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Estimation of tunneling times using Nelson's quantum stochastic process

Research Project

Project/Area Number 13640400
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 物理学一般
Research InstitutionFukui University

Principal Investigator

HASHIMOTO Takaaki  Applied Phys., Associate Prof., 工学部, 助教授 (30228415)

Co-Investigator(Kenkyū-buntansha) HORIBE Minoru  Associate Prof., 工学部, 助教授 (90143932)
HAYASHI Akihisa  Prof., 工学部, 教授 (80208610)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2002: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 2001: ¥3,100,000 (Direct Cost: ¥3,100,000)
Keywordsquantum stochastic process / half integer spin space / Wigner function / Nelson's method / tunneling time
Research Abstract

We have to take into account the half integer spin degree of freedom to the standart Nelson : s quantum stochastic process to estimate the tunneling time measured in the neutron spin echo experiments. In this research, we construct a quantum stochastic process using the Wigner function on a lattice phase space. The lattice composed of even lattice points represents a half integer spin space. The problem has been considered by Cohendet et al. in 1987 for odd lattice. In the first paper, we show that the Wigner functions do exit even on the even lattice contrary to the previous paper by Cohendet et al. There are infinitely many solution satisfying the conditions which reasonable Wigner function should respect and all of them are derived from one Wigner function by a orthogonal transformation. In the second paper, we propose a condition which ensures the correct marginal distributions of the Wigner function along tilted lines on a lattice. Under this condition we get the Wigner function without ambiguity if the lattice is odd. In the third manuscript we construct a quantum Markov process using the Wigner function formulated in the first and second paper. Introducing so-called ghost variables both on even and odd lattices, it is show that we can make the same kind of discussion as Cohendet et al.

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (8 results)

All Other

All Publications (8 results)

  • [Publications] A.Takami, T.Hashimoto, M.Horibe, A.Hayashi: "Wigner functions on a lattice"Physical Review A. 64. 032114,1-032114,6 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Horibe, A.Takami, T.Hashimoto, A.Hayashi: "Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice"Physical Review A. 65. 032105,1-032105,6 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A.Takami, T.Hashimoto, M.Horibe, A.Hayashi: "Wigner functions of a lattice"Physical Review A64. 032114. 1-6 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] M.Horibe, A.Takami, T.Hashimoto, A.Hayashi: "Existence of the Wigner function with correct Marginal distributions along tilted lines on a lattice"Physical Review A65. 032105. 1-6 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] A.Takami, T.Hashimoto, M.Horibe, A.Hayashi: "Wigner functions on a lattice"Physical Review A. 64. 032114,1-032114,6 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Horibe, A.Takami, T.Hashimoto, A.Hayashi: "Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice"Physical Review A. 65. 032105,1-032105,6 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Takami, T.Hashimoto, M.Horibe, A.Hayashi: "Wigner functions on a lattice"Physical Review A. 64, 3. 032114,1-032114,6 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Horibe, A.Takami, T.Hashimoto, A.Hayashi: "Existence of the Wigner function with correct marginal distributions Along tilted lines on a lattice"Physical Review A. 65, 3. 0321051,1-0321051,6 (2002)

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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