Macroscopic phonon wave functions and the Fröhlich one-dimensional superconductor

Abstract

A distortion in a crystal is characterized by the existence of a macroscopic phonon wave function whose equation of motion is obtained together with that for the electron first order reduced density matrix. These form a set of coupled integro-differential equations. The Fröhlich model of a one-dimensional superconductor is shown to describe a particular case of a system of electrons and phonons where the phonons are described by a microscopic wave function associated with the existence of off-diagonal long-range order in the phonon first order reduced density matrix. The electron first order reduced density matrix for this model exhibits dynamic diagonal long range order.