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Research Activity

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, Vol.348, 169-180, 2004.
2.Ruishi Kuwabara :
Difference spectrum of the Schrodinger operator in a magnetic field,
Mathematische Zeitschrift, Vol.233, No.3, 579-599, 2000.
(Elsevier: Scopus)
3.Ruishi Kuwabara :
Lax-type isospectral deformations on nilmanifolds,
Annals of Global Analysis and Geometry, Vol.14, No.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, Vol.46, No.1, 119-137, 1994.
5.Ruishi Kuwabara :
Isospectral connections on line bundles,
Mathematische Zeitschrift, Vol.187, No.4, 465-473, 1990.
6.Ruishi Kuwabara :
Spectrum of the Schrodinger operator on a line bundle over complex projective spaces,
Tohoku Mathematical Journal, Vol.40, No.2, 199-211, 1988.
7.Ruishi Kuwabara :
Spectrum of the Laplacian on vector bundles over C-manifolds,
Journal of Differential Geometry, Vol.27, No.2, 241-258, 1988.
8.Ruishi Kuwabara :
Band asymptotics of eigenvalues for the Zoll manifold,
Letters in Mathematical Physics, Vol.16, No.1, 19-25, 1988.
9.Ruishi Kuwabara :
A note on quantization of a free particle in the Zoll manifold,
Letters in Mathematical Physics, Vol.9, No.4, 331-336, 1985.
10.Ruishi Kuwabara :
Some spectral results for the Laplacian on line bundles over Sn,
Commentarii Mathematici Helvetici, Vol.59, No.3, 439-458, 1984.
11.Ruishi Kuwabara :
Spectrum and holonomy of the line bundle over the sphere,
Mathematische Zeitschrift, Vol.187, No.4, 481-490, 1984.
12.Ruishi Kuwabara :
Time-dependent mechanical symmetries and extended Hamiltonian systems,
Reports on Mathematical Physics, Vol.19, No.1, 27-38, 1984.
13.Ruishi Kuwabara :
On isospectral deformations of Riemannian metrics. II,
Compositio Mathematica, Vol.47, No.2, 195-205, 1982.
14.Ruishi Kuwabara :
On isospectral deformations of Riemannian metrics,
Compositio Mathematica, Vol.40, No.3, 319-324, 1980.
15.Ruishi Kuwabara :
On the characterization of flat metrics by the spectrum,
Commentarii Mathematici Helvetici, Vol.55, No.3, 427-444, 1980.
16.Ruishi Kuwabara :
Spectral invariants of linear differential operators and conservation laws of nonlinear equations,
Mathematica Japonica, Vol.24, No.4, 387-397, 1979.
17.Ruishi Kuwabara :
On the symmetry algebra of the Schrodinger wave equation,
Mathematica Japonica, Vol.22, No.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, Vol.45, No.0, 27-40, 2011.
(Tokushima University Institutional Repository: 84170,   CiNii: 110008729450)
2.Ruishi Kuwabara :
On a classical-quantum correspondence for mechanics in a gauge field,
Journal of Mathematics, The University of Tokushima, Vol.44, 33-46, 2010.
(Tokushima University Institutional Repository: 74316,   CiNii: 110007873782)
3.Ruishi Kuwabara :
A note on symmetric differential operators and binomial coefficients,
Journal of Mathematics, The University of Tokushima, Vol.42, 1-8, 2008.
(Tokushima University Institutional Repository: 74212,   CiNii: 110007127174)
4.Ruishi Kuwabara :
A note on a heat invariant and the Ricci flow on surfaces,
Journal of Mathematics, The University of Tokushima, Vol.40, No.0, 15-19, 2006.
(Tokushima University Institutional Repository: 74187,   CiNii: 110004849833)
5.Ruishi Kuwabara :
A Geometrical Formulation for Classical Mechanics in Gauge Fields,
Journal of Mathematics, The University of Tokushima, Vol.39, 23-46, 2005.
(Tokushima University Institutional Repository: 49027)
6.Ruishi Kuwabara :
On Maslov's quantization condition for mechanics in a magnetic field,
Journal of Mathematics Tokushima University, Vol.33, 33-54, 1999.
(Tokushima University Institutional Repository: 135)
7.Ruishi Kuwabara :
Correction and addendum to: On the classical and the quantum mechanics in a magnetic field,
Journal of Mathematics Tokushima University, Vol.30, 81-87, 1996.
(Tokushima University Institutional Repository: 119)
8.Ruishi Kuwabara :
On the classical and the quantum mechanics in a magnetic field,
Journal of Mathematics Tokushima University, Vol.29, 9-22, 1995.
(Tokushima University Institutional Repository: 109)
9.Ruishi Kuwabara :
A note on the deformations of Hamiltonian systems on nilmanifolds,
Journal of Mathematics Tokushima University, Vol.26, 19-29, 1992.
(Tokushima University Institutional Repository: 97)
10.Ruishi Kuwabara :
On spectra of the Laplacian on vector bundles,
Journal of Mathematics Tokushima University, Vol.16, 1-23, 1982.
(Tokushima University Institutional Repository: 56)

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, Vol.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, Vol.54, No.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, Vol.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, Vol.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, Vol.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, Vol.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)