Journal of Statistical Physics, Vol. 34, Nos. 1/2, 1984. p. 239-261.
A quantum-mechanical treatment of the evolution of an anharmonic oscillator coupled to a heat bath is given. It is shown that for a certain class of anharmonic potentials the heat bath drives the oscillator to an equilibrium state, close to the quantum Gibbs state associated to the potential. Thus a partial proof is provided for a conjecture of R. Benguria and M. Kac.