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Research

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Field of Study

○ Global Analysis

Subject of Study

○ Spectral Geometry and Analysis on Manifolds, Dynamical systems on manifolds, Graph Theory (manifold, Schrödinger operator, spectrum, dynamical system, Riemannian geometry, graph)

Book / Paper

Academic Paper (Judged Full Paper):

1. Ruishi Kuwabara :
Eigenvalues associated with a periodic orbit of the magnetic flow,
Contemporary Mathematics, 348, 169-180, 2004.
2. Ruishi Kuwabara :
Difference spectrum of the Schrodinger operator in a magnetic field,
Mathematische Zeitschrift, 233, 3, 579-599, 2000.
(Elsevier: Scopus)
3. Ruishi Kuwabara :
Lax-type isospectral deformations on nilmanifolds,
Annals of Global Analysis and Geometry, 14, 2, 193-218, 1996.
4. Ruishi Kuwabara :
Spectra and geodesic flows on nilmanifolds, --- Reductions of Hamiltonian systems and differential operators ---,
Journal of Mathematical Society of Japan, 46, 1, 119-137, 1994.
5. Ruishi Kuwabara :
Isospectral connections on line bundles,
Mathematische Zeitschrift, 187, 4, 465-473, 1990.
6. Ruishi Kuwabara :
Spectrum of the Schrodinger operator on a line bundle over complex projective spaces,
Tohoku Mathematical Journal, 40, 2, 199-211, 1988.
7. Ruishi Kuwabara :
Spectrum of the Laplacian on vector bundles over C2π-manifolds,
Journal of Differential Geometry, 27, 2, 241-258, 1988.
8. Ruishi Kuwabara :
Band asymptotics of eigenvalues for the Zoll manifold,
Letters in Mathematical Physics, 16, 1, 19-25, 1988.
9. Ruishi Kuwabara :
A note on quantization of a free particle in the Zoll manifold,
Letters in Mathematical Physics, 9, 4, 331-336, 1985.
10. Ruishi Kuwabara :
Some spectral results for the Laplacian on line bundles over Sn,
Commentarii Mathematici Helvetici, 59, 3, 439-458, 1984.
11. Ruishi Kuwabara :
Spectrum and holonomy of the line bundle over the sphere,
Mathematische Zeitschrift, 187, 4, 481-490, 1984.
12. Ruishi Kuwabara :
Time-dependent mechanical symmetries and extended Hamiltonian systems,
Reports on Mathematical Physics, 19, 1, 27-38, 1984.
13. Ruishi Kuwabara :
On isospectral deformations of Riemannian metrics. II,
Compositio Mathematica, 47, 2, 195-205, 1982.
14. Ruishi Kuwabara :
On isospectral deformations of Riemannian metrics,
Compositio Mathematica, 40, 3, 319-324, 1980.
15. Ruishi Kuwabara :
On the characterization of flat metrics by the spectrum,
Commentarii Mathematici Helvetici, 55, 3, 427-444, 1980.
16. Ruishi Kuwabara :
Spectral invariants of linear differential operators and conservation laws of nonlinear equations,
Mathematica Japonica, 24, 4, 387-397, 1979.
17. Ruishi Kuwabara :
On the symmetry algebra of the Schrodinger wave equation,
Mathematica Japonica, 22, 2, 243-252, 1977.

Academic Paper (Unrefereed Paper):

1. Ruishi Kuwabara :
Numbers associated to symmetric differential operators and the Bernoulli numbers,
Journal of Mathematics, The University of Tokushima, 45, 27-40, 2011.
(Tokushima University Institutional Repository: 2001625,   CiNii: 1050304183900462976)
2. Ruishi Kuwabara :
On a classical-quantum correspondence for mechanics in a gauge field,
Journal of Mathematics, The University of Tokushima, 44, 33-46, 2010.
(Tokushima University Institutional Repository: 2001209,   CiNii: 1050022708923935232)
3. Ruishi Kuwabara :
A note on symmetric differential operators and binomial coefficients,
Journal of Mathematics, The University of Tokushima, 42, 1-8, 2008.
(Tokushima University Institutional Repository: 2001208,   CiNii: 1050585658877356544)
4. Ruishi Kuwabara :
A note on a heat invariant and the Ricci flow on surfaces,
Journal of Mathematics, The University of Tokushima, 40, 15-19, 2006.
(Tokushima University Institutional Repository: 2001207,   CiNii: 1050867133854067840)
5. Ruishi Kuwabara :
A Geometrical Formulation for Classical Mechanics in Gauge Fields,
Journal of Mathematics, The University of Tokushima, 39, 23-46, 2005.
(Tokushima University Institutional Repository: 2001077)
6. Ruishi Kuwabara :
On Maslov's quantization condition for mechanics in a magnetic field,
Journal of Mathematics, Tokushima University, 33, 33-54, 1999.
(Tokushima University Institutional Repository: 2000485)
7. Ruishi Kuwabara :
Correction and addendum to: On the classical and the quantum mechanics in a magnetic field,
Journal of Mathematics, Tokushima University, 30, 81-87, 1996.
(Tokushima University Institutional Repository: 2000469)
8. Ruishi Kuwabara :
On the classical and the quantum mechanics in a magnetic field,
Journal of Mathematics, Tokushima University, 29, 9-22, 1995.
(Tokushima University Institutional Repository: 2000459)
9. Ruishi Kuwabara :
A note on the deformations of Hamiltonian systems on nilmanifolds,
Journal of Mathematics, Tokushima University, 26, 19-29, 1992.
(Tokushima University Institutional Repository: 2000447)
10. Ruishi Kuwabara :
On spectra of the Laplacian on vector bundles,
Journal of Mathematics, Tokushima University, 16, 1-23, 1982.
(Tokushima University Institutional Repository: 2000406)

