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From quantum theory to classical dynamics under the reduction of wave packets

A quantum master equation of the Lindblad form is obtained in this paper by considering the reduction of wave packets. Different classical equations are derived after exactly mapping such a quantum master equation to a continuous time random walk (CTRW). Although this CTRW is a quasiclassical walk, the effects due to the quantum interference can still be important in such a walk. It is shown that macroscopically we shall consider the uncertainty of the potential and determine the effective kernel (transition probability) of this CTRW by a family of Schrödinger equations (or operators).