under study is a moving quasiparticle interacting strongly with lattice vibrations. Our investigation uncovers the effects of finite temperature through an analytical study of the quasiparticle evolution in a dimer. We display appropriate Fokker-Planck equations at several stages and, through a generalized Kramers analysis, show that localized stationary states, which are the signature of nonlinear evolution, (polaronic/solitonic behavior) are destroyed above a characteristic temperature. This result agrees with recent computer simulations in extended systems and lends analytical support to the numerical finding of the destruction of nonlinear structures above a critical temperature.