Analytical approach to the transition to thermal hopping in the thin- and thick-wall approximations

TL;DR

This paper analytically investigates the transition from quantum tunneling to thermal hopping in scalar field theory, deriving solutions that describe the behavior in both thin-wall and thick-wall regimes, and characterizing the order of the transition.

Contribution

It provides an analytical bounce solution that captures the transition in both thin-wall and thick-wall limits, clarifying the nature and order of the transition.

Findings

Transition is first order in thin-wall regime.

Transition is second order in thick-wall regime.

Analytical solutions reproduce known limits.

Abstract

The nature of the transition from the quantum tunneling regime at low temperatures to the thermal hopping regime at high temperatures is investigated analytically in scalar field theory. An analytical bounce solution is presented, which reproduces the action in the thin-wall as well as thick-wall limits. The transition is first order for the case of a thin wall while for the thick wall case it is second order.