• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Quantization of unstable systems with action unbounded from below-Stochastic quantization by the use of kerneled Langevin equation

Research Project

Project/Area Number 08640393
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 素粒子・核・宇宙線
Research InstitutionWaseda University

Principal Investigator

OHBA Ichiro  Dept.of Phys., Waseda Univ., Prof., 理工学部, 教授 (10063695)

Project Period (FY) 1996 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1998: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1997: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1996: ¥300,000 (Direct Cost: ¥300,000)
Keywordsquantization of metastable systems / stochastic quantization / Kerneled Langevin equation / 'diffusive cut-off' / 不安定系の量子化 / Chern-Simons場
Research Abstract

In Parisi-Wu's quantization method, they assumed a stochasitic process according to a fictitious time which was introduced in addition to a real time. Quantum fluctuation was taken into the scheme as white noise term in the Langevin equation which describes the stochastic process. In case of systems with stable ground state, this scheme gives us the same quantum description as usual quantum mechanics in the limit of thermal equilibrium of this fictitious stochastic process.
In the stochastic quantization, they are only interested in the limit of thermal equilibrium itself, but not in the detailed process in which a stochastic process develops, as far as an arrow of fictitious time does dot reverse. Thus one can choose time scale arbitrary and take this freedom mathematically into the Langevin equation as an integration kernel. In this research, first we utilize this freedom. If we choose a kernel suitably, in the case where a system has unstable potential globally but has local metastable points, we can develop an algorism which prevents run away solution into unstable region in the Langevin simulation. Furthermore, we investigated the reason why a such mechanism does work in our modified algorism. Secondly, we cleared the mathematical structure of its mechanism analytically, and assure its utility.
In actual phenomena, though there exist many interesting unstable or meta-stable systems, we have no reliable method to quantize such systems in a definite way. The stochastic quantization utilizing the kernel is one of possibilities which are looked for and, indeed, it can work well. In this research, using a simple model, we showed mathematically the reason why it can work well, and gave it the theoretical bases. In future, we have to apply this method to more realistic problems.

Report

(4 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • Research Products

    (22 results)

All Other

All Publications (22 results)

  • [Publications] M.Kanenaga et al.: "On evaluation of path integrals for bottomless systems" Path Integrals : Dubna'96. 181-187 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] O.I.Zavialov et al.: "On quantization of systems with actions unbounded from below" Theor.Math.Phys.109(2). 1379-1387 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] I.Ohba, K.Imafuku and Y.Yamanaka: "Estimation of tunneling time based on the quantum diffusion process approach and neutron scattering" J.Phys.Soc.Jpn.65(1996)Suppl.A. 41-44 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Imafuku, I.Ohba and Y.Yamanaka: "Effects of inelastic scattering on tunneling time based on the generalized diffusion process approach" Phys.Rev.A. 56, No.2. 1142-1153 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] I.Ohba, K.Imafuku and Y.Yamanaka: "Tunneling time based on the quantum diffusion procss approach in multi-channel and optical potential cases" PRAMANA-journal of physics. 51, No.5. 603-614 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] I.Ohba: "A novel method to quantize systems of damped motion" Foundations of Physics. 27, No.12. 1725-1738 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Namiki, I.Ohba, K.Maeda and Y.Aizawa, Eds.: "Quantum Physics, Chaos Theory, and Cosmology" American Institute of Physics, 311 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 並木美喜雄・大場一郎: "「散乱の量子力学」" 岩波書店, 349 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Kanenaga, A.I.Kirillov, V.Yu.Mamakin, M.Namiki, I.Ohba, E.V.Polyachenko and O.I.Zavialov: "On evaluation of path integrals for bottomless systems" Path Integrals : Dubna'96. 181-187 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] O.I.Zavialov, M.Kanenaga, A.I.Kirillov, V.Yu.Mamakin, M.Namiki, I.Ohba and E.V.Polyachenko: "On quantization of systems with actions unbounded from below" Theor.Math.Phys.109, No.2. 1379-1387 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] I.Ohba, K.Imafuku and Y.Yamanaka: "Estimation of tunneling time based on the quantum diffusion process approach and neutron scattering" J.Phys.Soc.Jpn.65 Suppl.A. 41-44 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Imafuku, I.Ohba and Y.Yamanaka: "Effects of inelastic scattering on tunneling time based on the generalized diffusion process approach" Phys.Rev.A. 56, No.2. 1142-1153 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] I.Ohba, K.Imafuku, and Y.Yamanaka: "Tunneling time based on the quantum diffusion procss approach in multi-channel and optical potential cases" PRAMANA-journal of physics.51, No.5. 603-614 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] I.Ohba: "A novel method to quantize systems of damped motion" Foundations of Physics. 27, No.12. 1725-1738 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] I.Ohba: "A novel method to quantize systems of damped motion and its application to Nelson's quantum mechanics" Symmetries in Science X. Plenum Press. 325-336 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Nakamiki, I.Ohba, K.Maeda and Y.Aizawa, Eds.: Quantum Physics, Chaos Theory, and Cosmology. American Institute of Physics, (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Namiki and I.Ohba: Quantum Mechanics in Scattering Process (in Japanese). Iwanami-syoten, (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] I.Ohba,K.Imafuku and Y.Yamanaka: "Tunneling time based on the quantum diffusion process approach in multi-channel and optical potential cases" PRAMANA-jounal of physics. Vol.51,No.5. 603-614 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] Ichiro Ohba: "A novel method to quantize systems of damped motion and its application to Nelson's quantum mechanics" Symmetries in Science X,Plenum Press. 325-336 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Kanenaga, A.I.Kirillov, V.Yu.Mamakin, M.Namiki, I.Ohba, E.V.Polyachenko and O.I.Zavialov: Path Integrals: Dubna'96. 181-187 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] O.I.Zavialov, M.Kanenaga, A.I.Kirillov, V.Yu.Mamakin.M.Namiki, I.Ohba and E.V.Polyachenko: "On quantization of systems with actions unbounded from below" Theor.Math.Phys.109(1). 1371-1382 (1996)

    • Related Report
      1997 Annual Research Report
  • [Publications] M.Kanenaga,A.I.Kirillov,V.Yu.Mamakin,M.Namiki,I.Ohba,E.V.Polyachenko and O.I.Zavialov: "On quantization of systems with actions unbounded from below" Theor.Math.Phys.(Moscow). (in press). (1996)

    • Related Report
      1996 Annual Research Report

URL: 

Published: 1996-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi