Equilibrium Fluctuations for Some Stochastic Particle Systems

  • Herbert Spohn
Part of the Progress in Physics book series (PMP, volume 10)

Abstract

Our knowledge about the microscopic structure of macroscopic systems in thermal equilibrium is encoded as equilibrium time correlations. These objects are measured in scattering experiments: a purely angular resolution of the scattered beam translates into static correlations and its frequency (energy) resolution into time correlations. Despite their central physical importance our mathematical understanding of equilibrium time correlations is very modest, quite in contrast to their static counterpart on which we have a wealth of qualitative information.

Keywords

Gibbs Measure Martingale Problem Zero Range Process Reflect Boundary Condition Equilibrium Fluctuation 
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.

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References

  1. [1]
    R.A. Holley and D.W. Stroock, Comm.Math.Phys. 48, 2k9 (1976)Google Scholar
  2. [2]
    R.A. Holley and D.W. Stroock, Z. Wahrscheinlichkeitstheorie verw. Gebiete 35, 87 (1976)CrossRefGoogle Scholar
  3. [3]
    D. Wiek, Comm.Math.Phys. 8l, 361 (1981)CrossRefGoogle Scholar
  4. [4]
    H. Spohn, Large Scale Behavior of Equilibrium Time Correlation Functions for Some Stochastic Ising Models. In: Stochastic Processes in Quantum Theory and Statistical Physics, ed. S. Albeverio, Ph. Combe and M. Sirugue-Collin. Lecture Notes in Physics 173, p. 30U. Springer, Berlin 1982Google Scholar
  5. [5]
    A. De Masi, N. Ianiro, A. Pellegrinotti and A. Presutti, A Survey of the Hydrodynamical Behavior of Many-Particle Systems. In: Non-equilibrium Phenomena II, eds. J.L. Lebowitz and E.W. Montroll. North-Holland, Amsterdam 198UGoogle Scholar
  6. [6]
    K. Kawasaki, Kinetics of Ising Models. In: Phase Transitions and Critical Phenomena, eds. C. Domb and M. Green, vol. 2. Academic Press, New York 1972Google Scholar
  7. [7]
    T.M. Liggett, The Stochastic Evolution of Infinite Systems of Interacting Particles. Lecture Notes in Mathematics 598. Springer, Berlin 1978Google Scholar
  8. [8]
    T.M. Liggett, Ann.Prob. 240 (1973)Google Scholar
  9. [9]
    P.N. Pusey and R.J.A. Tough, J.Phys. A15, 1291 (1982)Google Scholar
  10. [10]
    P.N. Pusey and R.J.A. Tough in: Dynamic Light Scattering and Veloci-metry: Applications of Photon Correlation Spectroscopy, eds. R. Pe-cora. Plenum Press, New York 1981Google Scholar
  11. [11]
    J.W. Cahn and J.E. Hilliard, J.Chem.Phys. 28, 258 (1958)CrossRefGoogle Scholar
  12. [12]
    P.C. Hohenberg and B.I. Halperin, Rev.Mod.Phys. kg, 35 (1977)Google Scholar
  13. [13]
    R. Lang, Z. Wahrscheinlichkeitstheorie verw. Gebiete 38, 55 (1977)CrossRefGoogle Scholar
  14. [14]
    T. Shiga, Z. Wahrscienlichkeitstheorie verw. Gebiete Vf, 299 (1979)Google Scholar
  15. [15]
    W.H. Faris, J.Funct.Anal. 32, 32 (1979)CrossRefGoogle Scholar
  16. [16]
    S. Katz, J.L. Lebowitz, H. Spohn, J.Stat.Phys. 34, 497 (1980)CrossRefGoogle Scholar
  17. [17]
    A. De Masi, E. Presutti, H. Spohn, D. Wiek, Asymptotic Equivalence of Fluctuation Fields for Reversible Exclusion Processes with Speed Change, preprintGoogle Scholar
  18. [18]
    R.A. Holley and D.W. Stroock, RIMS Kyoto Publications A14, 741 (1978)CrossRefGoogle Scholar
  19. [19]
    T. Brox and H. Rost, Ann.Prob, to appearGoogle Scholar
  20. [20]
    H. Spohn, Equilibrium Fluctuations for Interacting Brownian Particles, preprintGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Herbert Spohn
    • 1
  1. 1.Theoretische PhysikUniversität München8 München 2Germany

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