For details, please look at the web pages of the members.
2024
Yasutaka Hanada and Akira Shudo
Quantum Tunneling and Complex Dynamics in the Suris's Integrable Map
Entropy, 26 (2024) 414 (16 pages)
Makoto Ohshika, Domenico Lippolis, Akira Shudo,
Escape-rate response to noise of all amplitudes in leaky chaos
Hajime Yoshino, Normann Mertig, and Akira Shudo
Uniform hyperbolicity of a class of scattering maps
Nonlinearity 36 (2023) 5097–5143
Ryonosuke Koda and Akira Shudo
Ergodicity of complex dynamics and quantum tunneling in nonintegrable systems
Phys.Rev.E, 108 (2023) 054219 (25 pages)
Domenico Lippolis and Akira Shudo
Towards the Resolution of a Quantized Chaotic Phase-Space: The Interplay of Dynamics with Noise
Entropy, 25(3) (2023) 411 (16 pages)
Yasutaka Hanada, Kensuke S. Ikeda and Akira Shudo
Dynamical tunneling across the separatrix
Phys.Rev.E, 108 (2023) 064210 (17 pages)
Riku Iijima, Ryonosuke Koda, Yasutaka Hanada and Akira Shudo
Quantum tunneling in ultra-near-integrable systems
Phys. Rev. E 106 (2022) 064205 (11 pages)
Yutaka Okabe and Akira Shudo
Spread of variants of epidemic disease based on the microscopic numerical simulations on networks: Supplementary Information
Scientific Reports 12 (2022) 523 (9 pages)
Ryonosuke Koda and Akira Shudo
Complexified stable and unstable manifolds and chaotic tunneling
J. Phys. A: Math. Theor. 55 (2022) 174004 (38 pages)
Kensuke Yoshida, Giulio Casati, Shingo Watanabe and Akira Shudo
Sublinear diffusion in the generalized triangle map
Phys. Rev. E 106 (2022) 014206 (10 pages)
Domenico Lippolis, Akira Shudo, Kensuke Yoshida, and Hajime Yoshino
Scarring in Classical Chaotic Dynamics
Phys. Rev. E. 103 (2021) L050202 (6 pages)
Kensuke Yoshida, Hajime Yoshino, Akira Shudo and Domenico Loppolis
Eigenfunctions of the Perron- Frobenius operator and the finite-time Lyapunov exponents in uniformly hyperbolic area-preserving maps
J. Phys. A: Math. Theor. 45 (2021) 285701 (30 pages)
Yutaka Okabe and Akira Shudo
Microscopic numerical simulations of epidemic models on networks
Naoaki Shimada and Akira Shudo
Numerical verification of the exact WKB formula for the general- ized Landau-Zener-Stueckelberg problem
Phys. Rev. A.12(2020) 022213 (25 pages)
Yutaka Okabe and Akira Shudo
A Mathematical Model of Epidemics―A Tutorial for Students
Mathematics. 8 (2020) 1174 (16 pages)
Atushi Tanaka, Takaaki Nakamura and Taksu Cheon
Generating a nonequilibrium stationary state from a ground-state condensate through an almost adiabatic cycle
Phys. Rev. A. 102(2020) 013308
Yasutaka Hanada, Akira Shudo, Teruaki Okushima and Kensuke S. Ikeda
Renormalized Perturbation Approach to Instanton-noninstanton Transition in Nearly-integrable Tunneling Process
Phys. Rev. E. 99 (2019) 052201 (18 pages)
Hajime Yoshino, Ryota Kogawa, and Akira Shudo
Uniform Hyperbolicity of a Scattering Map with Lorentzian Potential
Condens. Matter 5 (2020) 1-25
Normann Mertig and Akira Shudo
Open quantum maps from complex scaling of kicked scattering systems
Phys. Rev. E. 97 (2018) 042216 (23pages)
Akira Akaishi, Kazuki Aoki and Akira Shudo
Hierarchical structure in sharply-divided phase space for the piecewise linear map
Physical Review E 95 (2017) 052207
Hiromitsu Harada, Amaury Mouchet and Akira Shudo,
Riemann surfaces of complex classical trajectories and tunnelling splitting in one-dimensional systems,
J. Phys. A: Math. Theor. 30 (2017)– 435207 (27pp) (preprint at arXiv).
Atushi Tanaka and Taksu Cheon
Path topology dependence of adiabatic time evolution
in Functional Analysis and Operator Theory for Quantum Physics, eds. J. Dittrich, H. Kovarik, A. Laptev (EMS Publ. House, 2017), p.531-542 (preprint at arXiv).
