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The derivation theory of oporator algebras and its applications to statistical mechanics

Research Project

Project/Area Number 05640225
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionNihon University

Principal Investigator

SAKAI Shoichiro  Nihon University, Mathimatics, Professor, 文理学部, 教授 (30130503)

Co-Investigator(Kenkyū-buntansha) SUZUKI Masahiko  Nihon University, Mathimatics, Assistant professor, 文理学部, 助教授 (00171249)
NISHIOKA Kumiko  Nihon University, Mathimatics, Assistant professor, 文理学部, 助教授 (80144632)
SUZUKI Osamu  Nihon University, Mathimatics, Professor, 文理学部, 教授 (10096844)
夜久 竹夫  日本大学, 文理学部, 教授 (90102821)
Project Period (FY) 1993 – 1994
Project Status Completed (Fiscal Year 1994)
Budget Amount *help
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1994: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1993: ¥500,000 (Direct Cost: ¥500,000)
KeywordsC^<**>-algebras / Derivation / Phase transition / KMS state / quantum statistical mechanics / 非有界微分 / C^*_-力学系 / KMS Stateo / Phase transtions / C^*-代数 / C^*-力学系 / 量子統計力学 / KMS状態 / 相転移
Research Abstract

In this research, we have studied KMS states and phase transitions in quantum lattice systems, using the theory of unbounded derivations various results on KMS states obtained in the head investigator's book of "Operator algebras in dynamical systems" have been deepen by this research. The main results in this research have been published in the papers of "KMS states and phase transitions, I,II" by the head investigator.

Report

(3 results)
  • 1994 Annual Research Report   Final Research Report Summary
  • 1993 Annual Research Report
  • Research Products

    (10 results)

All Other

All Publications (10 results)

  • [Publications] 境正一郎: "作用素代数に於ける微分論とその応用" 数学.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] 境正一郎: "KMS states and phase transitions" Fields Institute publications. FI94 OA01. 1-5 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] 境正一郎: "The derivation theory of operator algebras and its applications" Sugaku Expositions,American Math.Soc.Vol.8 No.1. 39-58 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] 境正一郎: "KMS states and phase transitions,II" Fields Institute communications,American Math.Soc.1-8 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Shoichiro Sakai: "The derivation theory of operator algebras and its applications" Sugaku. (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Shoichiro Sakai: "KMS states and phase transitions" Fields Institule publications. FI94OA01. 1-5 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Shoichiro Sakai: "The derivation theory of operator algebras and its applications" Sugaku Expositions, American Math.Soc.Vol 8, No 1. 39-58 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Shoichiro Sakai: "KMS states and phase transitions, II" Field Institute Communication American Math.Soc.1-8 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] 境正一郎: "KMS states and phase transitions" Fields Institnte出版物.

    • Related Report
      1994 Annual Research Report
  • [Publications] 境正一郎: "KMS states and phase transitions II" (投稿準備中).

    • Related Report
      1994 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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