Weyl conjecture and thermal radiation of finite systems

TL;DR

This paper derives corrections to the Weyl law and conjecture in multiple dimensions, analyzing their effects on electromagnetic and acoustic systems, with applications to finite systems and experimental setups.

Contribution

It introduces a formalism for corrections to the Weyl law in finite systems and applies it to electromagnetic and acoustic quasithermodynamics, extending classical laws.

Findings

Corrections to the Stefan-Boltzmann law for finite systems.

Special focus on two-dimensional systems for experimental relevance.

Extensions to Debye model and Dulong-Petit law for finite solids.

Abstract

In this work, corrections for the Weyl law and Weyl conjecture in d dimensions are obtained and effects related to the polarization and area term are analyzed. The derived formalism is applied on the quasithermodynamics of the electromagnetic field in a finite $d$-dimensional box within a semi-classical treatment. In this context, corrections to the Stefan-Boltzmann law are obtained. Special attention is given to the two-dimensional scenario, since it can be used in the characterization of experimental setups. Another application concerns acoustic perturbations in a quasithermodynamic generalization of Debye model for a finite solid in d dimensions. Extensions and corrections for known results and usual formulas, such as the Debye frequency and Dulong-Petit law, are calculated.