# Formulating the Kramers problem in field theory

## TL;DR

This paper extends the classical Kramers escape problem to quantum field theory, deriving an explicit escape rate for a scalar field influenced by thermal fluctuations, with potential applications across physics disciplines.

## Contribution

It formulates a well-defined Kramers problem for scalar fields in quantum field theory and provides a method to compute the escape rate, addressing previous conceptual difficulties.

## Key findings

- Derived explicit escape rate for scalar fields with thermal fluctuations
- Established a framework for the Kramers problem in field theory
- Discussed applications in condensed matter and cosmology

## Abstract

The escape problem is defined in the context of quantum field theory. The escape rate is explicitly derived for a scalar field governed by fluctuation-dissipation dynamics, through generalizing the standard Kramers problem. In the presence of thermal fluctuations, there is a nonvanishing probability for a classical background field, initially located at a minimum of its potential in a homogeneous configuration, to escape from the well. The simple and well-known related problem of the escape of a classical point particle due to random forces is first reviewed. We then discuss the difficulties associated with a well-defined formulation of an escape rate for a scalar field and how these can be overcome. A definition of the Kramers problem for a scalar field and a method to obtain the rate are provided. Finally, we discuss some of the potential applications of our results, which can range from condensed matter systems, i.e., nonrelativistic fields, to applications in high-energy physics, like for cosmological phase transitions.