Quantum Mechanics of Two Hard Disks within a Circle Billiard

Progress of Theoretical Physics Supplement

Volumn 150, Issue , 2003, Pages 165-175

  Nakazono, Naofumi ^a   Kato, Takeo ^a   Nakamura, Katsuhiro ^a  

^a Osaka Prefecture University   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0344980690     PISSN: 03759687     EISSN: None     Source Type: Journal    
DOI: 10.1143/PTPS.150.165     Document Type: Conference Paper

References (20)

1. For books of quantum chaos on billiard systems, see: M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, Berlin, 1990). M. J. Giannoni et al. (eds.), Chaos and Quantum Physics, Session LII, Les Houches, 1989 (Elsevier, Amsterdam, 1991). K. Nakamura, Quantum Chaos - A New Paradigm of Nonlinear Dynamics (Cambridge University Press, Cambridge, 1993). H-J. Stöckmann, Quantum Chaos - An Introduction (Cambridge University Press, Cambridge, 1999). K. Nakamura, Quantum versus Chaos - Questions Emerging from Mesoscopic Cosmos (Kluwer Academic, Dordrecht, 1997).
2. For books of quantum chaos on billiard systems, see: M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, Berlin, 1990). M. J. Giannoni et al. (eds.), Chaos and Quantum Physics, Session LII, Les Houches, 1989 (Elsevier, Amsterdam, 1991). K. Nakamura, Quantum Chaos - A New Paradigm of Nonlinear Dynamics (Cambridge University Press, Cambridge, 1993). H-J. Stöckmann, Quantum Chaos - An Introduction (Cambridge University Press, Cambridge, 1999). K. Nakamura, Quantum versus Chaos - Questions Emerging from Mesoscopic Cosmos (Kluwer Academic, Dordrecht, 1997).
3. For books of quantum chaos on billiard systems, see: M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, Berlin, 1990). M. J. Giannoni et al. (eds.), Chaos and Quantum Physics, Session LII, Les Houches, 1989 (Elsevier, Amsterdam, 1991). K. Nakamura, Quantum Chaos - A New Paradigm of Nonlinear Dynamics (Cambridge University Press, Cambridge, 1993). H-J. Stöckmann, Quantum Chaos - An Introduction (Cambridge University Press, Cambridge, 1999). K. Nakamura, Quantum versus Chaos - Questions Emerging from Mesoscopic Cosmos (Kluwer Academic, Dordrecht, 1997).
4. For books of quantum chaos on billiard systems, see: M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, Berlin, 1990). M. J. Giannoni et al. (eds.), Chaos and Quantum Physics, Session LII, Les Houches, 1989 (Elsevier, Amsterdam, 1991). K. Nakamura, Quantum Chaos - A New Paradigm of Nonlinear Dynamics (Cambridge University Press, Cambridge, 1993). H-J. Stöckmann, Quantum Chaos - An Introduction (Cambridge University Press, Cambridge, 1999). K. Nakamura, Quantum versus Chaos - Questions Emerging from Mesoscopic Cosmos (Kluwer Academic, Dordrecht, 1997).
5. For books of quantum chaos on billiard systems, see: M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, Berlin, 1990). M. J. Giannoni et al. (eds.), Chaos and Quantum Physics, Session LII, Les Houches, 1989 (Elsevier, Amsterdam, 1991). K. Nakamura, Quantum Chaos - A New Paradigm of Nonlinear Dynamics (Cambridge University Press, Cambridge, 1993). H-J. Stöckmann, Quantum Chaos - An Introduction (Cambridge University Press, Cambridge, 1999). K. Nakamura, Quantum versus Chaos - Questions Emerging from Mesoscopic Cosmos (Kluwer Academic, Dordrecht, 1997).
6. For proceedings of quantum chaos in quantum dots, see: E. Akkermans et al. (eds.), Mesoscopic Quantum Physics, Proceedings of Les Houches Summer School (Elsevier, Amsterdam, 1995). K. Nakamura (ed.), Special issue on Chaos and Quantum Transport in Mesoscopic Cosmos, Chaos, Solitons and Fractals 8 (1997), No. 7&8. K. F. Berggren and S. Åberg (eds.), Quantum Chaos Y2K, Proceedings of Nobel Symposium (Royal Swedish Academy of Sciences/World Scientific, Singapore, 2001).
7. For proceedings of quantum chaos in quantum dots, see: E. Akkermans et al. (eds.), Mesoscopic Quantum Physics, Proceedings of Les Houches Summer School (Elsevier, Amsterdam, 1995). K. Nakamura (ed.), Special issue on Chaos and Quantum Transport in Mesoscopic Cosmos, Chaos, Solitons and Fractals 8 (1997), No. 7&8. K. F. Berggren and S. Åberg (eds.), Quantum Chaos Y2K, Proceedings of Nobel Symposium (Royal Swedish Academy of Sciences/World Scientific, Singapore, 2001).
8. For proceedings of quantum chaos in quantum dots, see: E. Akkermans et al. (eds.), Mesoscopic Quantum Physics, Proceedings of Les Houches Summer School (Elsevier, Amsterdam, 1995). K. Nakamura (ed.), Special issue on Chaos and Quantum Transport in Mesoscopic Cosmos, Chaos, Solitons and Fractals 8 (1997), No. 7&8. K. F. Berggren and S. Åberg (eds.), Quantum Chaos Y2K, Proceedings of Nobel Symposium (Royal Swedish Academy of Sciences/World Scientific, Singapore, 2001).
