Analysis on equilibrium/nonequilibrium statistical mechanics by theory of operator algebra

• Project/Area Number: 21740124
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: The University of Tokyo
• Principal Investigator: OGATA Yoshiko 東京大学, 数理(科)学研究科(研究院), 准教授 (80507955)
• Project Period (FY): 2009-04-01 – 2013-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 量子統計力学 / 非平衡統計力学 / 量子スピン系 / 仮説検定 / 量子系 / 作用素環論 / Evans-Searles / 大偏差原理 / 平均場モデル

Research Abstract

I studied properties of macroscopic observables in quantum spin systems and time reversal symmetry in quantum nonequilibrium systems. We showed that it is possible to approximate macroscopic observables in quantum spin systems with commuting matrices. We also showed that some known function in nonequilibrium statistical mechanics of quantum systems can be interpreted as a function that represent the rate of broken time reversal symmetry.

Research Products

• [Journal Article] Approximating macroscopic observables in quantum spin systems with commuting matrices (2013)
  • Author(s): Y. Ogata
  • Journal Title: J. Funct. Anal Volume: 264 Pages: 2005-2033
• [Journal Article] The Shannon McMillan Theorem for AF C*-systems (2013)
  • Author(s): Yoshiko Ogata
  • Journal Title: Letters in Mathematical Physics Volume: 103 Pages: 1367-1376
  • Peer Reviewed
• [Journal Article] Normal states of type III factors (2013)
  • Author(s): Y. Kawahigashi Y. Ogata E. Stormer
  • Journal Title: Pacific Journal of Mathematics Volume: 267 Pages: 131-139
  • Peer Reviewed
• [Journal Article] Approximating macroscopic observables in quantum spin systems with commuting matrices (2013)
  • Author(s): Yoshiko Ogata
  • Journal Title: J. Funct. Anal. Volume: 264 Issue: 9 Pages: 2005-2033
  • DOI: 10.1016/j.jfa.2013.01.021
• [Journal Article] Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics (2012)
  • Author(s): V. Jaksic, Y. Ogata, C.-A. Pillet, R. Seiringer
  • Journal Title: Rev. Math. Phys Volume: 24 Pages: 1230002-1230002
• [Journal Article] Quantum Hypothesis Testing and Non-Equilibrium Statistical Mechanics (2012)
  • Author(s): Yoshiko Ogata
  • Journal Title: Rev. Math. Phys. Volume: 24 Issue: 06 Pages: 1230002-1230002
  • DOI: 10.1142/s0129055x12300026
• [Journal Article] A Generalization of Powers-St￥o rmer Inequality (2011)
  • Author(s): Y. Ogata
  • Journal Title: Lett. Math. Phys Volume: 97 Pages: 339-346
• [Journal Article] A Generalization of Powers-Stormer Inequality (2011)
  • Author(s): Yoshiko Ogata
  • Journal Title: Lett. Math. Phys. Volume: 97 Issue: 3 Pages: 339-346
  • DOI: 10.1007/s11005-011-0504-y
• [Journal Article] Ruelle-Lanford functions and large deviations for asymptotically decoupled quantum systems (2011)
  • Author(s): Yoshiko Ogata Luc ReyBellet
  • Journal Title: Reviews in Mathematical Physics Volume: 23-2 Pages: 211-232
  • Peer Reviewed
• [Journal Article] Large deviations in quantum spin chains (2010)
  • Author(s): Yoshiko Ogata
  • Journal Title: Commun.Math.Phys 296 Pages: 35-68
  • Peer Reviewed
• [Presentation] Probabilistic analysis of AF C*-systems (2013)
  • Author(s): Yoshiko Ogata
  • Organizer: AMC 2013
  • Place of Presentation: プサン
  • Invited
• [Presentation] Hypothesis testing and non-equilibrium statistical mechanics (2012)
  • Organizer: Arizona School of Analysis and Mathematical Physics
  • Place of Presentation: Tucson, Arizona
• [Presentation] Non-Equilibrium Statistical Mechanics (2012)
  • Organizer: Conference on von Neumann Algebras and Related Topics
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] 量子スピン系における確率解析とその応用 (2011)
  • Organizer: 日本数学会
  • Place of Presentation: 信州大学
• [Presentation] Approximating macroscopic observables in quantum spin systems with commuting matrices (2011)
  • Organizer: Conference on C*-Algebras and Related Topics
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Approximating macroscopic observables in quantum spin systems with commuting matrices (2011)
  • Organizer: Summer school on "Non-equilibrium statistical mechanics"
  • Place of Presentation: Universite de Montreal Canada
• [Presentation] Large Deviations in Quantum Spin Chains (2009)
  • Author(s): Yoshiko Ogata
  • Organizer: 大規模相互作用系の確率解析
  • Place of Presentation: 東京大学数理科学研究科
  • Year and Date: 2009-10-07