arXiv subjects

John W. M. Bush

Publications and source records attributed to John W. M. Bush.

At least 19 recordsLinked to original sources

arXiv2026

Synchronization induces Bell violations in a model of walking droplets

We consider a reduced Lorenz-like model that describes two walking droplets interacting through their mutual wave field, and investigate the emergence of strong bipartite correlations in this classical wave-particle system. The coupled nonlinear dynamics admit two invariant synchronization manifolds associated with correlated and anticorrelated states, within which the droplets display synchronized chaotic intermittency. Employing measurement protocols inspired by Bell experiments, we compute position correlations from the long-time dynamics and identify parameter regimes for which the CHSH-Bell parameter $S$ exceeds 2, corresponding to violations of Bell's Inequality. We further introduce a procedure for isolating the two subsystems, thereby ensuring the absence of wave-mediated signaling between them. Changing measurement settings following this isolation allows us to execute dynamic Bell tests in which violations persist. Our results demonstrate that nonlinear deterministic dynamics can produce Bell violations through wave-mediated synchronization mechanisms; moreover, these violations may be rationalized on the grounds that the wave form is influenced by the measurement settings. We thus provide a consistent dynamical framework for the appearance of classical entanglement in pilot-wave systems.

nlin.CD↗

arXiv2026

Controlled drop generation via ligament extraction from a static or vibrating liquid bath

We introduce a simple method for generating droplets at the surface of a liquid bath by rapidly stretching a liquid ligament with a spring-loaded cylindrical probe. By varying the probe radius $a$ and retraction length $L$, we identify three regimes. Overstretching a thin ligament produces multiple drops, while insufficient stretching of a thick ligament yields none. The optimal regime for single-drop generation lies in between. In the single-drop regime, the drop radius scales as $R \sim a^{2/3} L^{1/3}$, consistent with volume conservation of the stretched ligament. This method enables repeatable generation of single droplets (with <5% variation in $R$) on both still and vibrating baths and of ordered droplet lattices for pilot-wave hydrodynamics experiments.

physics.flu-dyn↗

arXiv2026

Engineering classical waves with quantized energy spectra in periodic media

Field quantization is a central feature of modern physics, that underpins the concept of photons and forms the foundation of quantum electrodynamics as well as much of solid-state theory. Classical linear wave equations are not generally expected to reproduce the quantization arising in quantum systems without introducing additional ingredients such as ad hoc nonlinear constraints, resonant particle-wave couplings or stochastic background fields. Here, we show that appropriately engineered linear wave media can recover fundamental features evocative of energy quantization in quantum mechanics. The key is to tailor periodic media in which wave propagation is strongly suppressed, except over a discrete set of narrow pass bands. In this regime, stationary wave solutions exhibit discrete energy and frequency spectra analogous to those arising in quantum mechanics despite the underlying dynamics remaining linear. Owing to the universality of the proposed mechanism, these effects may be realized experimentally using mechanical, electrical, or electromagnetic waves in appropriately designed periodic media. This work opens new avenues for designing metamaterials that enable control over discrete wave states while strengthening the conceptual bridge between classical and quantum wave physics.

math-ph↗

arXiv2026

Capillary currents and viscous droplet spreading

We present the results of a combined experimental and theoretical study of the spreading of viscous droplets over rigid substrates. First, we experimentally investigate the wetting of a roughened glass surface by a viscous droplet of silicone oil, wide and shallow relative to the capillary length $\ell_c$. The horizontal radius of the droplet grows according to an $R_\mathrm{drop}\sim t^{1/8}$ scaling reminiscent of viscous gravity currents (Lopez et al. 1976). The droplet is preceded by a mesoscopic fluid film that percolates through the rough substrate, its radius increasing according to $R_\mathrm{film}\sim t^{3/8}/(\log t)^{1/2}$. To rationalize these observed scalings, we develop a new 'capillary current' model for the spreading of shallow droplets with arbitrary radius on rough surfaces. Furthermore, on the basis of established similarities between droplet spreading over wetted rough and smooth substrates (Cazabat & Cohen Stuart 1986), we argue its relevance to a broader class of spreading problems. We propose that, throughout their evolution, shallow droplets maintain a quasi-equilibrium balance between hydrostatic and curvature pressure, perturbed only by unbalanced contact line forces arising along the droplet's edge. For drops with horizontal radii small with respect to $\ell_c$, our model converges to the original description of Hervet & de Gennes (1984) and thereby recovers the classic spreading laws of Hoffman (1975), Voinov (1976), and Tanner (1979). For drops wide with respect to $\ell_c$, it rationalizes why millimetric, surface-tension-driven capillary currents exhibit the same spreading behavior as relatively large-scale viscous gravity currents.

