Geometric Diagnostics of Scrambling-Related Sensitivity in a Bohmian Preparation Space

• URL: http://arxiv.org/abs/2603.20803v1
• Date: Sat, 21 Mar 2026 12:56:12 GMT
• Title: Geometric Diagnostics of Scrambling-Related Sensitivity in a Bohmian Preparation Space
• Abstract summary: We propose a Bohmian framework for constructing a geometric diagnostic of scrambling-related sensitivity using Lagrangian Descriptors (LDs)<n>We show that the exponential growth of the associated preparation-space stability matrix yields an $mathcalO(eT)$ bound on the sensitivity of the wavepacket-center LDs.<n>In particular, away from the equilibrium origin, the exponential growth of the associated preparation-space stability matrix yields an $mathcalO(eT)$ bound on the sensitivity of the wavepacket-center LDs.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Out-of-Time-Order Correlator (OTOC) is a standard algebraic diagnostic of quantum information scrambling, but it offers limited direct geometric intuition. In this note, we propose a Bohmian, trajectory-based framework for constructing a geometric diagnostic of scrambling-related sensitivity using Lagrangian Descriptors (LDs). To avoid the uncertainty-principle obstruction to assigning independent initial position and momentum within a single wave function, we evaluate Bohmian dynamics over a two-dimensional preparation space of localized Gaussian wavepackets labeled by their initial center and momentum kick. For the inverted harmonic oscillator, this construction is analytically tractable: the wavepacket-center dynamics and their dependence on preparation parameters can be written explicitly. In particular, away from the equilibrium origin, the exponential growth of the associated preparation-space stability matrix yields an $\mathcal{O}(e^{ωT})$ bound on the sensitivity of the wavepacket-center LDs, motivating a semiclassical comparison with sensitivity structures associated with OTOC growth. In this sense, the LD provides a geometric indicator of scrambling-related sensitivity. We conclude by discussing how this preparation-space picture suggests a program for future work regarding the distinct microcanonical regimes previously reported for the inverted harmonic oscillator.

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