Damped oscillator with quantum noise
R. F. Streater · Journal of Physics A Mathematical and General · 1982
The author finds the general form of positive-energy Gaussian noise so that a linear damped (Bose or Fermi) oscillator obeying a quantum Langevin equation should remain canonical for all time. In a heat bath the system converges to a KMS state (see Kubo, 1957, Martin and Schwinger, 1959) as time t to infinity .