Generalisation of Wigner's theorem for dissipative quantum systems

Abstract

The author presents a quantum Langevin equation in the Schrodinger picture. The friction term is motivated by a natural generalisation of Wigner's theorem or, equivalently, of Dirac's superposition principle. The author applies the model to spin relaxation and to the Brownian motion of the harmonic oscillator. In both cases the state vectors evolve asymptotically to a distribution which has the Gibbs state as corresponding density matrix. It is shown that for any initial state, the harmonic oscillator tends to a coherent state.