Pointer States and Decoherence in Quantum Unitarity: Energy Conservation for Weak Interaction Model

TL;DR

This paper derives pointer states in a weak interaction quantum model, showing they emerge as localized states with energy conservation maintained, differing from typical quantum evolution.

Contribution

It introduces a simple perturbation method to identify pointer states in a macro-object model with weak environment interaction, ensuring energy conservation.

Findings

Pointer states are localized and emerge when interaction is weak.

Energy conservation holds due to dominant non-classical states.

Unitary evolution of pointer states differs from the total system's evolution.

Abstract

The purpose of the present paper is to derive the pointer states of a macro-object using a simple perturbation method. We study the model Hamiltonian involving the weak interaction between the center of mass and its environment. The main conclusion is that the pointer states emerge as the small part of the total state vector when the interaction Hamiltonian is not dominant: the degrees of freedom being at the center of interaction can be localized. In the weak interaction case, if the disappearance of the energy contribution from the off-diagonal terms is caused by the decoherence, it threatens the conservation law. In this study, however, the energy conservation reasonably holds, since the non-classical (i.e., normal quantum) states give main contribution to it. The emergence of the pointer states also implies the special initial state in which the localized state makes the deep well of the potential. In the result, the unitary time evolution of a pointer state is very different from that of the majority of the original state vector of the total system.