Atushi Tanaka and Taksu Cheon
Exotic Quantum Holonomy ― a Topological Aspect of Adiabatic/ Nonadiabatic Quantum Dynamics
Butsuri 72 (2017), 240-245.
Normann Mertig, Julius Kullig, Clemens Löbner, Arnd Bäcker, and Roland Ketzmerick
Perturbation-free prediction of resonance-assisted tunneling in mixed regular-chaotic systems
Physical Review E 94 (2016) 062220 (preprint at arXiv).
Akira Shudo and Kensuke S Ikeda,
Toward Pruning Theory of the Stokes Geometry for the Quantum Henon Map,
Nonlinearity 29 (2016) 375–425.
Akira Shudo, Yasutaka Hanada and Kensuke S. Ikeda
Quantum tunneling in nonintegrable systems:beyond the leading order semiclassical description
RIMS Kôkyûroku Bessatsu, B57 (2016) 27-38
Atushi Tanaka and Taksu Cheon
Complete population inversion of Bose particles by an adiabatic cycle,
New Journal of Physics 18 (2016) 045023 (7pages) (preprint at arXiv).
Sho Kasumie, Manabu Miyamoto and Atushi Tanaka
Adiabatic excitation of a confined particle in one dimension with a variable infinitely sharp wall
Physical Review A 93 (2016) 042105 (5pages) (preprint at arXiv).
首藤 啓
面積保存写像の解析力学
『数理科学』(2016) 11月号28-34.
Yasutaka Hanada, Akira Shudo and Kensuke S. Ikeda,
Origin of the enhancement of tunneling probability in the nearly integrable system,
Phys. Rev. E. 91 (2015) 042913 (16 pages)
Akira Shudo and Ruriko Ohashi,
Numerical verification of the exact WKB formula for the generalized Landau-Zener-Stueckelberg problem,
Advances in Science, Technology and Environmentology. Special issue : ASTE (Waseda University) B11 (2015) 75-80.
Yasutaka Hanada, Akira Shudo and Kensuke S. Ikeda,
Resonance-assisted tunneling in integrable and nonintegrable systems,
Advances in Science, Technology and Environmentology. Special issue : ASTE (Waseda University) B11 (2015) 127-130.
Hiromitsu Harada and Akira Shudo,
Non-linear resonances and singularity structures of complex classical dynamics,
Advances in Science, Technology and Environmentology. Special issue : ASTE (Waseda University) B11 (2015) 131-134.
Atushi Tanaka and Taksu Cheon,
A topological formulation for exotic quantum holonomy,
Nanosystems: physics, chemistry, mathematics 6 (2015) 786–792 (preprint at arXiv).
Atushi Tanaka and Taksu Cheon,
Bloch vector, disclination and exotic quantum holonomy,
Physics Letters A 379 (2015) 1693–1698 (preprint at arXiv).
Julius Kullig, Clemens Löbner, Normann Mertig, Arnd Bäcker and Roland Ketzmerick
Integrable approximation of regular regions with a nonlinear resonance chain,
Phys. Rev. E 90 (2014) 052906 (9 pages).
Akira Shudo, Yasutaka Hanada, Teruaki Okushima and Kensuke S. Ikeda,
Instanton-noninstanton transition in nonintegrable tunneling processes: A renormalized perturbation approach,
Europhys. Lett., 108 (2014) 50004.
Takashi Hotta and Akira Shudo,
Chaos in Jahn-Teller Rattling,
J. Phys. Soc. Jpn. 83 (2014) 083705.
Akira Shudo,
The Stokes geometry of the quantum Hénon map in the horseshoe regime,
RIMS Kokyuroku Bessatsu, B52 (2014) pp.263-282.
首藤 啓
「単純なカオス」と「複雑なカオス」
『サイエンスネット』第50号 (2014) pp14-15.
