Skip to main content
SpringerLink
Log in
Book cover

Lectures in Statistical Physics pp 1–52Cite as

Aspects of non-equilibrium quantum statistical mechanics: An introduction

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Physics ((LNP,volume 28))

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. VON NEUMANN: Gott. Nachr., 245, 273 (1927).

    Google Scholar 

  2. L. LANDAU: Z. Physik 45, 430 (1927)

    Article  Google Scholar 

  3. J. VON NEUMANN: Mathematical Foundations of Quantum Mechanics (Princeton University Press, 1955).

    Google Scholar 

  4. U. FANG: Rev. Mod. Phys. 29, 74 (1957).

    Article  Google Scholar 

  5. R. TOLMAN: The Principles of Statistical Mechanics (Oxford University Press, London, 1938), Chapter 9.

    Google Scholar 

  6. R. NEWTON: Scattering Theory of Waves and Particles (McGrawHill, New York, 1966), Chapter 8.

    Google Scholar 

  7. L. BOLTZMANN: “Further Studies on the Thermal Equilibrium of Gas Molecules”, translated and collected by S. G. Brush, Kinetic Theory Volume II (Pergamon Press, 1966).

    Google Scholar 

  8. E. ZERMELO: “On a Theorem of Dynamics and Mechanical Theory of Heat”, ibid. page 208.

    Google Scholar 

  9. I. SEGAL: Mathematical Problems of Relativistic Physics (Am. Math. Soc., Providence, Rhode Island, 1963).

    Google Scholar 

  10. G. EMCH: Algebraic Methods in Statistical Mechanics and Quantum Field Theory (Wiley-Interscience, New York, 1972).

    Google Scholar 

  11. R. E. PEIERLS: Quantum Theory of Solids (Oxford University Press, Oxford, 1955).

    Google Scholar 

  12. W. RAPPER: Rev. Mod. Phys. 44, 169 (1972).

    Article  Google Scholar 

  13. I. PRIGOGINE: Non-Equilibrium Statistical Mechanics (Interscience, New York, 1962).

    Google Scholar 

  14. R. ZWANZIG: Lectures in Theoretical Physics, Volume 3 (Boulder, 1960), 106. See also Physica 30, 1109 (1965).

    Google Scholar 

  15. J. W. MIDDLETON AND W. C. SCHIEVE: Physica 63, 139 (1973).

    Article  Google Scholar 

  16. R. BALESCU: Lectures in Statistical Physics, W. C. Schieve, M. G. Velarde and A. P. Grecos, eds. (Springer-Verlag, New York, 1971), page 149.

    Google Scholar 

  17. I. PRIGOGINE, C. GEORGE AND F. HENIN: Physica 45, 418 (1969).

    Article  Google Scholar 

  18. I. PRIGOGINE, C. GEORGE, F. HENIN AND L. ROSENFELD: “A Unified Formulation of Dynamics and Thermodynamics”, Chemica Scripta 4, 5 (1973).

    Google Scholar 

  19. W. C. SCHIEVE AND I. PRIGOGINE: “The Role of Subdynamics in Kinetic Theory”, Eighth Int. Symposium on Rarefied Gas Dynamics, proceedings to appear (Academic Press).

