The globally stable solution of a stochastic Nonlinear Schrodinger Equation

TL;DR

This paper derives the globally stable solution of a stochastic nonlinear Schrödinger equation in quantum systems, showing it corresponds to generalized coherent states that minimize certain covariance measures, advancing understanding of open quantum system dynamics.

Contribution

It identifies the stable solution of the sNLSE as a generalized coherent state for systems with spectrum-generating algebra, providing a new analytical insight into quantum measurement processes.

Findings

The stable solution of the sNLSE is a generalized coherent state.

Generalized coherent states minimize the trace-norm of the covariance matrix.

The result applies when the measured observables form the spectrum-generating algebra.

Abstract

Weak measurement of a subset of noncommuting observables of a quantum system can be modeled by the open-system evolution, governed by the master equation in the Lindblad form. The open-system density operator can be represented as statistical mixture over non unitarily evolving pure states, driven by the stochastic Nonlinear Schrodinger equation (sNLSE). The globally stable solution of the sNLSE is obtained in the case where the measured subset of observables comprises the spectrum-generating algebra of the system. This solution is a generalized coherent state (GCS), associated with the algebra. The result is based on proving that GCS minimize the trace-norm of the covariance matrix, associated with the spectrum-generating algebra.