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A quantum crystal model in the light-mass limit: Gibbs states. (English) Zbl 0976.82010

Summary: Ground and temperature quantum Gibbs states are constructed for a ferroelectric anharmonic quantum oscillator model with small masses. It is shown that they possess mixing properties. The construction relies on the Feynman-Kac-Nelson representation of the conditional reduced density matrices and on the cluster expansions for the corresponding Gibbs field of trajectories.

MSC:

82B10 Quantum equilibrium statistical mechanics (general)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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