Can One Determine the Shape of a Quantum Billiard Table through the Eigenenergies and Resonances?

スポンサーリンク

概要

• 論文の詳細を見る

• The quantum billiard problem, that is the Dirichlet problem for the Helmholtz equation, can be rewritten as a Fredholm integral equation of the second kind and the eigenenergies can be characterized as the zeros of the Fredholm determinant on the positive real axis. However the Fredholm determinant also has complex zeros corresponding to the resonances when the billiard table is regarded as a scatterer against the exterior wave function. That naturally leads us to a new question "Can one determine the shape of billiard table through the interior eigenenergies and exterior resonances, i.e., all zeros of the Fredholm determinant?" instead of the famous Kac's question "Can one hear the shape of a drum?" , which was solved negatively.

• 理論物理学刊行会の論文
• 2003-09-30

著者

• TASAKI Shuichi

  Department of Applied Physics, Waseda University

• 原山 卓久

  早大理工

• SHUDO Akira

  Department of Applied Physics, Waseda University

• HARAYAMA Takahisa

  ATR Adaptive Communications Research Laboratories

• Shudo A

  Tokyo Metropolitan Univ. Tokyo

• Shudo Akira

  Department Of Applied Physics Waseda University

• Shudo Akira

  Institute Of Molecular Science

• Tasaki S

  Department Of Applied Physics Waseda University

• Tasaki Shuichi

  Department Of Applied Physics School Of Science And Engineering Waseda University

• 原山 卓久

  Atr Adaptive Communications Research Laboratories

• OKADA Yuichiro

  Department of Applied Chemistry, Graduate School of Engineering, Osaka Prefecture Unviersity

• Okada Yuichiro

  Department Of Physics Tokyo Metropolitan University

• Okada Yuichiro

  Department Of Applied Chemistry Graduate School Of Engineering Osaka Prefecture Unviersity

