Statistical measure of complexity for quantum systems with continuous variables

TL;DR

This paper introduces a generalized Fisher-Shannon complexity measure for quantum systems with continuous variables, demonstrating its application to a free particle in a box and highlighting the limitations of traditional measures.

Contribution

It proposes a new integrated complexity measure over parameter space, extending the Fisher-Shannon measure for a more complete quantum system analysis.

Findings

Traditional measures in configuration and momentum spaces are insufficient.

The integrated measure provides a more comprehensive complexity assessment.

Application to a free particle in a box illustrates the method's effectiveness.

Abstract

The Fisher-Shannon statistical measure of complexity is analyzed for a continuous manifold of quantum observables. It is probed then than calculating it only in the configuration and momentum spaces will not give a complete description for certain systems. Then a more general measure for the complexity of a quantum system by the integration of the usual Fisher-Shannon measure over all the parameter space is proposed. Finally, these measures are applied to the concrete case of a free particle in a box.