Reconsideration of Mori's Theory of Generalized Brownian Motion and Its Application

Abstract

For every system with a passably general Hamiltonian of a quantum harmonic oscillator coupled to infinitely many scalar bosons, we estimate Heisenberg pictures of the annihilation and creation operators, describing the quantum harmonic oscillator, from only data on the autocorrelation function of the operators such that the pictures restore their autocorrelation functions to original ones, by reconsidering Mori's theory of generalized Brownian motion. And we then investigate the Liouville space and Liouville operator associated with the estimation.