Atushi Tanaka, Sang Wook Kim and Taksu Cheon,
Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops,
Physical Review E 89 (2014) 042904-1–042904-8 (preprint at arXiv).
N. Mertig, A. Bäcker, S. Löck, R. Ketzmerick and A. Shudo,
Complex paths for regular-to-chaotic tunneling rates,
Europhys. Lett. 102 (2013) 10005 (5 pages).
Taksu Cheon, Atushi Tanaka and Ondrej Turek,
Examples of quantum holonomy with topology change,
Acta Polytechnica 53 (2013) 410–415 (preprint at arXiv).
Atushi Tanaka, Nobuhiro Yonezawa and Taksu Cheon,
Exotic quantum holonomy and non-Hermitian degeneracies in two-body Lieb-Liniger model,
Journal of Physics A: Mathematical and Theoretical 46 (2013) 315302-1–315302-17 (preprint at arXiv).
Nobuhiro Yonezawa, Atushi Tanaka and Taksu Cheon,
Quantum holonomy in Lieb-Liniger model,
Physical Review A 87 (2013) 062113-1–062113-6 (preprint at arXiv).
A. Shudo and K. S. Ikeda,
Tunneling effect and natural boundary of invariant torus,
Phys. Rev. Lett. 109 (2012) 154102.
A. Ishikawa, A. Tanaka, A. Shudo, and K. S. Ikeda,
Diffraction and tunneling in systems with mixed phase space
Phys. Rev. E. 86 (2012) 036208 (14 pages).
A. Ishii, A. Akaishi, A. Shudo, and H. Schomerus,
Weyl law for open systems with sharply divided mixed phase space,
Phys. Rev. E, 85 (2012) 046203 (7 pages).
Akiyuki Ishikawa, Atushi Tanaka, Yasutaka Hanada and Akira Shudo,
Flooding of wave functions in multi-dimensional mixed systems and the possibility of experimental observation,
AIP Conference Proceedings Vol. 1468, Proceedings of “Let's Face Chaos Through Nonlinear Dynamics” 8th International Summer School and Conference,Edited by M. Robnik and V. Romanovski, (2012) pp.340-349.
Atushi Tanaka, Taksu Cheon and Sang Wook Kim,
Gauge invariants of eigenspace and eigenvalue anholonomies: Examples in hierarchical quantum circuits,
Journal of Physics A: Mathematical and Theoretical 45 (2012) 335305-1–335305-20 (preprint at arXiv).
A. Akaishi, M. Hirata, K. Yamamoto and A. Shudo,
Meeting time distributions in Bernoulli systems,
J. Phys. A : Math. Theor. 44 (2011) 375101 (12 pages)
首藤 啓
『古典と量子の間』
岩波書店 (2011).
Akira Shudo and Kensuke S. Ikeda
Complex semiclassical approach to chaotic tunneling
in Dynamical Tunneling edited by Srihari Keshavamurthy and Peter Schlagheck (CRC Press, 2011) Chapter 7, pp.139-176.
首藤 啓
『数理物理 私の研究』
(荒木 不二洋, 大矢 雅則, 江口 徹 編, 2011 シュプリンガー)
Takahisa Harayama and Akira Shudo,
Boundary element method and isospectrality in quantum billiards,
『物性研究』97 (2011) 414-420.
Atushi Tanaka,
Adiabatic Theorem for Discrete Time Evolution,
Journal of the Physical Society of Japan 80 (2011) 125002-1–125002-2 (preprint at arXiv).
Atushi Tanaka, Sang Wook Kim and Taksu Cheon,
Eigenvalue and eigenspace anholonomies in hierarchical systems,
Europhysics Letters 96 (2011) 10005-p1–10005-p6 (preprint at arXiv).
A. Ishikawa, A. Tanaka and A. Shudo,
Dynamical tunneling in many-dimensional chaotic systems,
Phys. Rev. Lett., 104 (2010) 224102 (4 pages).
Atushi Tanaka and Taksu Cheon,
Quantum anholonomies in time-dependent Aharonov-Bohm rings,
Physical Review A 82 (2010) 022104-1–022104-6 (preprint at arXiv).
Sang Wook Kim, Taksu Cheon and Atushi Tanaka,
Exotic quantum holonomy induced by degeneracy hidden in complex parameter space,
Physics Letters A 374 (2010) 1958–1961 (preprint at arXiv).
