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

Tomohiro Kanda, Taku Matsui

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We consider equilibrium states of weakly coupled anharmonic quantum oscillators(= anharmonic crystal) on an integer lattice Z. We employed standard functional analytic methods for Schrödinger operators and we show existence of the infinite volume limit of equilibrium states, and uniqueness of the regular KMS (Kubo–Martin–Schwinger) states in the frame of Resolvent CCR Algebra introduced by D. Buchholz and H. Grundling.

Original languageEnglish
Title of host publicationSpringer Optimization and Its Applications
PublisherSpringer International Publishing
Pages251-270
Number of pages20
DOIs
Publication statusPublished - Jan 1 2019

Publication series

NameSpringer Optimization and Its Applications
Volume146
ISSN (Print)1931-6828
ISSN (Electronic)1931-6836

Fingerprint

Resolvent
Equilibrium State
Crystal
Algebra
Anharmonic Oscillator
Uniqueness
Integer
Operator
Standards

All Science Journal Classification (ASJC) codes

  • Control and Optimization

Cite this

Kanda, T., & Matsui, T. (2019). Regular KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra. In Springer Optimization and Its Applications (pp. 251-270). (Springer Optimization and Its Applications; Vol. 146). Springer International Publishing. https://doi.org/10.1007/978-3-030-12661-2_12

Regular KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra. / Kanda, Tomohiro; Matsui, Taku.

Springer Optimization and Its Applications. Springer International Publishing, 2019. p. 251-270 (Springer Optimization and Its Applications; Vol. 146).

Research output: Chapter in Book/Report/Conference proceedingChapter

Kanda, T & Matsui, T 2019, Regular KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra. in Springer Optimization and Its Applications. Springer Optimization and Its Applications, vol. 146, Springer International Publishing, pp. 251-270. https://doi.org/10.1007/978-3-030-12661-2_12
Kanda T, Matsui T. Regular KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra. In Springer Optimization and Its Applications. Springer International Publishing. 2019. p. 251-270. (Springer Optimization and Its Applications). https://doi.org/10.1007/978-3-030-12661-2_12
Kanda, Tomohiro ; Matsui, Taku. / Regular KMS States of Weakly Coupled Anharmonic Crystals and the Resolvent CCR Algebra. Springer Optimization and Its Applications. Springer International Publishing, 2019. pp. 251-270 (Springer Optimization and Its Applications).
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