physics.flu-dyn↗

arXiv2025

Single-particle Fraunhofer diffraction in a classical pilot-wave model

Walking oil droplets offer a qualitative, classical analog of single-particle diffraction. Making this analog quantitative has proven challenging, leading recent authors to conjecture that no classical pilot-wave model could exhibit Fraunhofer diffraction. We revisit the problem with the recent, Lagrangian pilot-wave model of Darrow and Bush [Symmetry 16, 149 (2024)], and find agreement with both single- and double-slit Fraunhofer patterns. We identify two distinct dynamical features that enable our model to capture Fraunhofer diffraction and distinguish it from previous classical pilot-wave models.

quant-ph↗

arXiv2025

Non-resonant effects in pilot-wave hydrodynamics

Pilot-wave hydrodynamics concerns the dynamics of 'walkers,' droplets walking on a vibrating bath, and has provided the basis for the burgeoning field of hydrodynamic quantum analogs. We here explore a theoretical model of pilot-wave hydrodynamics that relaxes the simplifying assumption of resonance between the droplet and its pilot wave, specifically the assumption of a fixed impact phase between the bouncing drop and its wave field. The model captures both the vertical and horizontal dynamics of the drop, allowing one to examine non-resonant effects for both free and constrained walkers. The model provides new rationale for a number of previously reported but poorly understood features of free walker motion in pilot-wave hydrodynamics, including colinear swaying at the onset of motion, intermittent walking, and chaotic speed oscillations, all of which are accompanied by sporadic changes in the impact phase of the bouncing drop. The model also highlights the degeneracy in the droplets' vertical dynamics, specifically, the possibility of two distinct bouncing phases and of switching between the two. Consideration of this degeneracy is critical to understanding the droplet dynamics and statistics emerging in confined geometries at high memory and the interaction of walking droplets with standing Faraday waves.

physics.flu-dyn↗

arXiv2024

Diffraction of walking drops by a standing Faraday wave

The Kapitza-Dirac effect is the diffraction of quantum particles by a standing wave of light. We here report an analogous phenomenon in pilot-wave hydrodynamics, wherein droplets walking across the surface of a vibrating liquid bath are deflected by a standing Faraday wave. We show that, in certain parameter regimes, the statistical distribution of the droplet deflection angles reveals a diffraction pattern reminiscent of that observed in the Kapitza-Dirac effect. Through experiments and simulations, we show that the diffraction pattern results from the complex interactions of the droplets with the standing wave. Our study highlights non-resonant effects associated with the detuning of the droplet bouncing and the bath vibration, which are shown to lead to drop speed variations and droplet sorting according to the droplet's phase of impact. We discuss the similarities and differences between our hydrodynamic system and the discrete and continuum interpretations of the Kapitza-Dirac effect, and introduce the notion of ponderomotive effects in pilot-wave hydrodynamics.

physics.flu-dyn↗

arXiv2024

Potential Flows with Electromagnetically-Induced Circulation in a Hele-Shaw Cell

In Hele-Shaw cells, pressure-driven viscous fluid motion between two closely-spaced plates gives rise to a two-dimensional potential flow with zero circulation. Here, we show how the introduction of electromagnetic effects enables the realization of potential flows with circulation. We present canonical Hele-Shaw experiments with circulation prescribed by the electromagnetic configuration, and rationalize the observed flows theoretically. We also draw an analogy between this new class of circulatory potential flows and a class of electrostatic systems.

