Skip to main content
SpringerLink
Log in

Scattering, Transport & Stochasticity in Quantum Systems

  • Chapter
Dynamics: Models and Kinetic Methods for Non-equilibrium Many Body Systems

Part of the book series: NATO Science Series ((NSSE,volume 371))

Abstract

Recent work has shown the importance of chaotic behavior and of the sensitivity to initial conditions to understand how irreversible processes such as diffusion, viscosity, heat conductivity or reactions may arise in classical Hamiltonian systems [1, 2]. Indeed, the exponential separation between classical trajectories which are infinitesimally close can be shown to have for consequence exponential decays or relaxations in the Hamiltonian scattering by a hill, in some chaotic scattering systems, or in simple fully chaotic maps such as the multibaker map [2].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. R. Dorfman, An Introduction to Chaos in Nonequilibrium Statistical Mechanics, (Cambridge University Press, Cambridge, 1999).

    Book  MATH  Google Scholar 

  2. P. Gaspard, Chaos, Scattering, and Statistical Mechanics, (Cambridge University Press, Cambridge, 1998).

    Book  MATH  Google Scholar 

  3. P. Gaspard and G. Nicolis, Phys. Rev. Lett. 65, 1693 (1990).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. P. Gaspard and F. Baras, Phys. Rev. E 51, 5332 (1995).

    Article  MathSciNet  ADS  Google Scholar 

  5. J. R. Dorfman and P. Gaspard, Phys. Rev. E 51, 28 (1995).

    Article  MathSciNet  ADS  Google Scholar 

  6. P. Gaspard and J. R. Dorfman, Phys. Rev. E 52, 3525 (1995).

    Article  MathSciNet  ADS  Google Scholar 

  7. H. A. Posch and W. G. Hoover, Phys. Rev. A 38, 473 (1988); ibid. 39, 2175 (1989).

    Article  ADS  Google Scholar 

  8. D. J. Evans, E. G. D. Cohen, and M. P. Morriss, Phys. Rev. A 42, 5990 (1990).

    Article  ADS  Google Scholar 

  9. N. I. Chernov, G. L. Eyink, J. L. Lebowitz, and Ya. G. Sinai, Phys. Rev. Lett. 70, 2209 (1993).

    Article  ADS  Google Scholar 

  10. G. Gallavotti and E. G. D. Cohen, Phys. Rev. Lett. 74, 2694 (1995); J. Stat. Phys. 80, 931 (1995).

    Article  ADS  Google Scholar 

  11. H. van Beijeren, J. R. Dorfman, H. A. Posch, and Ch. Dellago, Phys. Rev. E 56, 5272 (1997).

    Article  ADS  Google Scholar 

  12. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).

    MATH  Google Scholar 

  13. P. Gaspard and S. A. Rice, J. Chem. Phys. 91, 2225, 2242, 2255 (1989).

    Article  ADS  Google Scholar 

  14. D. Wintgen, K. Richter, and G. Tanner, Chaos 2, 19 (1992).

    Article  ADS  Google Scholar 

  15. B. Grémaud and P. Gaspard, J. Phys. B: At. Mol. Phys. 31, 1671 (1998).

    Article  ADS  Google Scholar 

  16. P. Gaspard and S. A. Rice, Phys. Rev. A 93, 54 (1993).

    Article  ADS  Google Scholar 

  17. I. Burghardt and P. Gaspard, J. Chem. Phys. 100, 6395 (1994); J. Phys. Chem. 99, 2732 (1995); Chem. Phys. 225, 259 (1997).

