Nonlinear evolution of coarse-grained quantum systems with generalized purity constraints

TL;DR

This paper introduces a nonlinear dynamical equation for coarse-grained quantum systems constrained by generalized purity, linking it to pointer states and decoherence in open quantum systems.

Contribution

It proposes a new nonlinear evolution equation for pure states under generalized purity constraints, connecting coarse-graining, decoherence, and pointer states.

Findings

Constrained dynamics match pointer state equations in weak coupling.

The approach relates generalized coherent states to decoherence processes.

Open system models support the proposed nonlinear evolution.

Abstract

Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant fluctuation, and the coarse-grained pure states correspond to the generalized coherent i.e. generalized nonentangled states. Open system model of the coarse-graining is discussed. It is shown that in this model and in the weak coupling limit the constrained dynamical equations coincide with an equation for pointer states, based on Hilbert-Schmidt distance, that was previously suggested in the context of the decoherence theory.