- Access by Xinjiang University
Exact exponential function solution of the generalized Langevin equation for autocorrelation functions of many-body systems
Phys. Rev. E 85, 022102 – Published 17 February, 2012
DOI: https://doi.org/10.1103/PhysRevE.85.022102
Abstract
We show that an exact solution of the generalized Langevin equation (GLE) for the autocorrelations of a many-body classical system can be given in an exponential functionality (EF) form. As a consequence, the power spectrum of the correlation has a Lorentzian functionality, i.e., is represented by an infinite sum of Lorentzian functions corresponding to the eigenmodes of the considered correlation. By means of the simple derivation of the GLE by M. H. Lee [Phys. Rev. B 26, 2547 (1982)], we also show that, in practical cases of interest to experimental spectroscopies, possible approximations of the EF are related to a reduction of the relevant dynamical variables via a restriction of the dimensions of the orthogonalized space onto which the dynamics of the system is projected.
Article Text
References (10)
- H. Mori, Prog. Theor. Phys. 33, 423 (1965); 34, 399 (1965).
- R. Zwanzig, in Lectures in Theoretical Physics, edited by W. E. Brittin (Interscience, New York, 1961); Annu. Rev. Phys. Chem. 16, 67 (1965).
- R. Zwanzig, J. Stat. Phys. 13, 347 (1975).
- For an overview of the memory function method see, for example, J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, New York, 1980); J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, 2nd ed. (Academic Press, London, 1986); U. Balucani and M. Zoppi, Dynamics of the Liquid State (Clarendon, Oxford, 1994).
- M. H. Lee, Phys. Rev. B 26, 2547 (1982).
- M. H. Lee, Phys. Rev. Lett. 49, 1072 (1982).
- M. H. Lee, Phys. Rev. E 62, 1769 (2000).
- G. Szego, Orthogonal Polynomials (American Mathematical Society, Providence, RI, 1975); G. Grosso and G. Pastori Parravicini, in Memory Function Approaches to Stochastic Problems in Condensed Matter, edited by M. W. Evans, P. Grigolini, and G. Pastori Parravicini, Advances in Chemical Physics, Vol. LXII (John Wiley & Sons, New York, 1985), p. 81.
- U. Bafile, E. Guarini, and F. Barocchi, Phys. Rev. E 73, 061203 (2006); M. Sampoli, U. Bafile, E. Guarini, and F. Barocchi, Phys. Rev. B 79, 214203 (2009); U. Bafile, E. Guarini, M. Sampoli, and F. Barocchi, Phys. Rev. E 80, 040201(R) (2009).
- I. M. de Schepper, P. Verkerk, A. A. van Well, and L. A. de Graaf, Phys. Rev. Lett. 50, 974 (1983).