Effects from Additional Random Configuration to Linear Response and Modified Fluctuation-Dissipation Relation
Abstract
In this work, a physical system described by Hamiltonian Hω = H0 + Vω(x,t) consisted of a solvable model H and external random and time-dependent potential Vω(x,t) is investigated. Under the conditions that the average external potential with respect to the configuration ω is constant in time, and, for each configuration, the potential changes smoothly that the evolution of the system follows Schr\"odinger dynamics, the mean-dynamics can be derived from taking average of the equation with respect to configuration parameter ω. It provides extra contributions from the deviations of the Hamiltonian and evolved state along the time to the Heisenberg and Liouville-von Neumann equations. Consequently, the Kubo's formula and the fluctuation-dissipation relation obtained from the construction is modified in the sense that the contribution from the information of randomness and memory effect from time-dependence are present.