Path integral based transition probability evaluation in a quantum system with a diagonal density matrix of the final state

Abstract

The variant of transition probability evaluation in a quantum system, based on transition probability representation by a path integral using a density matrix formalism, is described. To estimate an integral's value, a set of variables is selected and the Monte Carlo method is used for integration over these variables. The stationary phase method is applied to integration over the remaining variables. In the case of the final state with a diagonal density matrix, this scheme leads to a simple expression for transition probability.