Quantization of the Electromagnetic Field in Non-dispersive Polarizable Moving Media above the Cherenkov Threshold

TL;DR

This paper develops a quantum description of electromagnetic fields in moving, polarizable media exceeding the Cherenkov threshold, revealing inherent instabilities and the necessity of external forces for sustained field amplitudes.

Contribution

It introduces a quantization framework for electromagnetic fields in non-dispersive moving media above the Cherenkov threshold, highlighting instability and the role of external pumping.

Findings

The quantized system is generally unstable with no ground state.

Field amplitudes can grow indefinitely under constant velocity.

External forces are required to sustain the system's energy.

Abstract

We quantize the macroscopic electromagnetic field in a system of non-dispersive polarizable bodies moving at constant velocities possibly exceeding the Cherenkov threshold. It is shown that in general the quantized system is unstable and neither has a ground state nor supports stationary states. The quantized Hamiltonian is written in terms of quantum harmonic oscillators associated with both positive and negative frequencies, such that the oscillators associated with symmetric frequencies are coupled by an interaction term that does not preserve the quantum occupation numbers. Moreover, in the linear regime the amplitudes of the fields may grow without limit provided the velocity of the moving bodies is enforced to be constant. This requires the application of an external mechanical force that effectively pumps the system.