• TASAKI Shuichi

  Department of Physics, Kyoto University

• SHUDO Akira

  Department of Physics, Tokyo Metropolitan University

• OKADA Yuichiro

  Department of Physics, Tokyo Metropolitan University

関連論文

• 30aXB-12 量子伝導デバイスの輸送現象におけるトンネル効果とカオス的挙動の関連性についてIII(30aXB 量子ドット,領域4(半導体,メゾスコピック系・局在))
• 20pYC-15 量子伝導デバイスの輸送現象におけるトンネル効果とカオス的挙動の関連性についてII(量子細線,量子ドット,バリスティック伝導,領域4(半導体,メゾスコピック系・局在))
• 24aPS-2 量子伝導デバイスの輸送現象におけるトンネル効果とカオス的挙動の関連性について(領域4ポスターセッション,領域4(半導体, メゾスコピック系・局在))
• 22pTH-13 結合量子ドット系における磁気ゆらぎのフラクタル解析
• Current-Density Dependence of the Charge-Ordering Gap in the Organic Salt θ-(BEDT-TTF)_2CsM(SCN)_4 (M=Zn, Co, and Co_Zn_)(Condensed matter: electronic structure and electrical, magnetic, and optical properties)
• 双曲型ビリアード系における周期軌道と半古典量子化(基研短期研究会「保存力学系カオスにおける古典論と量子論」,研究会報告)
• 27p-PSB-58 強いカオス系の波動関数
• 27p-PSB-57 境界要素法と半古典量子化
• Dispersing Billiardsの半古典論(講義ノート)
• dispersing billiard系の周期軌道と半古典量子化(基研短期研究会『少数多体系における量子カオスと関連する諸問題』,研究会報告)
• 29p-T-4 dispersing billiard系の周期軌道と半古典近似
• On a Random System Which Reveals Anomalous Localization of Wave Functions : Progress Letters
• A New Class of Disordered Systems : A Modified Bernoulli System with Long-Range Structural Correlation
• Stokes geometry for the quantized Henon map(6) Approaches from mathematical science and quantum information, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)
• Formalisms of Quantum Fluctuation Theorem(3) Chaos and nonlinear dynamics in dissipative systems(including BEC and pattern formations), Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)
• Whispering Gallery Mode Lasers
• KAM torus付近の相空間の構造(カオスとその周辺,研究会報告)
• 4p-PS-65 摂動による保存量の拡散
• 4a-C5-1 ビリヤード系のLong Time Tail
• Poincare-Birkhoff Chains in the Critical Regime between Chaos and Torus
• Stagnant Motions in Hamiltonian Systems : Part I. Classical Aspects : New Trends in Chaotic Dynamics of Hamiltonian Systems
• Numerical Validities of the Berry-Robnik's Surmise for Quantum Oval Billiard
• Non-Poissonian Level Spacing Statistics of Classically Integrable Quantum Systems Based on the Berry-Robnik Approach
• Long-Range spectral statistics of systems with infinitely many components : Investigation of classically integrable systems based on the Berry-Robnik theory(2) Equilibrium and nonequilibrium statistical mechanics in systems showing chaos and quantum chaos
• Long-Range Spectral Statistics of Classically Integrable Systems : Investigation along the Line of the Berry-Robnik Approach(Condensed Matter and Statistical Physics)
• Non-Poissonian Level Spacing Statistics of Classically Integrable Quantum Systems Based on the Berry-Robnik Approach
• Nambu-Hamiltonian Flows Associated with Discrete Maps (General)
• 30aZE-8 非線形波動ダイナミクスによるマイクロディスクキャビティのレーザー発振
• 25aYN-2 マイクロディスクキャビテイにおける非線形発振
• 3a-E-10 周期軌道量子化法において定常位相近似は破綻するか
• Synthesis of Diarylsulfoximines by the Friedel-Crafts Reaction of Sulfonimidoyl Chlorides
• Relationship between Level Spacing Property and Matrix Element Distribution in Quantum Nonintegrable Systems : Part II. Quantal Aspects : New Trends in Chaotic Dynamics of Hamiltonian Systems
• Quantum Chaos in Mixed Phase Space and the Julia Set
• Semiclassical Quantization and Periodic Orbits of Dispersing Billiards
• Statistical Properties of Eigenfunctions for Quantum Billiards with and without Positive Lyapunov Exponent
• Anomalous Decay of an Unstable State Coupled with Singular Continuous States : Weak-Coupling Limit(Condensed Matter and Statistical Physics)
• Anomalous Decay of Unstable State and Wave Propagation in the Friedrichs Model Consisting of a Discrete State and the Fibonacci Lattice(General and Mathamatical Physics)
• Nonequilibrium Steady States and Current Fluctuation in an AB ring with a Quantum Dot(1)Current topics of quantum chaos in nanosciences, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)
• Can One Determine the Shape of a Quantum Billiard Table through the Eigenenergies and Resonances?
• 29pYS-2 量子カオスと半古典理論
• 29pYS-2 量子カオスと半古典理論
• A Functional Equation for Semiclassical Fredholm Determinant for Strongly Chaotic Billiards
• 量子カオスと光学現象
• 量子カオスの周期軌道理論 (量子準位統計--カオスをとらえる新たな視点)
• Quantum Chaos in Mixed Phase Space and the Julia Set
• Toward the Classical Understanding of Quantum Chaological Phenomena : Dynamical Localization and Chaotic Tunneling
• Complex Trajectory Description for Chaotic Tunneling
• Nonequilibrium Steady States and Fano-Kondo Resonances in an AB Ring with a Quantum Dot(Condensed matter: electronic structure and electrical, magnetic, and optical properties)
• Level Spacing Distribution and Avoided Crossing in Quantum Chaos
• Specific Heat of He Adsorbed on Y-Zeolite : Cluster Model Approach
• Quantum statistical mechanics in infinitely extended systems : C^* algebraic approach(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)
• Boundary element method and isospectrality in quantum billiards(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)
• Multifractal Wave Functions of a System with a Monofractal Energy Spectrum
• Theory of Surface-Induced Magnetism in Adsorbed ^3He Films. III : Possibility of Anisotropic Phase : Condensed Matter and Statistical Physics
• Theory of Surface-Induced Magnetism in Adsorbed ^3He Films : Indirect Exchange via Almost-Localized-Fermionic ^3He Liquid : Condensed Matter and Statistical Physics
• Theory of Surface-Induced Magnetism in Adsorbed ^3He Films. II : Curie-Weiss Temperature (Reinvestigated), Curie Constant and Liquid-layer Susceptibility : General and Mathematical Physics
• Reformulation of Periodic s-d Model
• Sliding Conductivity of Charge Density Waves : A Model of Sliding Soliton Lattices
• Dynamical Fluctuations of Observables and the Ensemble of Classical Trajectories

もっと見る 閉じる

スポンサーリンク