Langevin description of gauged scalar fields in a thermal bath
  We study the dynamics of the oscillating gauged scalar field in a thermal
bath. A Langevin type equation of motion of the scalar field, which contains
both dissipation and fluctuation terms, is derived by using the real-time
finite temperature effective action approach. The existence of the quantum
fluctuation-dissipation relation between the non-local dissipation term and the
Gaussian stochastic noise terms is verified. We find the noise variables are
anti-correlated at equal-time. The dissipation rate for the each mode is also
studied, which turns out to depend on the wavenumber.
