Quantum dissipation and decay in a medium

Quantum dissipation in a thermal environment is investigated, using the path-integral approach. The reduced density matrix of the harmonic oscillator system coupled to a thermal bath of oscillators is derived for an arbitrary spectrum of bath oscillators. Time evolution and the end point of the two-body decay of unstable particles are then elucidated: After early transient times unstable particles undergo the exponential decay, followed by the power-law decay and finally ending in a mixed state of residual particles containing contributions from both on and off the mass shell, whose abundance does not suffer from the Boltzmann suppression.