Quantum Particle Statistics in Classical Shallow Water Waves
We present a new hydrodynamic analogy of nonrelativistic quantum particles in potential wells. Similarities between a real variant of the Schr\"odinger equation and gravity-capillary shallow water waves are reported and analyzed. We show that when locally oscillating particles are guided by rea...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
29.09.2024
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Subjects | |
Online Access | Get full text |
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Summary: | We present a new hydrodynamic analogy of nonrelativistic quantum particles in
potential wells. Similarities between a real variant of the Schr\"odinger
equation and gravity-capillary shallow water waves are reported and analyzed.
We show that when locally oscillating particles are guided by real wave
gradients, particles may exhibit trajectories of alternating periodic or
chaotic dynamics while increasing the wave potential. The particle probability
distribution function of this analogy reveals the quantum statistics of the
standard solutions of the Schr\"odinger equation and thus manifests as a
classical deterministic interpretation of Born's rule. Finally, a classical
mechanism for the transition between quasi-stationary states is proposed. |
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DOI: | 10.48550/arxiv.2409.19632 |