KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra

We consider equilibrium states of weakly coupled anharmonic quantum oscillators on Z. We consider the Resolvent CCR Algebra introduced by D.Buchholtz and H.Grundling, and we show that the infinite volume limit of equilibrium states satisfies the KMS (Kubo-Martin-Schwinger) condition with good regularity(= locally Fock representation). Uniqueness of the KMS states is proven as well.