Spontaneous Emission from Excited Quantum Kinks

TL;DR

This paper analytically investigates the decay processes of excited shape modes in 1+1d scalar kink models, providing decay rates that connect quantum and classical descriptions, especially in the $^4$ model.

Contribution

It offers the first analytical calculation of decay rates for twice-excited shape modes and coherent states in scalar kink models, linking quantum decay with classical results.

Findings

Decay rates for twice-excited shape modes are derived.

Coherent state decay rates match classical predictions in the $^4$ model.

Quantum and classical decay descriptions are connected.

Abstract

Many kink solutions enjoy internal excitations, called shape modes. In some 1+1d scalar models, such as the $\phi^4$ double-well model, when a kink's shape mode is excited twice it may decay to a ground state kink plus a meson. We analytically calculate the decay rates of both the twice-excited shape mode and also a coherent state corresponding to the classically excited shape mode. In the case of the $\phi^4$ model, we find that the latter agrees with the classical result of Manton and Merabet.