Abstract
The influence of initial deviations from bath equilibrium on the motion of a Brownian particle in a harmonic chain is investigated by exact calculation. These initial condition effects, which are excluded by convention in standard projection operator treatments of relaxation processes, are found to be relatively long-lived, contrary to usual assumption. For weak, localized initial deviations from bath equilibrium these effects on the motion are small in magnitude and may be accounted for by a modified initial condition on the particle velocity. For initial deviations involving many bath particles these effects are more substantial and retention of their time dependence in the particle equation of motion is generally required.
Similar content being viewed by others
References
P. C. Hemmer,Det. Fys. Seminar i Trondheim 2 (1959).
R. J. Rubin,J. Math. Phys. 1:309 (1960); (b)2:373 (1961); (c)Phys.Rev. 131:964 (1963).
F. O. Goodman,J. Phys. Chem. Solids 23:1491 (1962).
S. Takeno and J. Hori,Prog. Theor. Phys. (Kyoto) Suppl. 23:177 (1962); P. Mazur and E. Braun,Physica (Utr.)30:1973 (1964); P. Ullersma,Physica (Utr.)32:74 (1966)
J. M. Deutch and R. Silbey,Phys. Rev. A 3:2049 (1971). K. Wada and J. Hori,Prog. Theor. Phys. (Kyoto) 49:129 (1973).
P. Résibois,Electrolyte Theory, Harper and Row, New York (1968); U. Fano, inLectures on the Many Body Problem, E. R. Caianello, ed., Academic Press, New York (1964), Vol. 2; J. Albers and J. M. Deutch,J. Chem. Phys. 55:2613 (1971).
E. H. Hauge,Phys. Fluids 13:1201 (1970); M. Bixon, J. R. Dorfman, and K. C. Mo,Phys. Fluids 14:1049 (1971); J. T. Ubbink and E. H. Hauge,Physica (Utr.) 70:297 (1973)
J. T. Hynes,J. Chem. Phys. 59:3459 (1973).
S. Kashiwamura,Prog. Theor. Phys (Kyoto) 27:571 (1962);Prog. Theor. Phys. (Kyoto) Suppl. 23:207 (1962).
I. Fujiwara, P. C. Hemmer, and H. Wergeland,Prog. Theor. Phys. (Kyoto) Suppl. 37/38:141 (1966).
R. I. Cukier,Physica (Utr.) 61:321 (1972).
A. A. Maradudin, E. W. Montroll, G. H. Weiss, and I. P. Ipatova,Theory of Lattice Dynamics in the Harmonic Approximation, 2nd ed., Academic Press, New York (1971).
H. Nakazawa,Prog. Theor. Phys. (Kyoto) Suppl. 36:172 (1966).
M. Abramowitz and I. A. Stegun (eds.),Natl. Bur. Std. (U.S.),Appl. Math. Ser., Vol. 55 (1964), pp. 358, 480.
E. L. Chang, R. M. Mazo, and J. T. Hynes,Molec. Phys., to appear.
R. I. Cukier, K. E. Shuler, and J. D. Weeks,J. Stat. Phys. 5:99 (1972).
L. B. W. Jolley,Summation of Series, Dover, New York (1961), p. 94.
I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series, and Products, A. Jeffrey, transi., Academic Press, New York (1965), p. 401.
G. Roberts and H. Kaufman,Table of Laplace Transforms (W. B. Saunders, Philadelphia, Pennsylvania (1966), p. 57.
Author information
Authors and Affiliations
Additional information
For a correction to Ref. 2a see Ref. 3.
Rights and permissions
About this article
Cite this article
Hynes, J.T. Initial condition effects for a Brownian particle in a harmonic chain. J Stat Phys 11, 257–275 (1974). https://doi.org/10.1007/BF01010220
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01010220