    Article  ADS  Google Scholar 

  18. C. E. Porter, ed., Statistical Theories of Spectra: Fluctuations (Academic Press, New York, 1965).

    Google Scholar 

  19. M. J. Giannoni, A. Voros, and J. Zinn-Justin, eds., Chaos and Quantum Physics (North-Holland, Amsterdam, 1991).

    Google Scholar 

  20. P. van Ede van der Pals and P. Gaspard, Phys. Rev. E 49, 79 (1994).

    ADS  Google Scholar 

  21. M. Srednicki, Phys. Rev. E 50, 888 (1994); ibid. 54, 954 (1996).

    Article  ADS  Google Scholar 

  22. P. Gaspard and M. Nagaoka, J. Chem. Phys. 111, 5676 (1999).

    Article  ADS  Google Scholar 

  23. P. Gaspard, D. Alonso, and I. Burghardt, Adv. Chem. Phys. 90, 105 (1995).

    Article  Google Scholar 

  24. P. Carruthers and F. Zachariasen, Rev. Mod. Phys. 55, 245 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  25. M. V. Berry, J. Phys. A: Math. Gen. 10, 2083 (1977); A. Voros, Ann. Inst. Henri Poincaré A 24, 31 (1976); ibid. 26, 343 (1977).

    Article  ADS  MATH  Google Scholar 

  26. V. Colin de Verdière, Commun. Math. Phys. 102, 497 (1985); S. Zelditch, Duke Math. J. 55, 919 (1987).

    Article  MATH  Google Scholar 

  27. E. J. Heller, J. Chem. Phys. 68, 2066, 3891 (1978).

    Article  ADS  Google Scholar 

  28. B. Eckhardt, S. Fishman, K. Müller, and D. Wintgen, Phys. Rev. A 45, 3531 (1992).

    Article  ADS  Google Scholar 

  29. A. Voros, J. Phys. A: Math. Gen. 21, 685 (1988).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. P. Cvitanovic and B. Eckhardt, Phys. Rev. Lett. 63, 823 (1989).

    Article  MathSciNet  ADS  Google Scholar 

  31. R. Artuso, E. Aurell, and P. Cvitanovic, Nonlinearity 3, 325, 361 (1990).

    Article  MathSciNet  ADS  Google Scholar 

  32. P. Gaspard and I. Burghardt, Adv. Chem. Phys. 101, 491 (1997).

    Article  Google Scholar 

  33. P. Gaspard and S. R. Jain, Pramana-J. of Phys. 48, 503 (1997).

    Article  ADS  Google Scholar 

  34. B. Mehlig and K. Richter, Phys. Rev. Lett. 80, 1936 (1998).

    Article  ADS  Google Scholar 

  35. M. Pollicott, Invent. Math. 81, 413 (1985); D. Ruelle, Phys. Rev. Lett. 56, 405 (1986); J. Stat. Phys. 44, 281 (1986); J. Diff. Geom. 25, 99, 117 (1987).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. P. Cvitanovic and B. Eckhardt, J. Phys. A: Math. Gen. 24, L237 (1991).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. Ya. G. Sinai, Russ. Math. Surv. 27, 21 (1972); R. Bowen and D. Ruelle, Invent. Math. 29, 181 (1975).

    Google Scholar 

  38. D. Ruelle, Thermodynamic Formalism (Addison-Wesley, Reading, 1978).

    MATH  Google Scholar 

  39. D. Bessis, G. Paladin, G. Turchetti, and S. Vaienti, J. Stat. Phys. 51, 109 (1988).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. Z. Kovács and T. Tel, Phys. Rev. Lett. 64, 1617 (1990).

    Article  ADS  Google Scholar 

  41. A. Wirzba, Phys. Rep. 309, 1 (1999).

    Article  MathSciNet  ADS  Google Scholar 

  42. Y. Decanini, A. Folacci, E. Fournier, and P. Gabrielli, J. Phys. A: Math. Gen. 31, 7865, 7891 (1998).

    Article  ADS  MATH  Google Scholar 

  43. W. Lu, M. Rose, K. Pance, and S. Sridhar, Phys. Rev. Lett. 82, 5233 (1999).

    Article  ADS  Google Scholar 

  44. K. A. Holbrook, M. J. Pilling, and S. H. Robertson, Unimolecular Reactions, 2nd ed., (Wiley, Chichester, 1996).

    Google Scholar 

  45. F. Barra and P. Gaspard, J. Phys. A: Math. Gen. 32, 3357 (1999).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  46. P. Gaspard, in Quantum Chaos, G. Casati, I. Guarneri, and U. Smilansky, eds., (North-Holland, Amsterdam, 1993), p. 307.