Atushi Tanaka and Kae Nemoto,
Adiabatic quantum computation along quasienergies,
Physical Review A 81 (2010) 022320-1–022320-8 (preprint at arXiv).
A. Akaishi and A. Shudo,
Accumulation of unstable periodic orbits and the stickiness inthe two-dimensional piecewise linear map,
Phys. Rev. E, 80 (2009) 066211 (12 pages).
A. Ishikawa, A. Tanaka and A. Shudo,
Recovery of chaotic tunneling due to destruction of dynamical localization by an external noise,
Phys. Rev. E, 80 (2009) 046204 (13 pages).
A. Shudo, Y. Ishii and K. S. Ikeda,
Julia set and chaotic tunneling II,
J. Phys.A: Math. Theor. 42 (2009) 265102 (34pages).
A. Shudo, Y. Ishii and K. S. Ikeda,
Julia sets and chaotic tunneling I,
J. Phys.A: Math. Theor. 42 (2009) 265101 (26pages).
Taksu Cheon, Atushi Tanaka and Sang Wook Kim,
Exotic quantum holonomy in Hamiltonian systems,
Physics Letters A 374 (2009) 144–149 (preprint at arXiv).
Atushi Tanaka and Taksu Cheon,
A Unified Theory of Quantum Holonomies,
Annals of Physics (NY) 324 (2009) 1340–1359 (preprint at arXiv).
Taksu Cheon and Atushi Tanaka,
New anatomy of quantum holonomy,
Europhysics Letters 85 (2009) 20001-p1–20001-p5 (preprint at arXiv).
A. Shudo and K. S. Ikeda,
Stokes geometry for the quantum Hénon map,
Nonlinearity, 21 (2008) 1831-1880.
A. Shudo, Y. Ishii and K. S. Ikeda,
Chaos Attracts Tunneling Trajectories : A universal mechanism ofchaotic tunneling,
Europhys. Lett. 81 (2008) 50003 (5pages).
T. Onishi, A. Shudo and K. S. Ikeda,
Trajectory descriptions of ionaizaton processes in laser fields,
"Progress in Ultrafast Intense Laser Science III" (Springer, 2008) pp.33-52.
首藤 啓
ハミルトン系における遅い緩和：その数値的検証を巡るいくつかの話題
物性研究 (2008) in press.
首藤 啓
量子多項式写像のストークス幾何学における新しいストークス曲線の役割
数理解析研究所講究録 (2008) in press.
A. Akaishi and A. Shudo,
Unstable Periodic Orbits Accumulating to the Boundary between Torusand Chaos in Sharply Divided Phase Space,
AIP Conference Proceedings Vol. 1076, Proceedings of“Let's Face Chaos Through NonlinearDynamics” 7th International Summer School and Conference, Edited by M. Robnik and V. Romanovski, (2008) pp.1-4.
A. Akaishi and A. Shudo,
Algebraic correlations of hard spheres in a rectangular box,
AIP Conference Proceedings, 982 (2008) 744-747.
T. Aoki, N. Honda, T. Kawai, T. Koike, S. Sasaki, A. Shudo and Y. Takei,
Virtual turning points -- A gift of microlocal analysis to the exact WKB analysis --,
(Springer, 2007) pp.29-43.
A. Shudo,
A Role of Virtual Turning Points and New Stokes Curves in Stokes Geometry of the Quantum Hénon Map,
(Springer, 2007) pp.251-264.
A. Ishikawa, A. Tanaka and A. Shudo,
Quantum suppression of chaotic tunneling,
J. Phys.A: Math. Theor. 40 (2007) F1-F9.
A. Shudo,
Virtual Turning Points and New Stokes Curves in Stokes Geometry of Quantum Hénon map,
Nonlinear Phenomena in Complex Systems, 10 (2007) 41-50.
Manabu Miyamoto and Atushi Tanaka,
Cheon's anholonomies in Floquet operators,
Physical Review A 76 (2007) 042115-1–042115-9 (preprint at arXiv).
Atushi Tanaka and Manabu Miyamoto,
Quasienergy anholonomy and its application to adiabatic quantum state manipulation,
Physical Review Letters 98 (2007) 160407-1–160407-4 (preprint at arXiv).
