Z. Haba et H. Kleinert, Master and Langevin equations for electromagnetic dissipation and decoherence of density matrices, EUR PHY J B, 21(4), 2001, pp. 553-560
We set up a forward - backward path integral for a point particle in a bath
of photons to derive a master equation for the density matrix which descri
bes electromagnetic dissipation and decoherence. We also derive the associa
ted Langevin equation. As an application, we recalculate the, Wigner-Weissk
opf formula for the natural line width of an atomic state at zero temperatu
re and find, in addition, the temperature broadening caused by the decohere
nce term. Our master equation also yields the correct Lamb shift of atomic
levels. The two equations may have applications to dilute interstellar gase
s or to few-particle systems in cavities.