• Corpus ID: 239024760

Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity

  title={Lorenz-like systems emerging from an integro-differential trajectory equation of a one-dimensional wave-particle entity},
  author={Rahil N. Valani},
Vertically vibrating a liquid bath can give rise to a self-propelled wave-particle entity on its free surface. The horizontal walking dynamics of this wave-particle entity can be described adequately by an integro-differential trajectory equation. By transforming this integro-differential equation of motion for a one-dimensional wave-particle entity into a system of ordinary differential equations (ODEs), we show the emergence of Lorenz-like dynamical systems for various spatial wave forms of… 
1 Citations

Figures from this paper

Anomalous transport of a classical wave-particle entity in a tilted potential
A classical wave-particle entity in the form of a millimetric walking droplet can emerge on the free surface of a vertically vibrating liquid bath. Such wave-particle entities have been shown to


Bohr-Sommerfeld-like quantization in the theory of walking droplets.
Calculations show that the surface wave satisfies, in the long-memory limit, a Bohr-Sommerfeld quantization-like relation, which strongly suggest the possibility of a novel fundamental type of quantization in these experiments, which can simultaneously explain their emulation of the quantum behavior and shed light into some of the interpretational difficulties of the standard quantum theory.
Emergent order in hydrodynamic spin lattices.
Hydrodynamic spin lattices of 'walking' droplets are introduced as a class of active spin systems with particle-wave coupling that reveal various non-equilibrium symmetry-breaking phenomena, including transitions from antiferromagnetic to ferromagnetic order that can be controlled by varying the lattice geometry and system rotation.
Stop-and-go locomotion of superwalking droplets.
The emergence of stop-and-go motion of droplets is predicted, consistent with experimental observations, and lays a foundation for further studies of dynamically driven droplets, whereby the droplet's motion may be guided by engineering arbitrary time-dependent phase difference functions.
Unsteady dynamics of a classical particle-wave entity.
The dynamical and statistical aspects of irregular walking are explored and an equivalence between the droplet dynamics and the Lorenz system is shown, as well as making connections with the Langevin equation and deterministic diffusion.
A hydrodynamic analog of Friedel oscillations
This study elucidates a new mechanism for emergent quantum-like statistics in pilot-wave hydrodynamics and so suggests new directions for the nascent field of hydrodynamic quantum analogs.
An Image Encryption Algorithm Based on Random Walk and Hyperchaotic Systems
An image encryption algorithm based on random walk and two hyperchaotic systems to scramble the position of pixels within a block is proposed.
Bifurcations and chaos in a Lorenz-like pilot-wave system.
The results of a theoretical investigation of an idealized pilot-wave model, in which a particle is guided by a one-dimensional wave that is equipped with the salient features of the hydrodynamic system, are presented.
Faraday pilot-wave dynamics in a circular corral
A millimetric droplet of silicone oil may bounce and self-propel on the free surface of a vertically vibrating fluid bath due to the droplet’s interaction with its accompanying Faraday wave field.
Hydrodynamic Quantum Analogs.
  • J. M. Bush, A. Oza
  • Medicine, Physics
    Reports on progress in physics. Physical Society
  • 2020
The walking droplet system discovered by Yves Couder and Emmanuel Fort presents an example of a vibrating particle self-propelling through a resonant interaction with its own wave field, and a generalized theoretical framework that provides a mathematical bridge between the hydrodynamic pilot-wave system and various realist models of quantum dynamics is described.
Hydrodynamic Quantum Field Theory: The Onset of Particle Motion and the Form of the Pilot Wave
We consider the hydrodynamic quantum field theory proposed by Dagan and Bush, a model of quantum dynamics inspired by Louis de Broglie and informed by the hydrodynamic pilot-wave system discovered by