H. Tanaka and A. Shudo,
Recurrence time distribution in mushroom billiards with parabolic hat,
Phys. Rev. E 74 (2006) 036211 (5 pages).
A. Shudo, K. Ichiki and S. Saito,
Origin of slow relaxation in liquid water dynamics: A possible scenario for the presence of bottleneck in phase space,
Europhys. Lett. 73 (2006) 826-832.
首藤 啓
多準位非断熱遷移問題における仮想的変わり点と新しいストークス曲線の役割について
数理解析研究所講究録1516 (2006) 9-20.
Y. Okada and A. Shudo,
Inside-outside duality and isospectrality of planar billiards,
数理解析研究所講究録1500 (2006) 81-94.
A. Shudo,
Complex dynamics and quantum tunneling in the presence of chaos,
数理解析研究所講究録1493 (2006) 118-134.
首藤 啓
『物理学大事典』
（鈴木増雄 ・荒船次郎 ・和達三樹 編，2006 朝倉書店）667-670. 首藤 啓
（書評）「ランダム行列理論の基礎」永尾太郎著
『数理科学』 (2006) 1月号 66.
Atushi Tanaka,
Determination of the border between "shallow" and "deep" tunneling regions for Herman-Kluk method by asymptotic approach,
Physical Review A 73 (2006) 024101-1–024101-4 (preprint at arXiv).
Y. Okada and A. Shudo, T. Harayama and S. Tasaki,
On the boundary element method for billiards with corners,
J. Phys.A: Math. Theor. 38 (2005) 6675-6688.
T. Aoki, T. Kawai, S. Sasaki, A. Shudo and Y. Takei,
Virtual turning points and bifurcation of Stokes curves for higher order ordinary differential equations,
J. Phys.A. : Math. Theor. 38 (2005) 3317-3336.
Y. Okada and A. Shudo, T. Harayama and S. Tasaki,
"Can one hear the shape of a drum?": revisited,
J. Phys. A 38 (2005) L163-L170.
A. Shudo and S. Saito,
Slow relaxation in Hamiltonian systems with internal degrees of freedom,
Adv. Chem. Phys. Part B 130 (2005) 375-421.
首藤 啓
Stokes geometry for the quantized Hénon map
物性研究84 (2005) 546-549.
A. Shudo,
A recipe for finding Stokes geomtry in the quantized Hénon map,
数理解析研究所講究録 1433 (2005) 110-119.
A. Shudo,
Stokes geometry for the quantized Hénon map in the horseshoe regime,
数理解析研究所講究録 1431(2005) 107-115.
T. Aoki, T. Kawai, T. Koike, S. Sasaki, A. Shudo and Y. Takei,
A background story and some know-how of virtual turning points,
数理解析研究所講究録 1424 (2005) 53-63.
A. Shudo,
Stokes geometry for the quantized Hénon map,
数理解析研究所講究録 1424 (2005) 184-199.
A. Shudo,
Julia set describes quantum tunneling in the presence of chaos,
数理解析研究所講究録 1447 (2005) 187-197.
首藤 啓
『物理学大事典』
(培風館, 2005).
R. Hagiwara and A. Shudo,
Grammatical complexity for two-dimensional maps,
J. Phys. A. 37 (2004) 10545-10559.
R. Hagiwara and A. Shudo,
An algorithm to prune the area-preserving Hénon map,
J. Phys. A. 37 (2004) 10521-10543.
S. Saito, A. Shudo, J. Yamamoto and K. Yoshida,
Nambu-Hamiltonian flows associated with descrete map,
J. Phys. Soc. Jpn. 73 (2004) 557-565.
首藤 啓
量子カオスの半古典論
数理解析研究所講究録 1369(2004) 1-11.
Y. Okada and A. Shudo, T. Harayama and S. Tasaki,
Can one determine the shape of a quantum billiard table through the eigenenergies and resonances?,
Prog. Theor. Phys. Suppl. 150 (2003) 397-400.
A. Shudo and K. S. Ikeda,
Quantum chaos in mixed phase space and the Julia set,
Prog. Theor. Phys. Suppl. 150 (2003) 267-280.
