Spectral problem for instability of sphalerons in quartic Klein-Gordon models

Stephen C. Anco

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arXiv · 2508.12150

Spectral problem for instability of sphalerons in quartic Klein-Gordon models

Stephen C. Anco

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Abstract

In the energy functional of nonlinear Klein-Gordon models,sphalerons arise from a saddle point between true and false vacua. The spectral problem for the (in)stabilty of sphalerons in quartic models is shown be governed by a Heun differential equation, which has three finite regular singular points, after a certain change of variable. This allows an explicit formulation of the eigenfunctions and eigenvalues to be obtained in terms of local Heun functions. Good approximations are found for certain ranges of the parameter.

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Stephen C. Anco. 2025-08-16. Spectral problem for instability of sphalerons in quartic Klein-Gordon models. https://arxiv.org/abs/2508.12150

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