Dynamical Casimir Effect in a small compact manifold for the Maxwell vacuum

TL;DR

This paper investigates a novel contribution to the Maxwell vacuum on a small compact manifold, revealing tunneling effects between topologically distinct states that lead to measurable Casimir pressure and a new form of vacuum photon emission akin to the dynamical Casimir effect.

Contribution

It introduces a new topological tunneling mechanism in Maxwell theory on compact manifolds, leading to observable effects beyond standard photon contributions.

Findings

Additional Casimir pressure contributions due to topological effects

Vacuum photon emission triggered by time-dependent magnetic fields

Connection to persistent currents and potential cosmological implications

Abstract

We study novel type of contributions to the partition function of the Maxwell system defined on a small compact manifold ${\mathbb{M}}$ such as torus. These new terms can not be described in terms of the physical propagating photons with two transverse polarizations. Rather, these novel contributions emerge as a result of tunnelling events when transitions occur between topologically different but physically identical vacuum winding states. These new terms give an extra contribution to the Casimir pressure, yet to be measured. We argue that if the same system is considered in the background of a small external time-dependent magnetic field, than there will be emission of photons from the vacuum, similar to the Dynamical Casimir Effect (DCE) when real particles are radiated from the vacuum due to the time-dependent boundary conditions. The difference with conventional DCE is that the dynamics of the vacuum in our system is not related to the fluctuations of the conventional degrees of freedom, the virtual photons. Rather, the radiation in our case occurs as a result of tunnelling events between topologically different but physically identical $|k>$ sectors in a time -dependent background. We comment on relation of this novel effect with the well-known, experimentally observed, and theoretically understood phenomena of the persistent currents in normal metal rings. We also comment on possible cosmological applications of this effect.