A. Shudo, T. Onishi, K. S. Ikeda, and K. Takahashi,
Dynamical and energetic barrier tunneling in the presence of chaos,
Fundamental Aspects of Quantum Physicsedts; L. Accardi and S. Tasaki (World Scientific, 2003) pp. 157-177.
T. Onishi, A. Shudo, K. S. Ikeda and K. Takahashi,
Semiclassical study on tunneling processes via complex-domain chaos
Phys. Rev. E 68 (2003) 05211-1-05211-22.
首藤 啓
複素力学系と量子カオス
物性研究 80 (2003) 188-194.
岡田 雄一郎，首藤 啓，原山卓久，田崎秀一
内部固有値と外部共鳴から撞球台の形状を決定できるか？
物性研究 80 (2003) 177-181.
首藤 啓
近可積分系の量子論と高次元複素力学系
『数理科学』 (2003) 3月号 35-42.
Atushi Tanaka,
Semiclassical coherent state path integral around classically realizable trajectory,
Progress of Theoretical Physics 110 (2003) 407–424.
Hiroshi Fujisaki, Takayuki Miyadera and Atushi Tanaka,
Dynamical aspects of quantum entanglement for weakly coupled kicked tops,
Physical Review E 67 (2003) 066201-1–066201-11 (preprint at arXiv).
Atushi Tanaka,
A bracket calculus for adiabatic descriptions of quantum composite systems,
Journal of the Physical Society of Japan 72 Suppl. C (2003) 54–57.
Hiroshi Fujisaki, Takayuki Miyadera and Atushi Tanaka,
Dynamical aspects of quantum entanglement for coupled mapping systems,
Journal of the Physical Society of Japan 72 Suppl. C (2003) 111–114 (preprint at arXiv).
A. Shudo, Y. Ishii and K. S. Ikeda,
Julia set describes quantum tunneling in the presence of chaos,
J. Phys. A. 35 (2002) L225-L231. (IOP selected)
S. Saito, A. Shudo, J. Yamamoto and K. Yoshida,
Hamiltonian flows associated with discrete maps,
J. Math. Phys. 43 (2002) 4963-4965.
首藤 啓
近可積分ハミルトン系における古典量子化条件について
数理解析研究所講究録1282 (2002) 156-163.
Atushi Tanaka, Hiroshi Fujisaki and Takayuki Miyadera,
Saturation of the production of quantum entanglement between weakly coupled mapping systems in strongly chaotic region,
Physical Review E 66 (2002) 045201(R)-1–045201(R)-4 (preprint at arXiv).
Atushi Tanaka,
Semiclassical theory of weak values,
Physics Letters A 297 (2002) 307–312 (preprint at arXiv).
Y. Okada and A. Shudo,
Equivalence between isospectrality and iso-length spectrality for a certain class of billiard domains,
J. Phys. A. 34 (2001) 5911-5922.
T. Onishi, A. Shudo, K. S. Ikeda and K. Takahashi,
Tunneling mechanism due to chaos in complex phase space,
Phys. Rev. E 64 (2001) 025201-1-025201-4.
首藤 啓
内部自由度のある古典力学---等分配則をめぐるBoltzmann-Jeans 予想の解釈をめぐって---
『数理科学』(2001) 9 月号 19-26.
T. Harayama, A. Shudo, and S. Tasaki,
A functional equation for semiclassical Fredholm determinant for strongly chaotic billiards,
Prog. Theor. Phys. Suppl. 139 (2000) 460-469.
A. Shudo and K. S. Ikeda,
Complex trajectory description for chaotic tunneling,
Prog. Theor. Phys. Suppl. 139 (2000) 246-256.
首藤 啓、池田 研介
エノン写像の exact WKB 量子化に向けて
数理解析研究所講究録1180 (2000) 48-58.
首藤 啓、池田 研介
反可積分極限とエノン写像のストークス幾何
数理解析研究所講究録1168 (2000) 55-65.
首藤 啓、石井 豊、池田 研介
カオス的トンネル効果と複素力学系
『力学系と数理物理の諸問題』(2000) 139-154.
首藤 啓、池田 研介
量子エノン写像のストークス現象
数理解析研究所講究録1133(2000) 53-67.