    Google Scholar 

  20. E. A. UEHLING AND G. E. UHLENBECK: Phys. Rev. 43, 553 (1933).

    Article  Google Scholar 

  21. N. N. BOGOLIUBOV: Lectures on Quantum Statistics I, (Gordon and Breach, New York, 1967).

    Google Scholar 

  22. G. EMCH: Helv. Phys. Acta 37, 67 (1964).

    Google Scholar 

  23. H. PRIMAS: Helv. Phys. Acta 34, Appendix (1961).

    Google Scholar 

  24. S. NNAKAJIMA: Progr. Theor. Phys. 20, 948 (1958).

    Google Scholar 

  25. R. BALESCU: Statistical Mechanics of Charged Particles (Interscience-John Wiley, New York, 1963).

    Google Scholar 

  26. B. LEAF AND W. C. SCHIEVE: Physica 30, 1389 (1964).

    Article  Google Scholar 

  27. I. PRIGOGINE AND P. RÉSIBOIS: Physica 27, 629 (1961).

    Article  Google Scholar 

  28. G. JONES: J. Math. Phys. 5, 653 (1964).

    Article  Google Scholar 

  29. G. C. SEWELL: Lectures in Theoretical Physics, Volume 10 (Boulder, 1967), 289.

    Google Scholar 

  30. N. N. BOGOLIUBOV: Journal Phys. U.S.S.R. 10, 265 (1946).

    Google Scholar 

  31. L. LANZ AND L. A. LUGIATO: Physica 47, 345 (1970).

    Article  Google Scholar 

  32. P. RÉSIBOIS: Physica 27, 541 (1961).

    Article  Google Scholar 

  33. K. O. FRIEDRICHS: Commun. Pure and Applied Math. 1, 361 (1940).

    Google Scholar 

  34. J. L. PEITENPOL: Phys. Rev. 162, 1301 (1967).

    Article  Google Scholar 

  35. I. PRIGOGINE, C. GEORGE AND F. HENIN: Proc. Nat. Acad. Sci. USA 65, 789 (1970).

    Google Scholar 

  36. L. VAN HOVE in E.G.D. COHEN: Fundamental Problems in Statistical Mechanics (North Holland, Amsterdam, 1962).

    Google Scholar 

  37. K. HAUBOLD: Physica 28, 834 (1962).

    Article  Google Scholar 

  38. A. P. GRECOS AND I. PRIGOGINE: Physica 59, 77 (1972).

    Article  Google Scholar 

  39. W. PAULI: Festschr. Zum 60, Geburstag A. Sommefeld (Hirzl, Leipzig, 1928).

    Google Scholar 

  40. L. VAN HOVE: Physica 21, 517 (1955).

    Google Scholar 

  41. I. PRIGOGINE: Thermodynamics of Irreversible Processes (Interscience, New York, 1955).

    Google Scholar 

  42. P. G. BERGMANN AND J. L. LEBOWITZ: Phys. Rev. 99, 59 (1955).

    Article  Google Scholar 

  43. P. N. ARGYRES: Lectures in Theoretical Physics, Volume 8A (Boulder, 1966), 183. See also W. PEIER: Physica 57, 565 (1972).

    Google Scholar 

  44. W. PEIER AND A. THELLUNG: Physica 46, 577 (1970).

    Article  Google Scholar 

  45. C. GEORGE, I. PRIGOGINE AND L. ROSENFELD: Mat. Fys, Medd. Dan. Vid. Selsk. 38 (1972).

    Google Scholar 

  46. R. BALESCU: “Non-Equilibrium Statistical Mechanics”, Irreversibility in Many-Body Problems ed. by J. Biel and J. Rae (Plenum, New York, 1972); also text to appear (Harper and Row).

    Google Scholar 

  47. L. LANZ, L. A. LUGIATO AND R. RAMELLA: Physica 54, 94 (1971); also M. A. ALBERTI, P. COHA-RAMASINA, G. RAMELLA: “On a Banach Space Formulation of Subdynamics in Quantum Statistics”, preprint.

    Article  Google Scholar 

  48. P. J. M. BONGOARTS, M. FANNES, A. VERBEURE: “A Remark on Ergodicity, Dissipativity, Return to Equilibrium”, preprint.

    Google Scholar 

  49. M. DE HAAN AND F. HENIN: “Collision Operator in the Physical Representation, The Friedrichs Model”, to appear in Physica.

