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

Quantum Physics [Submitted on 21 Mar 2026] Geometric Diagnostics of Scrambling-Related Sensitivity in a Bohmian Preparation Space Stephen Wiggins 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^{\omega T}) 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. Comments: 6 pages, 1 figure Subjects: Quantum Physics (quant-ph); Chaotic Dynamics (nlin.CD); Chemical Physics (physics.chem-ph) Cite as: arXiv:2603.20803 [quant-ph]   (or arXiv:2603.20803v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20803 Focus to learn more Submission history From: Stephen Wiggins [view email] [v1] Sat, 21 Mar 2026 12:56:12 UTC (1,054 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: nlin nlin.CD physics physics.chem-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)