Review, Commentary:

1. Ruishi Kuwabara :
Spectral geometry for Schrodinger operators in a magnetic field focusing on geometrical and dynamical structures on manifolds,
American Mathematical Society Translations-Series 2, 211, 25-46, Oct. 2003.
2. Ruishi Kuwabara :
磁場におけるSchrodinger作用素のスペクトル幾何学,
数学, 54, 1, 37-57, Jan. 2002.

Proceeding of International Conference:

1. Ruishi Kuwabara :
Quantum energies and classical orbits in a magnetic field,
Conference on Spectra of Differential Operators and Inverse Problems, Kyoto, Oct. 2002.

Proceeding of Domestic Conference:

1. Ruishi Kuwabara :
磁場における力学系の量子化条件と量子エネルギー分布,
研究会「スペクトル幾何学」, Dec. 1999.
2. Ruishi Kuwabara :
磁場における力学系の量子化条件と量子エネルギー分布,
研究会「力学系と微分幾何学」, Jan. 1999.
3. Ruishi Kuwabara :
磁場における量子エネルギー分布と古典軌道,
研究会「経路空間上の解析とスペクトル」, Nov. 1997.
4. Ruishi Kuwabara :
磁場におけるシュレディンガー作用素のスペクトル幾何,
第44回幾何学シンポジウム, Aug. 1997.
5. Ruishi Kuwabara :
ベクトルポテンシャル場における古典力学と量子力学,
第35回幾何学シンポジウム, Jul. 1988.
6. Ruishi Kuwabara :
球面上の複素直線束のラプラシアンについて,
第30回幾何学シンポジウム, Aug. 1983.

Et cetera, Workshop:

1. Ruishi Kuwabara :
等スペクトル変形について (力学的視点から),
RIMS Kokyuroku, 1774, 147-162, Jan. 2012.
2. Ruishi Kuwabara :
ゲージ場における古典力学系と量子エネルギー,
数理解析研研究集会『力学系と微分幾何学』2005, Mar. 2006.
3. Ruishi Kuwabara :
On quantization condition for magnetic systems,
研究会「磁場付きシュレディンガー作用素のスペクトル解析」, Feb. 2004.
4. Ruishi Kuwabara :
Eigenvalues associated with a periodic orbit of the magnetic flow,
幾何学小研究会 岡山2003, Sep. 2003.

Report:

1. Ruishi Kuwabara :
多様体上の磁場における古典力学軌道と量子エネルギー分布,
RIMS Kokyuroku, 1255, 32-45, Kyoto, Apr. 2002.
2. Ruishi Kuwabara :
磁場における力学系の周期軌道と量子エネルギー分布,
RIMS Kokyuroku, 1180, 15-26, Kyoto, Dec. 2000.
3. Ruishi Kuwabara :
力学系の古典軌道と量子エネルギー分布,
RIMS Kokyuroku, 1119, 26-34, Kyoto, Nov. 1999.

Grants-in-Aid for Scientific Research (KAKEN Grants Database @ NII.ac.jp)

  • Studies of Correspondence between Classical and Quantum Dynamical Systems (Project/Area Number: 14540210 )
  • Spectra of Elliptic Operators on Manifolds and Classical Mechanics (Project/Area Number: 11640205 )
  • 多様体上の幾何構造および力学的構造の研究 (Project/Area Number: 07640120 )
  • 多様体上の力学系とスペクトル幾何学 (Project/Area Number: 06640149 )
  • 非線形可積分系による応用解析 (Project/Area Number: 06221111 )
  • シンプレクティック構造と数理物理学の研究 (Project/Area Number: 05640119 )
  • 超函数と数理物理学の研究 (Project/Area Number: 04640165 )
  • 数理物理学とスペクトル理論の研究 (Project/Area Number: 03640163 )
  • 可微分多様体に於ける幾何学的構造及び解析的構造 (Project/Area Number: 02640058 )
  • Search by Researcher Number (90127077)