Quantum Mechanics of Complex Systems, II

  • A. J. Leggett
Part of the NATO ASI Series book series (NSSB, volume 218)


So far our treatment has been general and schematic. In order actually to calculate the effect of the environment quantitatively, we need an explicit model of the dynamics of the environment and its interaction with the system. At this point one of two situations can arise, corresponding roughly to whether our system is microscopic (and relatively simple) or macroscopic. In the first case, we often have a good a priori knowledge of the Hamiltonian governing the environment and its interaction with the system. This is the case, for example, in small molecules (when for most purposes the total Hamiltonian of the molecule is just the sum of the nuclear and electron kinetic energies and the various Coulomb interactions); it may also be approximately true in other situations of interest in chemical physics or solid-state physics, e.g. in muon diffusion. On the other hand, if we are dealing with the motion of a macroscopic variable, such as the angle made by a pendulum with the vertical, or the relative phase of the Cooper pairs in a Josephson junction, then it is unlikely that we know the details of the microscopic Hamiltonian with any confidence. What is much more likely, and indeed the norm, in this type of case is that we know the effects of the environment on the classical motion of the system, as instantiated for example in the classical friction coefficient. It is then an important question, to which we shall return below, whether a knowledge of such classical effects is sufficient to determine the effects of the environment also on the quantum dynamics of the system.


Density Matrix Isolate System Coherence Energy Josephson Junction Reduce Density Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. O. Caldeira and A. J. Leggett, Ann. Phys. 149, 374 (1983).ADSCrossRefGoogle Scholar
  2. 2.
    A. J. Leggett, Phys. Rev. B30, 1208 (1984).ADSGoogle Scholar
  3. 3.
    C. C. Yu and P. W. Anderson, Phys. Rev. B29, 6165 (1984).ADSGoogle Scholar
  4. 4.
    L-D. Chang and S. Chakravarty, Phys. Rev. B31, 154 (1985).ADSGoogle Scholar
  5. 5.
    Y. C. Chen, J. Stat. Phys. 47, 17 (1987).ADSCrossRefGoogle Scholar
  6. 6.
    A. J. Leggett, in Frontiers and Borderlines in Many-Particle Physics, ed. R. A. Broglia and J. R. Schrieffer, Società Italiana di Fisica, Bologna (1988).Google Scholar
  7. 7.
    V. Ambegaokar and U. Eckern, Z. Phys. B69, 399 (1987).ADSCrossRefGoogle Scholar
  8. 8.
    H. Grabert, talk at 1986 Budapest Workshop on Quantum Tunnelling in Many-Dimensional Systems, unpublished.Google Scholar
  9. 9.
    W. Zwerger, A. T. Dorsey and M. P. A. Fisher, Phys. Rev. B34, 6518 (1986).ADSGoogle Scholar
  10. 10.
    W. H. Zurek and W. G. Unruh, Phys. Rev. D, in press.Google Scholar
  11. 11.
    A. J. Leggett and Anupam Garg, Phys. Rev. Lett. 54, 857 (1985).MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    A. J. Leggett, S. Chakravarty, A. T. Dorsey, Matthew P. A. Fisher, Anupam Garg and W. Zwerger, Revs. Mod. Phys. 59, 1 (1987).ADSCrossRefGoogle Scholar
  13. 13.
    R. A. Silbey and R. A. Harris, J. Chem. Phys. 80, 2615 (1984).ADSCrossRefGoogle Scholar
  14. 14.
    S. Chakravarty, Phys. Rev. Lett. 50, 1811 (1982).ADSCrossRefGoogle Scholar
  15. 15.
    A. J. Bray and M. A. Moore, Phys. Rev. Lett. 49, 1546 (1982).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • A. J. Leggett
    • 1
  1. 1.Department of PhysicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations