Quantum propagation for Berezin-Toeplitz operators

2020/09/11 by Laurent Charles, Charles, Laurent, Yohann Le Floch +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2009.05279

openalex publication_date 2020/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the asymptotic behaviour of the quantum propagator generated by a Berezin-Toeplitz operator with real-valued principal symbol. We also give precise asymptotics for smoothed spectral projectors associated with the operator in the autonomous case; this leads us to introducting quantum states associated with immersed Lagrangian submanifolds. These descriptions involve geometric quantities of two origins, coming from lifts of the Hamiltonian flow to the prequantum bundle and the canonical bundle respectively. The latter are the main contribution of this article and are connected to the Maslov indices appearing in trace formulas, as will be explained in a forthcoming paper.

Citations

• The spectral function of an elliptic operator

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