9. On classical billiards and ergodicity, see: N. S. Krylov, Works on the Foundations of Statistical Physics (Princeton University Press, Princeton, 1979). V. I. Arnold and A. Avez, Theorie Ergodique des Systems Dynamiques (Gauthier-Villars, Paris, 1968). L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. 78 (1980), 247; Commun. Math. Phys. 78 (1980), 479. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998). P. Gaspard and S. A. Rice, J. Chem. Phys. 90 (1989), 2225; J. Chem. Phys. 90 (1989), 2242; J. Chem. Phys. 90 (1989), 2255.
10. On classical billiards and ergodicity, see: N. S. Krylov, Works on the Foundations of Statistical Physics (Princeton University Press, Princeton, 1979). V. I. Arnold and A. Avez, Theorie Ergodique des Systems Dynamiques (Gauthier-Villars, Paris, 1968). L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. 78 (1980), 247; Commun. Math. Phys. 78 (1980), 479. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998). P. Gaspard and S. A. Rice, J. Chem. Phys. 90 (1989), 2225; J. Chem. Phys. 90 (1989), 2242; J. Chem. Phys. 90 (1989), 2255.
11. On classical billiards and ergodicity, see: N. S. Krylov, Works on the Foundations of Statistical Physics (Princeton University Press, Princeton, 1979). V. I. Arnold and A. Avez, Theorie Ergodique des Systems Dynamiques (Gauthier-Villars, Paris, 1968). L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. 78 (1980), 247; Commun. Math. Phys. 78 (1980), 479. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998). P. Gaspard and S. A. Rice, J. Chem. Phys. 90 (1989), 2225; J. Chem. Phys. 90 (1989), 2242; J. Chem. Phys. 90 (1989), 2255.
12. On classical billiards and ergodicity, see: N. S. Krylov, Works on the Foundations of Statistical Physics (Princeton University Press, Princeton, 1979). V. I. Arnold and A. Avez, Theorie Ergodique des Systems Dynamiques (Gauthier-Villars, Paris, 1968). L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. 78 (1980), 247; Commun. Math. Phys. 78 (1980), 479. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998). P. Gaspard and S. A. Rice, J. Chem. Phys. 90 (1989), 2225; J. Chem. Phys. 90 (1989), 2242; J. Chem. Phys. 90 (1989), 2255.
13. On classical billiards and ergodicity, see: N. S. Krylov, Works on the Foundations of Statistical Physics (Princeton University Press, Princeton, 1979). V. I. Arnold and A. Avez, Theorie Ergodique des Systems Dynamiques (Gauthier-Villars, Paris, 1968). L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. 78 (1980), 247; Commun. Math. Phys. 78 (1980), 479. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998). P. Gaspard and S. A. Rice, J. Chem. Phys. 90 (1989), 2225; J. Chem. Phys. 90 (1989), 2242; J. Chem. Phys. 90 (1989), 2255.
14. On classical billiards and ergodicity, see: N. S. Krylov, Works on the Foundations of Statistical Physics (Princeton University Press, Princeton, 1979). V. I. Arnold and A. Avez, Theorie Ergodique des Systems Dynamiques (Gauthier-Villars, Paris, 1968). L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. 78 (1980), 247; Commun. Math. Phys. 78 (1980), 479. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998). P. Gaspard and S. A. Rice, J. Chem. Phys. 90 (1989), 2225; J. Chem. Phys. 90 (1989), 2242; J. Chem. Phys. 90 (1989), 2255.
15. On classical billiards and ergodicity, see: N. S. Krylov, Works on the Foundations of Statistical Physics (Princeton University Press, Princeton, 1979). V. I. Arnold and A. Avez, Theorie Ergodique des Systems Dynamiques (Gauthier-Villars, Paris, 1968). L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. 78 (1980), 247; Commun. Math. Phys. 78 (1980), 479. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998). P. Gaspard and S. A. Rice, J. Chem. Phys. 90 (1989), 2225; J. Chem. Phys. 90 (1989), 2242; J. Chem. Phys. 90 (1989), 2255.
16. On classical billiards and ergodicity, see: N. S. Krylov, Works on the Foundations of Statistical Physics (Princeton University Press, Princeton, 1979). V. I. Arnold and A. Avez, Theorie Ergodique des Systems Dynamiques (Gauthier-Villars, Paris, 1968). L. A. Bunimovich and Ya. G. Sinai, Commun. Math. Phys. 78 (1980), 247; Commun. Math. Phys. 78 (1980), 479. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, Cambridge, 1998). P. Gaspard and S. A. Rice, J. Chem. Phys. 90 (1989), 2225; J. Chem. Phys. 90 (1989), 2242; J. Chem. Phys. 90 (1989), 2255.
17. On semiclassical physics, see: M. Brack and R. K. Bhaduri, Semiclassical Physics (Addison Wesley, New York, 1997).
18. A. Awazu, Phy. Rev. E 63 (2001), 032102. K. H. Ahn et al., Phys. Rev. Lett. 83 (1999), 4144. T. Papenbrock and T. Prosen, Phys. Rev. Lett. 84 (2000), 262.
19. A. Awazu, Phy. Rev. E 63 (2001), 032102. K. H. Ahn et al., Phys. Rev. Lett. 83 (1999), 4144. T. Papenbrock and T. Prosen, Phys. Rev. Lett. 84 (2000), 262.
20. A. Awazu, Phy. Rev. E 63 (2001), 032102. K. H. Ahn et al., Phys. Rev. Lett. 83 (1999), 4144. T. Papenbrock and T. Prosen, Phys. Rev. Lett. 84 (2000), 262.