Null energy condition violation: Tunnelling versus the Casimir effect

TL;DR

This paper explores how quantum tunnelling and Casimir energy influence the Null Energy Condition violation in finite-volume quantum field systems, revealing a complex interplay dependent on temperature and length scales.

Contribution

It introduces a detailed analysis of how tunnelling and Casimir effects jointly affect the Null Energy Condition in finite systems, highlighting the importance of discrete momenta.

Findings

Tunnelling causes non-extensive symmetric ground states leading to NEC violation at low temperatures.

Casimir energy can modify the tunnelling effects depending on system size.

The interplay between tunnelling and Casimir energy depends critically on length scales and temperature.

Abstract

We show that tunnelling between two degenerate minima, as allowed in a finite volume, leads to a non-extensive symmetric ground state. This results in Null Energy Condition violation for sufficiently low temperatures, when a continuous set of momenta in the box containing the field is assumed. Taking into account discrete momenta can modify this picture and is achieved via the addition of the Casimir energy to the tunnelling-induced ground state energy. Focusing on zero-temperature, these non-trivial effects are found to compete, depending on the typical length scales involved.