aiqbench analysis
This research delves into the quantum bouncing ball problem, specifically analyzing how classical caustics manifest as phase singularities and regions of superenergy within a Gaussian wavepacket. By linking these phenomena to semiclassical Pearcey functions and Bohmian trajectories, the study offers fundamental insights into interference patterns that transcend standard eigenstate descriptions. Such theoretical advancements are crucial for understanding complex quantum dynamics in systems where trajectory-based intuition meets rigorous wave mechanics.
Caustics and Superenergy in the Quantum Bouncer
arXiv:2608.02427v1 Announce Type: new Abstract: We investigate the quantum interference and energetic phenomena associated with classical caustics in the quantum bouncing ball problem, we refer to as quantum caustics. By considering an initial Gaussian wavepacket, we show that caustics associated with the underlying classical trajectory families are exhibited. We connect the associated phase singularity chains in the vicinity of the caustic with the semiclassical Pearcey function built on the cusp catastrophe lines. We also quantify the amount of superenergy exhibited in these solutions - regions of space where the local energy exceeds the largest constituent energy eigenvalue. We give a complimentary description of the caustic and superenergy behavior using the Madelung/Bohm trajectories, which gives additional insight about the energy of the trajectories and how they traverse the phase singularity chains.
Abstract:We investigate the quantum interference and energetic phenomena associated with classical caustics in the quantum bouncing ball problem, we refer to as quantum caustics. By considering an initial Gaussian wavepacket, we show that caustics associated with the underlying classical trajectory families are exhibited. We connect the associated phase singularity chains in the vicinity of the caustic with the semiclassical Pearcey function built on the cusp catastrophe lines. We also quantify the amount of superenergy exhibited in these solutions - regions of space where the local energy exceeds the largest constituent energy eigenvalue. We give a complimentary description of the caustic and superenergy behavior using the Madelung/Bohm trajectories, which gives additional insight about the energy of the trajectories and how they traverse the phase singularity chains.
Quantum Physics (quant-ph); Mathematical Physics (math-ph); Pattern Formation and Solitons (nlin.PS); Exactly Solvable and Integrable Systems (nlin.SI)
arXiv:2608.02427 [quant-ph]
(or arXiv:2608.02427v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2608.02427 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 157 words
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