Transition probability among quantum states and their asymptotic behavior

• Project/Area Number: 26400113
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nagoya University
• Principal Investigator: Yamagami Shigeru 名古屋大学, 多元数理科学研究科, 教授 (90175654)
• Co-Investigator(Renkei-kenkyūsha): MATSUI Taku 九州大学, 数理学研究院, 教授 (50199733) ; NAGISA Masaru 千葉大学, 理学研究科, 教授 (50189172) ; HIAI Fumio 東北大学, 名誉教授 (30092571)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 量子状態 / 遷移確率 / 非可換積分論 / quantum algebra / Weyl unitary / projection / quantum probability / trace formula / quantum state / CCR algebra / CCR代数

Outline of Final Research Achievements

In a mathematical treatment of quantum phenomena ranging from finite to infinite freedom systems,representation theory of relevant quantum algebras bears fundamental importance and lots of investigations have been pursued.
In the present research, we focus on quasi-free states, which are quantum analogues of classical Gaussian measures,together with transition probability among them and have obtained several remarkable results concerning the related quantum probability and the dichotomy criterion on quasi-free representations.

Research Products

• [Journal Article] Around trace formulas in non-commutative integration (2018)
  • Author(s): Shigeru Yamagami
  • Journal Title: Publ. RIMS Kyoto Univ. Volume: 54 Issue: 1 Pages: 181-211
  • DOI: 10.4171/prims/54-1-7
  • Peer Reviewed
• [Presentation] Around tensor product measures (2017)
  • Author(s): Shigeru Yamagami
  • Organizer: Workshop on Harmonic Analysis
  • Place of Presentation: 奈良女子大学
  • Year and Date: 2017-03-28
  • Invited
• [Presentation] On the Haagerup's trace formula in non-commutative integration (2017)
  • Author(s): 山上 滋
  • Organizer: RIMS meeting, Recent Developments in Operator Algebras
• [Remarks] SSS on Mathematics
  • URL: http://math.nagoya-u.ac.jp/~yamagami/
• [Remarks] SSS on Mathematics
  • URL: http://www.math.nagoya-u.ac.jp/~yamagami/