# Simple Gradient Flow Equation for the Bounce Solution

## TL;DR

This paper introduces a new simple gradient flow equation to efficiently derive bounce solutions for false vacuum decay, building on classical methods and demonstrating robustness in convergence.

## Contribution

The paper presents a novel gradient flow approach for bounce solutions, simplifying the derivation process and ensuring stable convergence regardless of initial conditions.

## Key findings

- The method reliably finds bounce solutions in false vacuum decay.
- The approach is robust against different initial configurations.
- It simplifies the computational process for decay rate analysis.

## Abstract

Motivated by the recent work of Chigusa, Moroi, and Shoji, we propose a new simple gradient flow equation to derive the bounce solution which contributes to the decay of the false vacuum. Our discussion utilizes the discussion of Coleman, Glaser, and Martin and we solve a minimization problem of the kinetic energy while fixing the potential energy. The bounce solution is derived as a scale-transformed of the solution of this problem. We also show that the convergence of our method is robust against a choice of the initial configuration.