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

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Title: Quantum-like behavior of an active particle in a double-well potential.
Authors: Valani, Rahil N.1,2 (AUTHOR) rahil.valani@physics.ox.ac.uk, López, Álvaro G.3 (AUTHOR)
Source: Chaos, Solitons & Fractals. Sep2024, Vol. 186, pN.PAG-N.PAG. 1p.
Subjects: Distribution (Probability theory), Energy levels (Quantum mechanics), Equations of motion, Integro-differential equations, Liquid surfaces
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. [ABSTRACT FROM AUTHOR]
Copyright of Chaos, Solitons & Fractals is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: Quantum-like behavior of an active particle in a double-well potential.
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  Data: <searchLink fieldCode="JN" term="%22Chaos%2C+Solitons+%26+Fractals%22">Chaos, Solitons & Fractals</searchLink>. Sep2024, Vol. 186, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+levels+%28Quantum+mechanics%29%22">Energy levels (Quantum mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Equations+of+motion%22">Equations of motion</searchLink><br /><searchLink fieldCode="DE" term="%22Integro-differential+equations%22">Integro-differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Liquid+surfaces%22">Liquid surfaces</searchLink>
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Chaos, Solitons & Fractals is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=178885400
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      – Type: doi
        Value: 10.1016/j.chaos.2024.115253
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      – Code: eng
        Text: English
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        Type: general
      – SubjectFull: Energy levels (Quantum mechanics)
        Type: general
      – SubjectFull: Equations of motion
        Type: general
      – SubjectFull: Integro-differential equations
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      – SubjectFull: Liquid surfaces
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      – TitleFull: Quantum-like behavior of an active particle in a double-well potential.
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              M: 09
              Text: Sep2024
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              Y: 2024
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