2024/11/16 by Chaoming Song, Song, Chaoming
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2411.10691
openalex publication_date 2024/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Gutzwiller trace formula establishes a profound connection between the quantum spectrum and classical periodic orbits. However, its application is limited by its reliance on the semiclassical saddle point approximation. In this work, we explore the full quantum version of the trace formula using the Lefschetz thimble method by incorporating complexified periodic orbits. Upon complexification, classical real periodic orbits are transformed into cycles on compact Riemann surfaces. Our key innovation lies in the simultaneous complexification of the periods of cycles, resulting in a fully quantum trace formula that accounts for all contributions classified by the homology classes of the associated Riemann surfaces. This formulation connects the quantum spectrum to contributions across all complex time directions, encompassing all relevant homology classes. Our approach naturally unifies and extends two established methodologies: periodic orbits in real time, as in Gutzwiller's original work, and quantum tunneling in imaginary time, as in the instanton method.