UNIFIED TIME-PATH APPROACH TO THE GENERATING FUNCTIONAL OF THE BROWNIAN OSCILLATOR SYSTEM - THE BILINEARLY CORRECTED FEYNMAN RULE FOR NONEQUILIBRIUM PROCESSES

We derive fully corrected propagators of a bilinearly interacting Brow nian oscillator system by summing up an infinite number of Feynman dia grams. The generating functional of a nonequilibrium system is calcula ted in terms of the bilinearly corrected propagators thus obtained. Th e result offers the Feynman rule for systematically studying the effec ts of both anharmonicity of the potential and nonbilinear system-bath couplings on the Brownian oscillator system. The reduced density matri x, which is useful for investigating the dynamics of the system, is al so calculated. The unified time path, which is powerful in calculating propagators, is introduced and used effectively throughout the work.