physics.flu-dyn↗

arXiv2024

Waves beneath a drop levitating over a moving wall

In recent experiments, Sawaguchi et al. directly probed the lubrication layer of air beneath a droplet levitating inside a rotating cylindrical drum. For small rotation rates of the drum, the lubrication film beneath the drop adopted a steady shape, while at higher rotation rates, travelling waves propagated along the drop's lower surface with roughly half the wall velocity. We here rationalize the physical origin of these waves. We begin with a simplified model of the lubrication flow beneath the droplet, and examine the linear stability of this base state to perturbations of the Tollmien--Schlichting type. Our developments lead to the Orr-Sommerfeld equation (OSE), whose eigenvalues give the growth rates and phase speeds of the perturbations. By considering wavelengths long relative to the lubrication film thickness, we solve the OSE perturbatively and so deduce the wavelength and phase velocity of the most unstable mode. We find satisfactory agreement between experiment and theory over the parameter regime considered in the laboratory.

physics.flu-dyn↗

arXiv2024

Revisiting de Broglie's Double-Solution Pilot-Wave Theory with a Lorentz-Covariant Lagrangian Framework

The relation between de Broglie's double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie's theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with a view to reformulating and studying de Broglie's double-solution program in the modern language of classical field theory. Notably, the entire family is local and Lorentz-invariant, follows from a variational principle, and exhibits time-invariant, two-way coupling between particle and pilot-wave field. We first introduce a variational framework for generic pilot-wave systems, including a derivation of particle-wave exchange of Noether currents. We then focus on a particular limit of our system, in which the particle is propelled by the local gradient of its pilot wave. In this case, we see that the Compton-scale oscillations proposed by de Broglie emerge naturally in the form of particle vibrations, and that the vibration modes dynamically adjust to match the Compton frequency in the rest frame of the particle. The underlying field dynamically changes its radiation patterns in order to satisfy the de Broglie relation $p=\hbar k$ at the particle's position, even as the particle momentum $p$ changes. The wave form and frequency thus evolve so as to conform to de Broglie's "harmony of phases", even for unsteady particle motion. We show that the particle is always dressed with a Compton-scale Yukawa wavepacket, independent of its trajectory, and that the associated energy imparts a constant increase to the particle's inertial mass. Finally, we see that the particle's wave-induced Compton-scale oscillation gives rise to a classical version of the Heisenberg uncertainty principle.

quant-ph↗

arXiv2023

Misinference of interaction-free measurement from a classical system

Interaction-free measurement is thought to allow for quantum particles to detect objects along paths they never traveled. As such, it represents one of the most beguiling of quantum phenomena. Here, we present a classical analog of interaction-free measurement using the hydrodynamic pilot-wave system, in which a droplet self-propels across a vibrating fluid surface, guided by a wave of its own making. We argue that existing rationalizations of interaction-free quantum measurement in terms of particles being guided by wave forms allow for a classical description manifest in our hydrodynamic system, wherein the measurement is decidedly not interaction-free.

quant-ph↗

arXiv2022

Pilot-Wave Dynamics: Using Dynamic Mode Decomposition to characterize Bifurcations, Routes to Chaos and Emergent Statistics

We develop a data-driven characterization of the pilot-wave hydrodynamic system in which a bouncing droplet self-propels along the surface of a vibrating bath. We consider drop motion in a confined one-dimensional geometry, and apply the {\em Dynamic mode decomposition} (DMD) in order to characterize the evolution of the wave field as the bath's vibrational acceleration is increased progressively. DMD provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of spatio-temporal data. The DMD characterization of the wave field yields a fresh perspective on the bouncing-droplet problem that forges valuable new links with the mathematical machinery of quantum mechanics. Moreover, it provides a low-rank characterization of the bifurcation structure of the pilot wave physics. Specifically, the analysis shows that as the vibrational acceleration is increased, the pilot-wave field undergoes a series of Hopf bifurcations that ultimately lead to a chaotic wave field. The established relation between the mean pilot-wave field and the droplet statistics allows us to characterize the evolution of the emergent statistics with increased vibrational forcing from the evolution of the pilot-wave field. We thus develop a numerical framework with the same basic structure as quantum mechanics, specifically a wave theory that predicts particle statistics.

