Finite temperature Cherenkov radiation in the presence of a magnetodielectric medium

TL;DR

This paper develops a comprehensive quantum framework for analyzing Cherenkov radiation in magnetodielectric media at finite temperatures, revealing a natural frequency cutoff absent in classical theory.

Contribution

It introduces a canonical quantum approach to Cherenkov radiation in magnetodielectric media, covering both nonrelativistic and relativistic regimes, and explores finite temperature effects.

Findings

Derived explicit equations of motion for the system.

Calculated energy loss due to radiation at finite temperature.

Identified a natural high-frequency cutoff in quantum regimes.

Abstract

A canonical approach to Cherenkov radiation in the presence of a magnetodielectric medium is presented in classical, nonrelativistic and relativistic quantum regimes. The equations of motion for the canonical variables are solved explicitly for both positive and negative times. Maxwell and related constitute equations are obtained. In the large-time limit, the vector potential operator is found and expressed in terms of the medium operators. The energy loss of a charged particle, emitted in the form of radiation, in finite temperature is calculated. A Dirac equation concerning the relativistic motion of the particle in presence of the magnetodielectric medium is derived and the relativistic Cherenkov radiation at zero and finite temperature is investigated. Finally, it is shown that the Cherenkov radiation in nonrelativistic and relativistic quantum regimes, unlike its classical counterpart, introduces automatically a cutoff for higher frequencies beyond which the power of radiation emission is zero.