Preferred Basis in a Measurement Process

TL;DR

This paper demonstrates that in a dissipative environment, a free particle's density matrix becomes diagonal in momentum space over time, establishing momentum as the preferred basis contrary to common expectations.

Contribution

It provides an exact solution showing the environment selects momentum as the preferred basis, challenging the usual assumption that position is preferred due to the coupling.

Findings

Density matrix becomes diagonal in momentum over time

Position space density matrix remains nonlocal

Momentum basis emerges as the preferred basis

Abstract

The effect of decoherence is analysed for a free particle, interacting with an environment via a dissipative coupling. The interaction between the particle and the environment occurs by a coupling of the position operator of the particle with the environmental degrees of freedom. By examining the exact solution of the density matrix equation one finds that the density matrix becomes completely diagonal in momentum with time while the position space density matrix remains nonlocal. This establishes the momentum basis as the emergent 'preferred basis' selected by the environment which is contrary to the general expectation that position should emerge as the preferred basis since the coupling with the environment is via the position coordinate.