physics.flu-dyn↗

arXiv2022

Superradiant droplet emission from parametrically excited cavities

Superradiance occurs when a collection of atoms exhibits cooperative, spontaneous emission of photons at a rate that exceeds that of its component parts. Here, we reveal a similar phenomenon in a hydrodynamic system consisting of a pair of vibrationally-excited cavities, coupled through their common wavefield, that spontaneously emit droplets via interfacial fracture. We show that the droplet emission rate of two coupled cavities is higher than the emission rate of two isolated cavities. We further show that the amplified emission rate varies sinusoidally with distance between the cavities, thus demonstrating a hydrodynamic phenomenon that captures the essential features of superradiance in optical systems.

quant-ph↗

arXiv2022

Real surreal trajectories in pilot-wave hydrodynamics

In certain instances, the particle paths predicted by Bohmian mechanics are thought to be at odds with classical intuition. A striking illustration arises in the interference experiments envisaged by Englert, Scully, Süssmann and Walther, which lead the authors to claim that the Bohmian trajectories can not be real and so must be `surreal'. Through a combined experimental and numerical study, we here demonstrate that individual trajectories in the hydrodynamic pilot-wave system exhibit the key features of their surreal Bohmian counterparts. These real surreal classical trajectories are rationalized in terms of the system's non-Markovian pilot-wave dynamics. Our study thus makes clear that the designation of Bohmian trajectories as surreal is based on misconceptions concerning the limitations of classical dynamics and a lack of familiarity with pilot-wave hydrodynamics.

quant-ph↗

arXiv2021

Hydrodynamic superradiance in wave-mediated cooperative tunneling

Superradiance and subradiance occur in quantum optics when the emission rate of photons from multiple atoms is enhanced and diminished, respectively, owing to interaction between neighboring atoms. We here demonstrate a classical analog thereof in a theoretical model of droplets walking on a vibrating bath. Two droplets are confined to identical two-level systems, a pair of wells between which the drops may tunnel, joined by an intervening coupling cavity. The resulting classical superradiance is rationalized in terms of the system's non-Markovian, pilot-wave dynamics.

nlin.CD↗

arXiv2020

Collective vibrations of confined levitating droplets

We report a new type of fluid-based driven dissipative oscillator system consisting of a lattice of millimetric fluid droplets bouncing on a vertically vibrating liquid bath and bound within an annular ring. We characterize the system behavior as it is energized through a progressive increase in the bath's vibrational acceleration. Depending on the number of drops, the onset of motion of the lattice may take the form of either out-of-phase oscillations or a striking solitary wave-like instability. Theoretical modeling demonstrates that these behaviors may be attributed to different bifurcations at the onset of instability. The results presented here demonstrate the potential and utility of the walking droplet system as a platform for investigating wave-mediated, inertial, non-equilibrium particle dynamics at the macroscale.

cond-mat.soft↗

arXiv2016

Pilot-wave dynamics in a harmonic potential: Quantization and stability of circular orbits

We present the results of a theoretical investigation of the dynamics of a droplet walking on a vibrating fluid bath under the influence of a harmonic potential. The walking droplet's horizontal motion is described by an integro-differential trajectory equation, which is found to admit steady orbital solutions. Predictions for the dependence of the orbital radius and frequency on the strength of the radial harmonic force field agree favorably with experimental data. The orbital quantization is rationalized through an analysis of the orbital solutions. The predicted dependence of the orbital stability on system parameters is compared with experimental data and the limitations of the model are discussed.

physics.flu-dyn↗

arXiv2015

Polygonal instabilities on interfacial vorticities

We report the results of a theoretical investigation of the stability of a toroidal vortex bound by an interface. Two distinct instability mechanisms are identified that rely on, respectively, surface tension and fluid inertia, either of which may prompt the transformation from a circular to a polygonal torus. Our results are discussed in the context of three experiments, a toroidal vortex ring, the hydraulic jump, and the hydraulic bump.

physics.flu-dyn↗