Vacuum Cherenkov effect in logarithmic nonlinear quantum theory

TL;DR

This paper investigates vacuum Cherenkov radiation phenomena within a logarithmic nonlinear quantum framework, calculating key characteristics and suggesting broader applicability to Lorentz-violating theories of the vacuum.

Contribution

It introduces a detailed analysis of vacuum Cherenkov effects using logarithmic nonlinear quantum theory, highlighting the radiation's dependence on vacuum energy scales and potential generalization.

Findings

Radiation yield proportional to the square of the vacuum energy scale

Computed cone angle, flash duration, and spectral distribution of the radiation

Results applicable to Lorentz-invariance-violating theories in the long-wavelength limit

Abstract

We describe the radiation phenomena which can take place in the physical vacuum such as Cherenkov-type shock waves. Their macroscopical characteristics - cone angle, flash duration, radiation yield and spectral distribution - are computed. It turns out that the radiation yield is proportional to the square of the proper energy scale of the vacuum which serves also as the vacuum instability threshold and the natural ultraviolet cutoff. While the analysis is mainly based on the theory engaging the logarithmic nonlinear quantum wave equation, some of the obtained results must be valid for any Lorentz-invariance-violating theory describing the vacuum by (effectively) continuous medium in the long-wavelength approximation.