Local scaling asymptotics in phase space and time in Berezin-Toeplitz quantization

TL;DR

This paper investigates the local semiclassical behavior of quantum evolution operators in Berezin-Toeplitz quantization, focusing on scaled phase space and time variables, and explores implications for the trace asymptotics over time.

Contribution

It introduces new local scaling asymptotics in phase space and time for Berezin-Toeplitz quantization, linking quantum dynamics to classical trajectories.

Findings

Derived local asymptotics of quantum evolution operators.

Established global trace asymptotics related to classical dynamics.

Connected local phase space behavior with global spectral properties.

Abstract

This paper deals with the local semiclassical asymptotics of a quantum evolution operator in the Berezin-Toeplitz scheme, when both time and phase space variables are subject to appropriate scalings in the neighborhood of the graph of the underlying classical dynamics. Global consequences are then drawn regarding the scaling asymptotics of the trace of the quantum evolution as a function of time.