Massive Scalar Field in an One-Dimensional Oscillating Region

TL;DR

This paper investigates how a massive scalar field behaves in a one-dimensional region with oscillating boundaries, showing that energy can grow exponentially even with small mass, similar to the massless case.

Contribution

It extends the analysis of energy growth in oscillating regions to include massive scalar fields, providing new estimates for mass-induced effects.

Findings

Energy can grow exponentially for small mass in oscillating regions.

Massive fields exhibit similar growth behavior as massless fields under certain conditions.

The study provides estimates for mass-related corrections to the energy growth.

Abstract

The classical scalar massive field satisfying the Klein-Gordon equation in a finite one-dimensional space interval of periodically varying length with Dirichlet boundary conditions is studied. For the sufficiently small mass, the energy can exponentially grow with time under the same conditions as for the massless case. The proofs are based on estimates of exactly given mass-induced corrections to the massless case.