首藤 啓、池田 研介
量子カオスと複素半古典論
物性研究1133(2000) 647-662．
T. Harayama and A. Shudo, and S. Tasaki,
Semiclassical Fredholm determinant for quantum billiards,
Nonlinearity 12 (1999) 1113-1149.
首藤 啓
複素半古典論とトンネル現象
物性研究71(1999) 581-591.
首藤 啓、池田 研介
カオスと量子トンネル現象
物性研究71(1999) 806-827.
首藤 啓, 斎藤真司
内部自由度をもつハミルトン系の遅い緩和の起源
物性研究73(1999) 63-83.
首藤 啓、池田 研介
カオス的トンネル効果
『日本物理学会誌』54 (1999) 716-725.
A. Shudo and K. S. Ikeda,
Chaotic tunneling I: A remarkable manifestation of complex dynamical system in nonintegrable quantum phenomena,
Physica D 115 (1998) 234-292.
S. Tasaki, T. Harayama and A. Shudo
Interior Dirichlet eigenvalue problem, exterior Neumann scattering problem and boundary element method for two-dimensional quantum billiards
Phys. Rev. E 56 (1997) R13-R16.
首藤 啓
複素古典軌道と非可積分系のトンネル現象
総合研究大学院大学共同研究『非線形現象の数理科学』論文集 1997年3月
首藤 啓
トンネル現象と複素古典力学
『数理科学』(1997) 9月号 33-39.
首藤 啓
量子カオス ---カオスの量子化条件と古典軌道間の相関---
『数理科学』（カオス研究の最前線（連載））(1997) 3月号 66-74.
A. Shudo and K. S. Ikeda,
Stokes phenomenon in chaotic systems: Pruning trees of tunneling paths with principle of exponential dominance,
Phys. Rev. Lett. 76 (1996) 4151-4154.
A. Shudo and K. S. Ikeda,
Complex classical trajectories and chaotic tunneling,
Phys. Rev. Lett. 74 (1995) 682-685.
Y. Shimizu and A. Shudo,
Polygonal billiards: Correspondence between classical trajectories and quantum eigenstates,
Chaos, Solitons and Fractals 5 (1995) 1337-1347.
首藤 啓、池田 研介
カオス系の量子トンネリング
『パリティ』(1995) 11月号 30-33.
A. Shudo,
Level Statistics and Semiclassical Periodic-orbit Expansion for Polygonal Billiards,
Advanced Series in Dynamical Systems, Vol. 14, Geometry and Analysis in Dynamical Systems, pp.71-82, (World Scientific Publ.,1994, Singapore).
T. Harayama, A. Shudo and Y. Shimizu,
Semiclassical quantization and periodic orbits of dispersing billiards,
Prog. Theor. Phys. Suppl. 116 (1994) 259-265.
Y. Shimizu and A. Shudo,
Statistical properties of eigenfunctions for quantum billiard systems with and without positive Lyapunov exponent,
Prog. Theor. Phys. Suppl. 116 (1994) 267-276.
A. Shudo and K. Ikeda,
Toward the classical understanding of quantum chaological phenomena: Dynamical localization and chaotic tunneling,
Prog. Theor. Phys. Suppl. 116 (1994) 283-293.
A. Shudo, Y. Shimizu, J. Stein, H.-J. Stöckmann, P. Seba and K. \.Zyczkowski,
Statistical properties of spectra of pseudo-integrable systems,
Phys. Rev. E49 (1994) 3748-3756.
首藤 啓
多角形ビリヤード系の量子準位統計と半古典論
数理解析研究所講究録 863 (1994) 67-77.
首藤 啓
擬可積分系とレベル統計
『数理科学』(1994) 10月号 36-43.
K. Takahashi and A. Shudo,
Dynamical fluctuation of observable and the ensemble of classical trajectories,
J. Phys. Soc. Jpn. 62 (1993) 2612-2635.
A. Shudo and Y. Shimizu,
Extensive numerical study of quantum spectral statistics for rational and irrational polygonal billiards,
Phys. Rev. E1 (1993) 54-62.
首藤 啓、池田 研介
時間領域における半古典論の破綻と古典系の軌道間相関
物性研究 59(1993) 757-778.
原山 卓久、首藤 啓
Dispersing Billiardsの半古典論
物性研究（特別寄稿）61 (1993) 222-281.
