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.
Highlights
The problem of escaping a potential well has been an active field of research over the last century and has applications in several scientific disciplines, such as in physics and chemistry
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
For a better interpretation of the escape problem, we introduce, in the Appendix, the framework of the MFPTand show its formal equivalence with the flux-over-population method, which proves that the escape rate is the inverse of the MFPT
Summary
The problem of escaping a potential well has been an active field of research over the last century and has applications in several scientific disciplines, such as in physics and chemistry. In any realistic physical system, we expect the presence of fluctuation and dissipation dynamics, which, for example, naturally emerge through the interactions of the system with a thermal bath. Under these conditions, an escape from the potential well might be allowed. The derivation of the escape rate is called the Kramers problem [1] and is, to a large extent, well understood for the simplest systems, such as a classical point particle. In its original zero-dimensional (usual field theory nomenclature for a point particle as a zero space and one time dimensional field) formulation, the escape problem is defined regardless of what is beyond the top of the energy barrier. No explicit extension of this problem to a relativistic
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