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

A Study of Quantum Transport Phenomena by use of Multipole Expansions

Research Project

Project/Area Number07640398
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 InstitutionKYOTO UNIVERSITY

Principal Investigator

SHIZUYA Ken-ichi  Kyoto University, Yukawa Inst.for Theor.Phys., Professor, 基礎物理学研究所, 教授 (50154216)

Project Period (FY) 1995 – 1997
Project Status Completed(Fiscal Year 1997)
Budget Amount *help
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 1997 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1996 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1995 : ¥700,000 (Direct Cost : ¥700,000)
KeywordsQuantum Transport / Quantum Hall Effect / Multipole Expansion / Edge Current / Gauge Theory / Symmetry / Localization / de Haas-van Alphen Oscillation
Research Abstract

The key idea of multipole expansions lies in a systematic classification of long-and short-distance dynamics and is useful in many branches of physics, especially in the description of quantum transport phenomena. Under a Grant-Aid over the past three years, we have studied some problems pertaining to the foundation of the quantum Hall effect by use of multipole expansions.
1. The current distribution in a Hall sample is a subject of interest. We pointed out earlier that a considerable portion of the Hall current would flow along the sample edges as a consequence of expulsion out of the localization-dominated sample interior. Crucial to this theoretical consideration is exact compensation of the Hall current among extended and localized states. A paper has been presented to show that the current-compensation theorem actually rests on the principle of gauge invariance.
2. A numerical experiment has been made of the current distributions in finite-width Hall bars with disorder, with the result in support of the theoretical consideration mentioned above. It is confirmed that the edge states are not the principal carriers of the Hall current. A paper is now in preparation.
3. A mechanism for the breakdown of the quantum Hall effect, suggested from the above numerical experiment, is now under investigation.
4. A numerical analysis has also been made for a clean Hall bar. The edge current is observed to alternate in direction with the emergence of the edge states, in close connection to the de Haasvan Alphen oscillation.
5. A paper has been presented to show that macroscopic electromagnetic properties of Hall-electron systems are neatly summarized in the form of a W_* gauge theory.

Report

(4results)
  • 1997 Annual Research Report   Final Research Report Summary
  • 1996 Annual Research Report
  • 1995 Annual Research Report

Research Products

(16results)

All Other

All Publications

  • [Publications] K.Shizuya: "W_∞ gauge theory and the quantum Hall effect" Physical Review. B52. 2747-2753 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] 静谷 謙一: "整数量子ホール効果" 数理科学. 391. 39-45 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Shizuya: "Current compensation and edge current in the quantum Hall effect" Proceedings of "Frontiers In Quantum Field Theory". 379-383 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Shizuya: "Current distributions and the de Haas-van Alphen oscillation in a planar system of Hall electrons" International Journal of Modern Physics. B11. 1799-1812 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Shizuya: "Localization and exact current compensation in the quantum Hall effect" Physical Review. B57. 1731-1739 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Shizuya: "W_* gauge theory and the quantum Hall effect." Physical Review. B52. 2747-2753 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Shizuya: "Integer Quantum Hall Effect (in Japanese)" Suuri Kagaku. No.391. 391-340 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Shizuya: "Current compensation and edge current in the quantum Hall effect" Proceedings of "Frontiers In Quantum Field Theory". 370-383 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Shizuya: "Current distributions and the de Haas-van Alphen oscillationin a planar system of Hall electrons" International Journal of Modern Physics. B11. 1799-1812 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Shizuya: "Localization and exact current compensation in the quantum Hall effect" Physical Review. B57. 1731-1739 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1997 Final Research Report Summary
  • [Publications] K.Shizuya: "Current distributions and the de Haas-van Alphen oscillation in a planar system of Hall electrons" International Journal of Modern Physics. B11. 1799-1812 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Shizuya: "Localization and exact current compensation in the quantum Hall effect" Physical Review. B57. 1731-1739 (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] K.Shizuya: "Current compensation and edge current in the quantum Hall effect" Proceedings of Frontiers In Quantum Field Theory. 379-383 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] K.Shizuya: "Current distributions and the de Haas-van Alphen oscillation in a planar system of Hall electrons" International Journal of Modern Physics B. (掲載予定). (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] K. Shizuya: "W_∞gauge theory and thequantum Hall effect" Physical Review. B52. 2747-2753 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 静谷謙一: "整数量子ホール効果" 数理科学. 391. 39-45 (1996)

    • Related Report
      1995 Annual Research Report

URL :

Published : 1995-04-01   Modified : 2016-04-21  

Information FAQ News Terms of Use

Powered by NII kakenhi