Quantization of Lagrangian Descriptors
Abstract
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply organize classical transport, become finite-width phase space structures under quantum fluctuations, and their overlap provides a geometric mechanism consistent with tunneling as fluctuation-induced delocalization of transport barriers. We demonstrate this approach for the Hamiltonian saddle, where path integral sampling reveals manifold broadening and barrier penetration. This establishes a geometric framework for studying phase space transport and tunneling beyond the classical regime, while also providing a natural route toward the application of LDs to field theory.
Cite
@article{arxiv.2604.04128,
title = {Quantization of Lagrangian Descriptors},
author = {Javier Jiménez-López and V. J. García-Garrido},
journal= {arXiv preprint arXiv:2604.04128},
year = {2026}
}