The analysis on the single particle model of CDW

TL;DR

This paper analyzes the single particle model of charge-density waves using rotated vector fields theory, deriving relations between applied electric field and periodic solutions, and confirming the nonlinear conductivity and noise formulas with empirical data.

Contribution

It provides a mathematical analysis of the charge-density wave model, establishing the fixed critical electric field and deriving key nonlinear properties.

Findings

Relation between electric field and periodic solutions established

Critical electric field value fixed in over-damped case

Derived formulas for nonlinear conductivity and narrow-band noise

Abstract

Gruner put forward a single particle model of charge-density wave, which is a typical nonlinear differential equation, and also a mathematical model of pendulum. This Letter analyzes the solution of equation by the rotated vector fields theory, providing the relation between the applied field E and the periodic solution, and the conclusion that the critical value of E for the periodic solution is fixed in the over-damped situation. With these conclusions, it derives the formulae of nonlinear conductivity, narrow-band noise, which are consistent with the empirical ones given by Fleming.