Instability of quantum fluctuation around classical nonlinear massive wave solution in Higgs potential and particle creations

TL;DR

This paper investigates the stability of quantum fluctuations around nonlinear massive wave solutions in the Higgs potential, revealing instability regions and their implications for particle creation during phase transitions.

Contribution

It provides a detailed analysis of the stability conditions of quantum fluctuations in the Higgs potential using Hill's equation and Floquet theory, highlighting new instability mechanisms.

Findings

Identified instability regions of mode functions via Hill's equation analysis.

Linked particle number instabilities to Floquet exponents.

Enhanced understanding of quantum field dynamics during phase transitions.

Abstract

We discuss the dynamics of the quantum fluctuation around the nonlinear massive wave solution in the Higgs potential. In particular, we analyze the stability and instability of the mode function. Using the stability condition for Hill's equation, we obtain the instability region of the mode function in the quantum fluctuation as the function of the parameters in the mode equation. We show that the two types of the instabilities of the system in the particle number can be understood by the Floquet's exponents in the instability parameter region. The analysis will be useful to understand the dynamics of the quantum field theory around the nonlinear massive wave solution when the classical background slightly deviates from the constant background during the middle stage of the phase transition.