Quantization of Lagrangian Descriptors

• URL: http://arxiv.org/abs/2604.04128v1
• Date: Sun, 05 Apr 2026 14:16:27 GMT
• Title: Quantization of Lagrangian Descriptors
• Abstract summary: We formulate Lagrangian descriptors (LDs) in the path integral framework.<n>Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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