    Google Scholar 

  47. B. D. Simons, Physica A 263, 148 (1999).

    Article  MathSciNet  ADS  Google Scholar 

  48. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957).

    Article  MathSciNet  ADS  Google Scholar 

  49. E. Helfand, Phys. Rev 119, 1 (1960); Phys. Fluids 4, 681 (1961).

    Article  MathSciNet  ADS  Google Scholar 

  50. P. Gaspard, in Nonlinear Dynamics and Computational Physics, V.B. Sheorey, ed., (Narosa Publishing House, New Delhi, 1999), p. 54.

    Google Scholar 

  51. P. Gaspard and P. van Ede van der Pals, Chaos, Solitons, and Fractals 5, 1183 (1995).

    Article  MathSciNet  ADS  Google Scholar 

  52. P. van Ede van der Pals, Etude de systèmes quantiques dans les limites semi-classique et thermodynamique, Thèse de doctorat, Université Libre de Bruxelles (1997).

    Google Scholar 

  53. V. E. Kravtsov, I. V. Yurkevich, and C. M. Canali, in Super symmetry and Trace Formulae: Chaos and Disorder, I.V. Lerner, J.P. Keating, and D.E. Khmelnitskii, eds., (Kluwer/Plenum, New York, 1999), p. 269.

    Google Scholar 

  54. A. G. Redfield, IBM J. Research Devel. 1, 19 (1957); Adv. Magn. Reson. 1, 1 (1965).

    Google Scholar 

  55. N. van Kampen, Stochastic Processes in Physics and Chemistry, 2nd ed., (North-Holland, Amsterdam, 1992).

    Google Scholar 

  56. M. B. Plenio and P. L. Knight, Rev. Mod. Phys. 70, 101 (1998).

    Article  ADS  Google Scholar 

  57. G. Lindblad, Commun. Math. Phys. 48, 119 (1976).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  58. P. Gaspard and M. Nagaoka, J. Chem. Phys. 111, 5668 (1999).

    Article  ADS  Google Scholar 

  59. I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinai Ergodic Theory (Springer, Berlin, 1982).

    Book  MATH  Google Scholar 

  60. A. Connes, H. Narnhofer, and W. Thirring, Commun. Math. Phys. 112, 691 (1987).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  61. H. Narnhofer and W. Thirring, Lett. Math. Phys. 14, 89 (1987).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  62. P. Gaspard, Prog. Theor. Phys. Suppl. 116, 369 (1994).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  63. R. Alicki and M. Fannes, Lett. Math. Phys. 32, 75 (1994).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  64. R. B. Griffiths, J. Stat. Phys. 36, 219 (1984); M. Gell-Mann and J. B. Hartle, in Foundations of Quantum Mechanics in the Light of New Technology, S. Kobayashi, H. Ezawa, Y. Murayama, and S. Nomura, eds., (Physical Society of Japan, Tokyo, 1990); R. Omnès, Rev. Mod. Phys. 64, 339 (1992).

    Article  ADS  MATH  Google Scholar 

  65. P. van Ede van der Pals and P. Gaspard, in Quantum Classical Correspondence, D. H. Feng and B. L. Hu, eds., (International Press, Cambridge MA, 1997), p. 483.

    Google Scholar 

  66. L. Onsager and S. Machlup, Phys. Rev. 91, 1505 (1953).

    Article  MathSciNet  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Nonlinear Phenomena and Complex Systems & Service de Chimie Physique, Campus Plaine, Université Libre de Bruxelles, Code Postal 231, B-1050, Brussels, Belgium

    Pierre Gaspard

Authors
  1. Pierre Gaspard
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Physics, Marquette University, Milwaukee, WI, USA

    John Karkheck

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Gaspard, P. (2000). Scattering, Transport & Stochasticity in Quantum Systems. In: Karkheck, J. (eds) Dynamics: Models and Kinetic Methods for Non-equilibrium Many Body Systems. NATO Science Series, vol 371. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4365-3_25

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-4365-3_25

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6554-9

  • Online ISBN: 978-94-011-4365-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation