Equilibrium and Nonequilibrium States of the Model Fröhlich–Peierls Hamiltonian

Abstract

The model Fröhlich–Peierls Hamiltonian for electrons interacting with phonons only in some infinite discrete modes is considered. It is shown that, in the equilibrium case, this model is thermodynamically equivalent to the model of electrons with periodic potential and free phonons. In the one-dimensional case, the potential is determined exactly in terms of the Weierstrass elliptic function, and the eigenvalue problem can also be solved exactly. Nonequilibrium states are described by the nonlinear Schrödinger and wave equations, which have exact soliton solutions in the one-dimensional case.