The Discrete Nonlinear Schroedinger Equation: Nonadiabatic Effects, Finite Temperature Consequences, and Experimental Manifestations

Abstract

Exciting and powerful new ways of describing quasiparticle transport in solids have recently appeared in the literature1, 2. Thus, strong interactions of moving quasiparticles with vibrations can give rise to the discrete nonlinear Schroedinger equation which, in other physical contexts has gone under the name of the discrete self-trapping equation. Our recent theoretical work3, 4 has shown that the nonlinearity in such an equation can have profound effects, some expected and others novel, in the evolution of experimental observables. That work, which has been based on exact solutions for the time evolution for small systems and on numerical solutions for large systems, is described with reference to observables such as fluorescence depolarization in molecular dimers and chains, muon spin relaxation and the neutron scattering function. The rotational polaron and the random nonlinear dimer are also described. Going beyond the usual adiabatic limit, striking effects of slow vibrational relaxation5, 6 are pointed out, and a simple theory of the Brownian motion in the nonadiabatic limit7, 8, 9 is presented in the context of the discrete nonlinear Schroedinger equation. The temperature behaviour of the Kramers escape rate and the stability of nonlinear excitations are discussed. Comments are also made concerning the interesting problem of the microscopic derivation of these equations.KeywordsVibrational RelaxationStriking EffectPhysical ContextRecent Theoretical Work3Nonlinear ExcitationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.