Explosive particle creation by instantaneous change of boundary condition

TL;DR

This paper studies the dynamic Casimir effect in a 1+1 dimensional scalar field with instantaneous boundary condition changes, revealing divergent flux components and their dependence on boundary conditions, with implications for quantum gravity phenomena.

Contribution

It provides a detailed analysis of diverging flux components during instantaneous boundary condition changes, highlighting differences between Neumann and Dirichlet cases and correcting previous overlooked results.

Findings

Two diverging flux components in Neumann-to-Dirichlet cases.

Only one diverging flux component in Dirichlet-to-Neumann cases.

Divergence type depends on initial and final boundary conditions.

Abstract

We investigate the dynamic Casimir effect (DCE) of a $1+1$ dimensional free massless scalar field in a finite or semi-infinite cavity for which the boundary condition (BC) instantaneously changes from the Neumann to Dirichlet BC or reversely. While this setup is motivated by the gravitational phenomena such as the formation of strong naked singularities or wormholes, and the topology change of spacetimes or strings in quantum gravity, the analysis is quite general. For the Neumann-to-Dirichlet cases, we find two components of diverging flux emanate from the point where the BC changes. We carefully compare this result with that of Ishibashi and Hosoya (2002) obtained in the context of a quantum version of cosmic censorship hypothesis, and show that one of the diverging components was overlooked by them and is actually non-renormalizable, suggesting to bring non-negligible backreaction or semiclassical instability. On the other hand, for the Dirichlet-to-Neumann cases, we reveal for the first time that only one component of diverging flux emanates, which is the same kind as that overlooked in the Neumann-to-Dirichlet cases. This result suggests not only the robustness of the appearance of diverging flux in instantaneous limits of DCE but also that the type of divergence sensitively depends on the combination of initial and final BCs.