Dissipative dynamics in semiconductors at low temperature

TL;DR

This paper introduces a mathematical model for electron dissipation in lightly doped semiconductors at low temperatures, analyzing the dissipation operator's properties and demonstrating exponential return to equilibrium.

Contribution

It provides a rigorous mathematical framework for electron dissipation, proving key properties of the dissipation operator and its spectral characteristics.

Findings

Dissipation operator is densely defined and positive.

Zero eigenvalue is simple, ensuring unique equilibrium.

Spectral gap implies exponential convergence to equilibrium.

Abstract

A mathematical model is introduced which describes the dissipation of electrons in lightly doped semi-conductors. The dissipation operator is proved to be densely defined and positive and to generate a Markov semigroup of operators. The spectrum of the dissipation operator is studied and it is shown that zero is a simple eigenvalue, which makes the equilibrium state unique. Also it is shown that there is a gap between zero and the rest of its spectrum which makes the return to equilibrium exponentially fast in time.