On lattice oscillator-type Gibbs systems with superstable many-body potentials

W. I. Skrypnik

Institute of Mathematics of the NAS of Ukraine, 3, Tereshchenkivs'ka Str., Kyiv, Ukraine

Abstract: The grand canonical correlation functions of lattice oscillator-type Gibbs systems with a general one-body phase measure space and many-body superstable interaction potentials are found in the thermodynamic limit at low activities as a solution of the ordered lattice Kirkwood–Salzburg equation. For special choices of the measure space, they describe the equilibrium states of lattice classical and quantum linear oscillator systems and the states of stochastic gradient lattice systems of interacting oscillators with Gibbs initial states.

Keywords: Lattice oscillator-type Gibbs systems, superstable many-body potential, thermodynamic limit, Kirkwood–Salzburg equation.

MSC: 70F45

Language: English

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