title: Exact exponential function solution of the generalized Langevin equation for autocorrelation functions of many-body systems.
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.
authors.affiliation: Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy.
authors.forename: Fabrizio
authors.initials: F
authors.lastname: Barocchi
authors.forename: Ubaldo
authors.initials: U
authors.lastname: Bafile
authors.forename: Marco
authors.initials: M
authors.lastname: Sampoli
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical