Linear response theory for open quantum systems within the framework of the ABL formalism

Abstract

A linear response theory of the strong and weak values in open quantum systems is developed within the framework of the Aharonov–Bergmann–Lebowitz formalism of quantum mechanics. The measurement of an observable influenced by an external field is performed between pre-selection and post-selection. The system irreversibly evolves from a pre-selected state to a post-selected one due to an interaction with a surrounding environment. The effect of the external field on the measured observable is described in terms of forward and backward response functions. A backward response function appears in the theory since the post-selection of the system is performed. Furthermore, the results are extended beyond the strong and weak values.