    Google Scholar 

  50. A. P. GRECOS: Physica 51, 50 (1971).

    Article  Google Scholar 

  51. R. BALESCU AND L. BRENIG: Physica 54, 504 (1971).

    Article  Google Scholar 

  52. P. A. M. DIRAC: Rev. Mod. Phys. 21 (1949).

    Google Scholar 

  53. R. BALESCU AND R. KOTERA: Physica 33, 558 (1967).

    Article  Google Scholar 

  54. R. BALESCU: Physica 38, 119 (1968).

    Article  Google Scholar 

  55. A. W. SAENZ: Phys. Rev. 105, 546 (1957).

    Article  Google Scholar 

  56. H. MORI AND J. ROSS: Phys. Rev. 109, 1877 (1958).

    Article  Google Scholar 

  57. R. F. SNIDER: J. Chem. Phys. 32, 1051 (1960).

    Article  Google Scholar 

  58. D. K. HOFFMAN, J. MUELLER, C. F. CURTISS: J. Chem. Phys. 43, 2878 (1965).

    Article  Google Scholar 

  59. P. RÉSIBOIS: Physica 31, 645 (1965).

    Article  Google Scholar 

  60. G. SEVERNE: Trans. Th. and Stat. Phys. l(2), 145 (1971).

    Google Scholar 

  61. J. YVON: La Théorie Statistique des Fluides et l'Equation d'Etat (Herman, Paris, 1935).

    Google Scholar 

  62. N. N. BOGOLIUBOV: “Problemi, Dynamitcheskij Theorie v Statistitcheskey Physikie”, (Odis, Moskow, 1946); translated by E. K. Gora in J. de Boer and G. E. Uhlenbeck, ed. Studies in Statistical Mechanics, Volume I (North-Holland, Amsterdam, 1962).

    Google Scholar 

  63. M. BORN AND H. S. GREEN: A General Kinetic Theory of Fluids (Cambridge University Press). See also H. S. GREEN: Molecular Theory of Fluids (North-Holland, Amsterdam, 1952).

    Google Scholar 

  64. J. G. KIRKWOOD: J. Chem. Phys. 14, 180 (1946); 15, 72 (1947).

    Article  Google Scholar 

  65. L. WALDMAN: “On the Kinetic Equations with Internal Degrees of Freedom” in Acta Physica Austriaca Suppl. X The Boltzmann Equation ed. by E.G.D. Cohen and W. Thirring (Springer-Verlag, 1973), 223.

    Google Scholar 

  66. J. J. N. BEENAKKER: “Non-Equilibrium Angular Momentum Polarization in Rotating Molecules”, reference 65, p. 267.

    Google Scholar 

  67. L. WALDMAN: “Transporterschienung in Gases von Mittleren Druch”, in Handbuch der Physik ed. by S. Flugge 12 (Springer, Berlin, 1958).

    Google Scholar 

  68. A. P. GRECOS AND W. C. SCHIEVE: Physica 46, 475 (1970).

    Article  Google Scholar 

  69. M. BARANGER: Phys. Rev. III, 481, 494 (1958); 112, 855 (1954)

    Article  Google Scholar 

  70. U. FANG: Phys. Rev. 131, 254 (1963).

    Google Scholar 

  71. P. L. RONEY: “On the Theory of Combined Doppler and Binary Collision Foreign Gas Line Broadening”, Thesis, Free University of Brussels, June 1973.

    Google Scholar 

  72. S. CHAPMAN AND T. G. COWLING: The Mathematical Theory of Non-Uniform Gases (Cabrige University Press, New York, 1952).

    Google Scholar 

  73. J. O. HIRSCHFELDER, C. F. CURTISS, R. B. BIRD: Molecular Theory of Gases and Liquids (John Wiley, New York, 1954).

    Google Scholar 

  74. J. H. FERZIGER AND H. G. KAPER: Mathematical Theory of Transport Processes in Gases (North Holland, Amsterdam, 1972).

