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

Rahil N. Valani, Álvaro G. López
Nonlinear Sciences, Chaotic Dynamics, Chaotic Dynamics (nlin.CD), Fluid Dynamics (physics.flu-dyn)
2024-01-11 00:00:00
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 wave-particle entity 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.
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