Quantum Decoherence and Pointer Basis: Dynamics in State Vectors

TL;DR

This paper explores the dynamics of quantum decoherence, showing how pointer states are selected through the action's saddle point condition, providing insights into the decoherence mechanism in quantum systems.

Contribution

It introduces a new formulation linking pointer basis selection to the action's saddle point condition, enhancing understanding of decoherence dynamics.

Findings

Pointer basis diagonalizes the interaction Hamiltonian.

Pointer states branch according to the action values.

Decoherence mechanism is clarified through phase analysis.

Abstract

It is well-known that the pointer basis of a quantum system satisfies the condition to diagonalize the interaction Hamiltonian between the subsystems. We show that this condition can be translated into the form $\delta\Lambda=0,$ where $\Lambda$, so-called the action, is the time integrated interaction energy: it is found out naturally in the phase of state vectors due to diagonal interaction. The careful treatment of a two states system demonstrates that the states of the total system branch into the states with different values of the action. Mathematically the pointer states are selected out by the saddle point condition on the phase $\Lambda$. This study helps us to understand the precise mechanism and the general dynamics of decoherence.