    Google Scholar 

  75. A. TIP: Physica 52, 493 (1971).

    Article  Google Scholar 

  76. K. HAWKER AND W. C. SCHIEVE: Fourth Canadian Symposium on Theoretical Chemistry, Vancouver, July 1971.

    Google Scholar 

  77. J. T. LOWRY: “fScattering Theory in Three-Body Quantum Kinetic Equations”, Thesis, University of Texas, Austin, 1970; also J. T. LOWRY AND W. C. SCHIEVE: Trans. Th. and Stat. Phys. 1(3), 225 (1971).

    Google Scholar 

  78. E.G.D. COHEN: in Fundamental Problems in Statistical Mechanics, ed. by C.G.D. Cohen (North-Holland, Amsterdam, 1962).

    Google Scholar 

  79. M. C. GOLDBERGER AND K. M. WATSON: Collision Theory (John Wiley, New York, 1964).

    Google Scholar 

  80. E. P. WIGNER: Phys. Rev. 40, 479 (1932).

    Article  Google Scholar 

  81. D. MASSIGNON: Mécanique Statistique des Fluides (Dunod, Paris, 1957).

    Google Scholar 

  82. H. MORI, I. OPPENHEIM AND J. ROSS: in Studies in Statistical Mechanics I, J. de Boer and G. E. Uhlenbeck, ed. (NorthHolland, Amsterdam, 1962).

    Google Scholar 

  83. H. WEYL: The Theory of Groups and Quantum Mechanics, Second Edition (Dover Publ., New York, 1961).

    Google Scholar 

  84. L. COHEN: J. Math. Phys. 7, 781 (1966).

    Article  Google Scholar 

  85. K. HAWKER: “Considerations of Formal Quantum Kinetic Theory”, Thesis, University of Texas at Austin, June, 1974.

    Google Scholar 

  86. D. BRASON: Phys. Rev. 135, 513; B 1255 (1964).

    Google Scholar 

  87. S. IMAM-RAHAJOE AND C. F. CURTISS: J. Chem. Phys. 47, 5269 (1967).

    Article  Google Scholar 

  88. M. W. THOMAS AND R. F. SNIDER: J. Stat. Phys. 2, 2 (1970).

    Article  Google Scholar 

  89. E.C.G. STUECKELBERG: Helv. Phys. Acta 25, 577 (1952).

    Google Scholar 

  90. J. WEINSTOCK: Phys. Rev. 132, 454 (1967); 140A, 460 (1965).

    Article  Google Scholar 

  91. J. R. DORFMAN AND E.G.D. COHEN: Phys. Letters 16, 124 (1965)

    Article  Google Scholar 

  92. J. Math. Phys. 8, 282 (1967).

    Google Scholar 

  93. G. E. UHLENBECK: “The Validity and Limitations of the Boltzmann Equation”, page 107, reference 65.

    Google Scholar 

  94. E.G.D. COHEN: “The Generalizations of the Boltzmann Equation to Higher Order in the Densities”, page 157, reference 65.

    Google Scholar 

  95. T. NEAL: Phys. Rev. 1691, 508 (1968).

    Article  Google Scholar 

  96. P. RÉSIBOIS AND M. G. VELARDE: Physica 51, 541 (1971).

    Article  Google Scholar 

  97. J. V. SENGERS: “The Three Particle Collision Term in the Generalized Boltzmann Equation”, page 177, reference 65.

    Google Scholar 

  98. B. J. ALDER AND T. E. WAINWRIGHT: Phys. Rev. A1, 18 (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Texas at Austin, Texas

    William C. Schieve

Authors
  1. William C. Schieve
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

J. Ehlers J. Ford C. George R. Miller E. Montroll W. C. Schieve J. S. Turner

Rights and permissions

Reprints and permissions

Copyright information

© 1974 Springer-Verlag

About this chapter

Cite this chapter

Schieve, W.C. (1974). Aspects of non-equilibrium quantum statistical mechanics: An introduction. In: Ehlers, J., et al. Lectures in Statistical Physics. Lecture Notes in Physics, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008852

Download citation

  • DOI: https://doi.org/10.1007/BFb0008852

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06711-5

  • Online ISBN: 978-3-540-38006-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation