Quartic Gradient Flow

TL;DR

This paper introduces Quartic Gradient Flow, a novel numerical method designed to efficiently locate saddle-point configurations like bounce solutions and sphalerons by modifying the eigenvalue spectrum of fluctuations.

Contribution

The paper presents a new Quartic Gradient Flow technique that improves the search for saddle-point configurations by altering fluctuation eigenvalues.

Findings

Successfully applied to Euclidean bounce configurations

Effective in locating sphaleron solutions

Eigenvalues of fluctuations are squares of original eigenvalues

Abstract

Saddle-point configurations, such as the Euclidean bounce and sphalerons, are known to be difficult to find numerically. In this Letter we study a new method, Quartic Gradient Flow, to search for such configurations. The central idea is to introduce a gradient-flow-like equation in such a way that all the fluctuations around the saddle-point have eigenvalues that are square of the eigenvalues of the original quadratic operator. We illustrate how the method works for the Euclidean bounce and sphalerons.