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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.20803 |
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| _version_ | 1866910062558052352 |
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| author | Wiggins, Stephen |
| author_facet | Wiggins, Stephen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20803 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric Diagnostics of Scrambling-Related Sensitivity in a Bohmian Preparation Space Wiggins, Stephen Quantum Physics Chaotic Dynamics Chemical Physics 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. |
| title | Geometric Diagnostics of Scrambling-Related Sensitivity in a Bohmian Preparation Space |
| topic | Quantum Physics Chaotic Dynamics Chemical Physics |
| url | https://arxiv.org/abs/2603.20803 |