Semi-Phenomenological Analysis of Dynamics of Nonlinear Excitations in One-Dimensional Electron-Phonon System

TL;DR

This paper semi-phenomenologically analyzes the dynamics of nonlinear excitations in one-dimensional electron-phonon systems, deriving an effective action to determine excitation width and velocity, with results aligning well with numerical simulations.

Contribution

It introduces a semi-phenomenological effective action approach that treats the width of nonlinear excitations as a dynamical variable in 1D electron-phonon systems.

Findings

Derived a maximum velocity for nonlinear excitations.

Determined velocity dependence of width and energy.

Results agree with numerical simulations.

Abstract

The structure of moving nonlinear excitations in one-dimensional electron-phonon systems is studied semi-phenomenologically by using an effective action in which the width of the nonlinear excitation is treated as a dynamical variable. The effective action can be derived from Su, Schrieffer and Heeger's model or its continuum version proposed by Takayama, Lin-Liu and Maki with an assumption that the nonlinear excitation moves uniformly without any deformation except the change of its width. The form of the action is essentially the same as that discussed by Bishop and coworkers in studying the dynamics of the soliton in polyacetylene, though some details are different. For the moving excitation with a velocity $v$, the width is determined by minimizing the effective action. A requirement that there must be a minimum in the action as a function of its width provides a maximum velocity. The velocity dependence of the width and energy can be determined. The motions of a soliton in p olyacetylene and an acoustic polaron in polydiacetylene are studied within this formulation. The obtained results are in good agreement with those of numerical simulations.