IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v186y2024ics0960077924008051.html
   My bibliography  Save this article

Quantum-like behavior of an active particle in a double-well potential

Author

Listed:
  • Valani, Rahil N.
  • López, Álvaro G.

Abstract

A macroscopic, self-propelled wave–particle entity (WPE) that emerges as a walking droplet on the surface of a vibrating liquid bath exhibits several hydrodynamic quantum analogs. We explore the rich dynamical and quantum-like features emerging in a model of an idealized one-dimensional WPE in a double-well potential. The integro-differential equation of motion for the WPE transforms to a Lorenz-like system, which we explore in detail. We observe the analog of quantized eigenstates as discrete limit cycles that arise by varying the width of the double-well potential, and also in the form of multistability with coexisting limit cycles. These states show narrow as well as wide energy level splitting. Tunneling-like behavior is also observed where the WPE erratically transitions between the two wells of the double-well potential. We rationalize this phenomena in terms of crisis-induced intermittency. Further, we discover a fractal structure in the escape time distribution of the particle from a well based on initial conditions, indicating unpredictability of this tunneling-like intermittent behavior at all scales. The chaotic intermittent dynamics lead to wave-like emergent features in the probability distribution of particle’s position that show qualitative similarity with its quantum counterpart. Lastly, rich dynamical features are also observed such as a period doubling route to chaos as well as self-similar periodic islands in the chaotic parameter set.

Suggested Citation

  • Valani, Rahil N. & López, Álvaro G., 2024. "Quantum-like behavior of an active particle in a double-well potential," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008051
    DOI: 10.1016/j.chaos.2024.115253
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924008051
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115253?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. López, Álvaro G. & Benito, Fernando & Sabuco, Juan & Delgado-Bonal, Alfonso, 2023. "The thermodynamic efficiency of the Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Pedro J. Sáenz & Giuseppe Pucci & Sam E. Turton & Alexis Goujon & Rodolfo R. Rosales & Jörn Dunkel & John W. M. Bush, 2021. "Emergent order in hydrodynamic spin lattices," Nature, Nature, vol. 596(7870), pages 58-62, August.
    3. Stéphane Perrard & Matthieu Labousse & Marc Miskin & Emmanuel Fort & Yves Couder, 2014. "Self-organization into quantized eigenstates of a classical wave-driven particle," Nature Communications, Nature, vol. 5(1), pages 1-8, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Maxime Hubert & Stéphane Perrard & Nicolas Vandewalle & Matthieu Labousse, 2022. "Overload wave-memory induces amnesia of a self-propelled particle," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    2. Rahman, Aminur & Blackmore, Denis, 2016. "Neimark-Sacker bifurcations and evidence of chaos in a discrete dynamical model of walkers," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 339-349.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008051. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.