MOLECULAR TIME-SCALE GENERALIZED LANGEVIN EQUATION THEORY AND POLYNOMIAL MAXIMUM-ENTROPY IMAGING OF SPECTRAL DENSITIES

Molecular time scale generalized Langevin equation (MTGLE) theory is d iscussed as an approach to condensed phase dynamics. A polynomial maxi mum entropy (MaxEnt) process for imaging required MTGLE spectral densi ties based on knowledge of the moments of the spectral density is intr oduced. The process is based on the use of interpolation polynomials w hich serve both to image the spectral density as well as provide a num erical procedure to compute the inverse Hessian matrix in a Newton-typ e minimization. A default model is added to allow for the inclusion of additional information in forming the image. The polynomial MaxEnt im aging process is found to be a fast, numerically stable, computational procedure which produces images comparable in quality to images obtai ned by other imaging processes. The polynomial MaxEnt imaging process is examined in the context of imaging MTGLE bath spectral densities wi th special emphasis on a coupled linear chain model. Standard harmonic oscillator, Hamiltonian bath models such as Ohmic-exponential and Ohm ic-Gaussian are shown to possess regions of parameter space for which the MTGLE adiabatic frequency is imaginary. When the adiabatic frequen cy is zero, it is shown that imaging of the friction kernel is the bes t approach. (C) 1998 American Institute of Physics. [S0021-9606(98)515 43-7].