Decay of an inhomogeneous state via resonant tunnelling

TL;DR

This paper explores how inhomogeneous initial states can enable resonant tunnelling in scalar quantum field theory, providing explicit models and demonstrating the dependence of tunnelling rates on initial state energy.

Contribution

It introduces a mechanism for resonant tunnelling via inhomogeneous states, circumventing previous no-go theorems that applied to homogeneous false vacua.

Findings

Resonant tunnelling occurs with inhomogeneous initial states.

Tunnelling rate depends on the energy of initial bubble configurations.

Explicit model demonstrates the transition from contracting bubbles to tunnelling.

Abstract

We recently investigated the nature of resonant tunnelling in standard scalar Quantum Field Theory, uncovering the conditions required for resonance. It was shown that whereas the homogeneous false vacuum may decay via bubble nucleation, it may not decay in a resonant fashion. The no-go theorem given there is circumvented in this study by considering an initial state other than the homogeneous false vacuum, and we confirm our mechanism by showing in an explicit model how resonant tunnelling occurs. Using this model we demonstrate how the tunnelling rate depends on the energy of specially constructed initial states, with these states corresponding to contracting spherical bubbles of some vacuum that evolve to a minimum radius and then tunnel to another vacuum, instead of the classical motion where the bubble would just start to expand.