Inferring topology of quantum phase space

TL;DR

This paper explores whether semiclassical particles retain phase space topology information using Berezin-Toeplitz quantization and topological data analysis, introducing a calculus of Toeplitz operators with piecewise constant symbols.

Contribution

It introduces a novel approach combining topological data analysis with Berezin-Toeplitz quantization to study phase space topology in quantum systems.

Findings

Demonstrates the application of topological data analysis to quantum phase space

Develops a calculus for Toeplitz operators with piecewise constant symbols

Provides insights into the topological properties of quantum phase space

Abstract

Does a semiclassical particle remember the phase space topology? We discuss this question in the context of the Berezin-Toeplitz quantization and quantum measurement theory by using tools of topological data analysis. One of its facets involves a calculus of Toeplitz operators with piecewise constant symbol developed in an appendix by Laurent Charles.