Einselection without pointer states

TL;DR

This paper proves that small subsystems of large quantum systems naturally exhibit decoherence in their local energy eigenbasis over time, without approximations or special assumptions, highlighting decoherence as an inherent property of weak interactions.

Contribution

It provides a rigorous proof that decoherence occurs in the local energy eigenbasis for almost all initial states and times in weakly interacting quantum systems, without relying on approximations.

Findings

Off-diagonal elements of the subsystem's density matrix are small for large energy differences.

Decoherence in the local energy basis is a natural property of weakly interacting quantum systems.

Decoherence occurs for almost all initial states and times without special assumptions.

Abstract

We consider small subsystems of large, closed quantum systems that evolve according to the von Neumann equation. Without approximations and without making any special assumptions on the form of the interaction we prove that, for almost all initial states and almost all times, the off-diagonal elements of the density matrix of the subsystem in the eigenbasis of its local Hamiltonian must be small, whenever the energy difference of the corresponding eigenstates is larger than the interaction energy. This proves that decoherence with respect to the local energy eigenbasis is a natural property of weakly interacting quantum systems.