首藤 啓
（書評）Chaos and Quantum Physics (Les Houches Summer School Lectures)"
『日本物理学会誌』 (1993) 8月号 660-661.
N. Saitô and A. Shudo,
Ergodicity, irreversibility and approach to equilibrium,
J. Phys. Soc. Jpn. 62 (1992) 53-63.
A. Shudo,
Length spectrum and semiclassical density of states for an almost integrable billiard system,
Phys. Rev. A46 (1992) 809-824.
T. Harayama and A. Shudo
Zeta function derived from the boundary element method
Phys. Lett. A165 (1992) 417-426.
T. Harayama and A. Shudo,
Periodic orbits and semiclassical quantization of dispersing billiards,
J. Phys. A25 (1992) 4595-4611.
Y. Aizawa, A. Shudo, K. Kurumi, M. Goda, and H. Yamada,
On a random system which reveals anomalous localization of wave functions,
Prog. Theor. Phys. 86 (1991) 1-6.
M. Goda, H. Yamada, Y. Aizawa, K. Kurumi, A. Shudo and H. Kubo,
A new class of disordered systems I -- A modified Bernoulli system with long-range structural correlation --,
J. Phys. Soc. Jpn. 60 (1991) 2295-2304.
首藤 啓、斎藤 信彦
量子カオス II –シュレディンガー方程式による取扱い–
『パリティ』 (1991)3 月号 51-56.
A. Shudo and Y. Shimizu,
Universality and non-universality of level statistics in stadium billiard,
Phys. Rev. A42 (1990) 6264-6267.
A. Shudo and T. Matsushita,
Regularity versus randomness in matrix-element distributions for quantum nonintegrable Hamiltonian systems II. Colored random matrix as a phenomenological model for level spacing statistics of many-degree-of-freedom Hamiltonian systems,
Phys. Rev. A41 (1990) 1912-1922.
清水 寧、首藤 啓
多角形ビリヤード系の量子力学的性質
物性研究 53(1990) 593-595.
高橋 公也、首藤 啓
力学量の長時間発展と量子カオス
物性研究 53(1990) 599-603.
首藤 啓
非可積分系の量子力学
物性研究 54(1990)649-651.
A. Shudo,
Algorithmic complexity of the eigenvalue sequence of a nonintegrable Hamiltonian system,
Phys. Rev. Lett. 63 (1989) 1897-1901.
A. Shudo,
Relationship between level spacing property and matrix element distribution in quantum nonintegrable systems,
Prog. Theor. Phys. Suppl. 98 (1989) 173-197.
K. Nakamura, A. R. Bishop and A. Shudo,
Quantum dynamics of a pulsed spin system: Long-time behavior of semiclassical wave functions,
Phys. Rev. B39 (1989) 12 422-12 425.
A. Shudo and T. Matsushita
Regularity versus randomness in matrix-element distributions in quantum nonintegrable Hamiltonian systems
Phys. Rev. A39 (1989) 282-296.
高橋 公也、首藤 啓
量子カオスにおける力学量の時間発展II
物性研究 51(1989) 823-826.
A. Shudo, M. Mizutani and T. Fukai,
Canonical correlation of a nonintegrable quantum system,
Phys. lett. A130 (1988) 338-343.
首藤 啓、水谷 正大、深井 朋樹
量子カオスの情報論的特徴づけ
物性研究50(1988) 687-691.
首藤 啓、水谷 正大、深井 朋樹
カノニカル相関による波動関数の特徴づけ
物性研究49(1988) 479-481.
胡桃 薫、首藤 啓、合田 正毅、相沢 洋二
長距離相関をもつランダム場中の電子状態
物性研究 49(1988) 488-489.
首藤 啓、松下 利樹
非可積分ハミルトン系も行列要素分布をめぐって
物性研究 49 (1988) 467-468.
A. Shudo and N. Saitô,
Level spacing distribution and avoided crossing in quantum chaos,
J. Phys. Soc. Jpn. 56 (1987) 2641-2652.
相沢 洋二、胡桃 薫、首藤 啓、合田 正毅
一次元ランダム系の統計的性質
物性研究 48 (1987) 400-402.
首藤 啓、松下 利樹
ハミルトニアン行列の乱雑さとレベルの統計的性質
物性研究 48 (1987) 396-400.