Particle Creation by a Moving Boundary with Robin Boundary Condition

TL;DR

This paper analyzes particle creation by a moving boundary with Robin boundary conditions, deriving a Bogoliubov transformation to compute the particle spectrum and showing how boundary oscillation frequency affects emission.

Contribution

It introduces a method to calculate particle creation spectra for Robin boundary conditions, unifying Dirichlet and Neumann cases as limits, and explores how boundary oscillation frequency modulates emission.

Findings

Dirichlet and Neumann spectra are upper bounds for Robin case.

Particle emission can be significantly suppressed by tuning boundary oscillation frequency.

Derived a Bogoliubov transformation linking input and output field operators.

Abstract

We consider a massless scalar field in 1+1 dimensions satisfying a Robin boundary condition (BC) at a non-relativistic moving boundary. We derive a Bogoliubov transformation between input and output bosonic field operators, which allows us to calculate the spectral distribution of created particles. The cases of Dirichlet and Neumann BC may be obtained from our result as limiting cases. These two limits yield the same spectrum, which turns out to be an upper bound for the spectra derived for Robin BC. We show that the particle emission effect can be considerably reduced (with respect to the Dirichlet/Neumann case) by selecting a particular value for the oscillation frequency of the boundary position.