Relation between Tunneling and Particle Production in Vacuum Decay

TL;DR

This paper investigates how quantum fluctuations and particle production are affected by tunneling in vacuum decay, revealing a resonance effect in mode functions and analyzing the connection between excitations and tunneling phase shifts.

Contribution

It introduces a functional Schrödinger approach to study quantum fluctuations during tunneling with a time-dependent mass term, uncovering a novel resonance phenomenon.

Findings

Resonance effect in mode functions near the bubble curvature scale

Relation between particle excitations and tunneling phase shifts analyzed

Quantum fluctuations influenced by tunneling dynamics

Abstract

The field-theoretical description of quantum fluctuations on the background of a tunneling field $\sigma$ is revisited in the case of a functional Schrodinger approach. We apply this method in the case when quantum fluctuations are coupled to the $\sigma$ field through a mass-squared term, which is 'time-dependent' since we include the dynamics of $\sigma$ . The resulting mode functions of the fluctuation field, which determine the quantum state after tunneling, display a previously unseen resonance effect when their mode number is comparable to the curvature scale of the bubble. A detailed analysis of the relation between the excitations of the field about the true vacuum (interpreted as particle creation) and the phase shift coming from tunneling is presented.