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Analysis of macroscopic observables in asymptotically abelian systems

Research Project

Project/Area Number 25800057
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionThe University of Tokyo

Principal Investigator

Ogata Yoshiko  東京大学, 大学院数理科学研究科, 准教授 (80507955)

Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords量子スピン系 / 巨視的物理量 / ハミルトニアン / 基底状態 / 量子シャノンマクミランの定理
Outline of Final Research Achievements

We considered the macroscopic observables in quantum spin systems. As quantum systems are given by non-commutative algebras, the physical observables do not commute with each others. However, macroscopic observables can be approximated by commuting observables.One of the key ingredient of the proof ot this theorem is the quantum Shannon McMillan theorem. We gave a simple new proof of this theorem. Furthermore,we extended this theorem to general AF C^*-systems. We also carried out the classification of gapped Hamiltonians(which are a kind of macroscopic observables.)

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (13 results)

All 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (1 results) Journal Article (7 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 7 results,  Acknowledgement Compliant: 4 results) Presentation (5 results) (of which Int'l Joint Research: 3 results,  Invited: 5 results)

  • [Int'l Joint Research] Universitat Munchen(ドイツ)

    • Related Report
      2015 Research-status Report
  • [Journal Article] A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization III2017

    • Author(s)
      Yoshiko Ogata
    • Journal Title

      Comm. Math.Phys.

      Volume: 352 Issue: 3 Pages: 1205-1263

    • DOI

      10.1007/s00220-016-2810-9

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization I2016

    • Author(s)
      Yoshiko Ogata
    • Journal Title

      Comm. Math.Phys.

      Volume: 348 Issue: 3 Pages: 1011-1042

    • DOI

      10.1007/s00220-016-2696-6

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization II2016

    • Author(s)
      Yoshiko Ogata
    • Journal Title

      Comm. Math.Phys.

      Volume: 348 Issue: 3 Pages: 847-895

    • DOI

      10.1007/s00220-016-2697-5

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] C^1-Classification of Gapped Parent Hamiltonians of Quantum Spin Chains2015

    • Author(s)
      Bachmann Ogata
    • Journal Title

      Communications in Mathematical Physics

      Volume: 1432-0916 Issue: 3 Pages: 1011-1042

    • DOI

      10.1007/s00220-015-2350-8

    • Related Report
      2015 Research-status Report 2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Normal states of type III factors2014

    • Author(s)
      Y. Kawahigashi, {Y. Ogata}, E. Stormer
    • Journal Title

      Pacific Journal of Mathematics

      Volume: 267 Pages: 131-139

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Approximating macroscopic observables in quantum spin systems with commuting matrices2013

    • Author(s)
      Yoshiko Ogata
    • Journal Title

      Journal of Functional Analysis

      Volume: 264 Pages: 2005-2033

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Shannon-McMillan Theorem for AF C*-systems2013

    • Author(s)
      Yoshiko Ogata
    • Journal Title

      Letters in Mathematical Physics

      Volume: 103 Pages: 1367-1376

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] A class of asymmetric gapped Hamiltonians on quantum spin chains and its characterization2016

    • Author(s)
      Yoshiko Ogata
    • Organizer
      QMath13
    • Place of Presentation
      アトランタ
    • Year and Date
      2016-10-08
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of gapped Hamiltonians in quantum spin chains2016

    • Author(s)
      Yoshiko Ogata
    • Organizer
      MSJ-SI Operator Algebras and Mathematical Physics
    • Place of Presentation
      仙台
    • Year and Date
      2016-08-01
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A class of asymmetric gapped Hamiltonians on quantum spin chains and its C^1-classification2015

    • Author(s)
      Yoshiko Ogata
    • Organizer
      International Congress on Mathematical Physics
    • Place of Presentation
      Santiago
    • Year and Date
      2015-07-29
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A classification of finitely correlated states2013

    • Author(s)
      Yoshiko Ogata
    • Organizer
      Disordered quantum many-body systems
    • Place of Presentation
      Banff International Research Station カナダ
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Probabilistic analysis of AF C*-systems2013

    • Author(s)
      Yoshiko Ogata
    • Organizer
      AMC 2013
    • Place of Presentation
      Busan 韓国
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2014-07-25   Modified: 2019-07-29  

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