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  • Letter
  • Open Access

Megastable quantization in generalized pilot-wave hydrodynamics

Álvaro G. López1,* and Rahil N. Valani2,†

  • 1Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, Móstoles 28933, Madrid, Spain
  • 2Rudolf Peierls Centre for Theoretical Physics, Parks Road, University of Oxford, Oxford OX1 3PU, United Kingdom

  • *Contact author: alvaro.lopez@urjc.es
  • †Contact author: rahil.valani@physics.ox.ac.uk
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Phys. Rev. E 111, L022201 – Published 14 February, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.L022201

Abstract

A classical particle in a harmonic potential gives rise to a continuous energy spectra, whereas the corresponding quantum particle exhibits countably infinite quantized energy levels. In recent years, classical non-Markovian wave-particle entities that materialize as walking droplets have been shown to exhibit various hydrodynamic quantum analogs, including quantization in a harmonic potential by displaying few coexisting limit cycle orbits. By considering a truncated-memory stroboscopic pilot-wave model of the system in the low dissipation regime, we obtain a classical harmonic oscillator perturbed by oscillatory nonconservative forces that display countably infinite coexisting limit-cycle states, also known as megastability. Using averaging techniques in the low-memory regime, we derive analytical approximations of the orbital radii, orbital frequency and Lyapunov energy function of this megastable spectrum, and further show average energy conservation along these quantized states. Our formalism extends to a general class of self-excited oscillators and can be used to construct megastable spectrum with different energy-frequency relations.

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Phys. Rev. E 111, L022201– Published 14 February, 2025
  • Received 23 October 2024
  • Accepted 3 February 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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