Formulating the Kramers problem in field theory
  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.
