KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra
T. Kanda, Taku Matsui
TL;DR
This paper studies equilibrium states of weakly coupled anharmonic quantum oscillators on an infinite lattice, demonstrating that their infinite volume limits satisfy the KMS condition with good regularity and establishing the uniqueness of these states.
Contribution
It introduces the use of the Resolvent CCR Algebra to analyze KMS states of anharmonic oscillators and proves their existence, regularity, and uniqueness in the infinite volume limit.
Findings
Infinite volume KMS states satisfy the KMS condition with good regularity
Uniqueness of the KMS states is established
The Resolvent CCR Algebra effectively describes equilibrium states of anharmonic oscillators
Abstract
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.
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Taxonomy
TopicsCold Atom Physics and Bose-Einstein Condensates · Quantum optics and atomic interactions · Quantum many-body systems