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  • Open Access

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

Yoshio Kitadono*

Tomohiro Inagaki†

  • Information Media Center and Core of Research for Energetic Universe, Hiroshima University, No. 1-3-2, Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8521, Japan

  • *Contact author: kitadono@ncut.edu.tw
  • †Contact author: inagaki@hiroshima-u.ac.jp
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Phys. Rev. D 112, 016020 – Published 22 July, 2025

DOI: https://doi.org/10.1103/rd8q-nxpp

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.

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Phys. Rev. D 112, 016020– Published 22 July, 2025
  • Received 8 May 2025
  • Accepted 23 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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