Scaling asymptotics for quantized Hamiltonian flows

TL;DR

This paper investigates the local scaling asymptotics of Toeplitz quantization of Hamiltonian symplectomorphisms, extending previous work on Szeg"{o} kernel asymptotics to quantum-classical correspondence.

Contribution

It introduces a new analysis of how quantized Hamiltonian flows concentrate on classical graphs, generalizing near-diagonal asymptotics in symplectic geometry.

Findings

Derived asymptotic formulas for quantized Hamiltonian flows

Showed concentration of quantum states on classical graphs

Extended Szeg"{o} kernel asymptotics to Hamiltonian symplectomorphisms

Abstract

In recent years, the near diagonal asymptotics of the equivariant components of the Szeg\"{o} kernel of a positive line bundle on a compact symplectic manifold have been studied extensively by many authors. As a natural generalization of this theme, here we consider the local scaling asymptotics of the Toeplitz quantization of a Hamiltonian symplectomorphism, and specifically how they concentrate on the graph of the underlying classical map.