arXiv subjects

Arnaud Lazarus

Publications and source records attributed to Arnaud Lazarus.

11 recordsLinked to original sources

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

A granular B\"uttiker-Landauer motor

Random walkers usually diffuse according to Fick's law. On average, they move down the gradient of their concentration and, in the absence of external force, tend to distribute themselves uniformly. In some experiments, however, this familiar notion is at odds with observation. Sand grains, for instance, gather along the nodal lines of a vibrated elastic plate to form a Chladni figure, thus accumulating where fluctuations are weak -- a fact that escapes the reach of Fick's law. On theoretical grounds, B\"uttiker [Zeitschrift f\"ur Physik B, 68, 1987] and Landauer [J Stat Phys, 53, 1988] proposed that particles submitted to a non-uniform temperature field would indeed gather where the temperature is low. They also predicted that, in the presence of a potential force, a non-uniform temperature could drive a steady current of particles, powered only by noise. Here, we present an experimental realization of these phenomena in a macroscopic system, which confirms the quantitative predictions of B\"uttiker.

cond-mat.stat-mech↗

arXiv2026

Thermodynamics of bouncing grains

When a horizontal plate vibrates strongly enough, it causes small particles such as sand grains to continually bounce on it and, over time, to diffuse across its surface. This phenomenon is the cause of the well-known Chladni figure, which is drawn by a higher density of grains gathering along the nodal lines of a resonating elastic plate. Using a heterogeneous, non-resonating plate, we investigate experimentally this type of diffusion. We find that, for the most part, is it comparable to classical molecular diffusion. We can define a temperature for the bouncing grains, and the system then obeys the fluctuation-dissipation theorem. We also recover Maxwell-Boltzmann statistics at equilibrium, when temperature is uniform. However, when temperature varies across the vibrating plate, the microscopic details of the grains' dynamics affect their macroscopic behavior: Fick's law, for instance, no longer applies. Instead, our experiments support a new transport relation that was recently proposed to represent diffusion in Chladni's experiment. Finally, we propose an expression for the heat flux associated to the non-equilibrium steady state predicted by this new relation, and test it against observations.

cond-mat.stat-mech↗

arXiv2025

Observation of the Aharonov-Bohm Effect in Pilot-Wave Hydrodynamics

We report the results of an experimental study of an analog of the Aharonov-Bohm (AB) effect achieved with the hydrodynamic pilot-wave system. A walking droplet is confined to an annular cavity that encircles a shielded vortex, but lies outside its range of direct influence. While there is no vortex-induced flow in the immediate vicinity of the droplets, the vortex modifies the droplet's spatially extended pilot-wave field that guides its motion, producing a vortex-dependent bias in the droplet's orbital speed. High-speed tracking and delay-embedding reconstructions yield Wigner-like phase-space distributions for this hydrodynamic system that exhibits a rigid, flux-dependent translation, providing a force-free, gauge-like realization of an AB-type phase.

physics.flu-dyn↗

arXiv2025

Harnessing Oscillatory Dynamics for Reprogrammable Mechanical Functionality

A long-standing goal in the field of "mechanical computing" is the creation of truly reprogrammable mechanical structures, where the function of each unit can be dynamically defined, modified, and accessed on demand, much like rewriting data on a hard drive. Prior efforts have largely focused on bistable building blocks, which mimic binary states, but robust and efficient methods for programming large arrays of such units remain limited. In this study, we introduce a new approach for defining and reconfiguring the state of mechanical bits. Specifically, we investigate arrays of pendula whose boundary conditions break symmetry, effectively transforming them into mechanical bits. When actuation times are short compared to the natural oscillation periods, the state of each pendulum can be controlled solely by adjusting the timing of global boundary conditions. This mechanism enables rapid reprogramming, arbitrary information writing, and even the construction of a "mechanical piano" capable of generating user-defined note and chord sequences within only a few oscillation cycles. Because it integrates seamlessly with diverse functionalities, our strategy establishes a scalable framework for reprogrammable mechanical systems and can be readily generalized to other oscillatory systems like membranes or beams.

physics.class-ph↗

arXiv2025

Wave-number lock-in in buckled elastic structures: an analogue to parametric instabilities

Parametric instabilities are a known feature of periodically driven dynamic systems; at particular frequencies and amplitudes of the driving modulation, the system's quasi-periodic response undergoes a frequency lock-in, leading to a periodically unstable response. Here, we demonstrate an analogous phenomenon in a purely static context. We show that the buckling patterns of an elastic beam resting on a modulated Winkler foundation display the same kind of frequency lock-in observed in dynamic systems. Through simulations and experiments, we reveal that compressed elastic strips with modulated height alternate between predictable quasi-periodic and periodic buckling modes. Our findings uncover previously unexplored analogies between structural and dynamic instabilities, highlighting how even simple elastic structures can give rise to rich and intriguing behaviors.

math-ph↗

arXiv2025

Optimal dynamical stabilization

Stability is a fundamental concept that refers to a system's ability to return close to its original state after disturbances. The minimal conditions for stability when system parameters vary in time, though common in physics, have been largely overlooked. Here, we study the minimal amount of periodic stiffness a linear mass-spring system requires to remain stable and apply our findings to optimally trap the upside-down state of a compass in a time-varying magnetic field. We show that the ability to return close to its original state only needs to be ensured over small but precisely defined durations within each period for the system to achieve dynamic stability. These precise durations form a discrete set, remarkably predicted by rules analogous to those of quantum mechanics. This unexpected connection opens new avenues for controlling dynamical systems.

nlin.CD↗

arXiv2025

A meaningful optimal control problem in quantum and classical physics

In this paper we study and solve an optimal control problem motivated by applications in quantum and classical physics. Although apparently simple, this optimal control problem is not easy to solve and we resort to various elaborated methods of optimal control theory. We finally show its relationships to two problems in physics: the computation of the ground state for 1D Schr{ö}dinger operators with a finite potential well, and the optimal dynamical Kapitza stabilization problem.

math.OC↗

arXiv2025

Discrete dynamical stabilization of a naturally diverging mass in a harmonically time-varying potential

We numerically investigate the stability and linear oscillatory behavior of a naturally diverging mass whose potential energy is harmonically modulated. It is known that in the Kapitza limit, i.e. when the period of modulation is much smaller than the diverging time, the collapsing mass can be dynamically stabilized and behave like an effective classic harmonic oscillator. We find that in the regime where the period of modulation is larger than the collapsing time of the mass, dynamical stabilization is still possible but in a discrete fashion. Only almost-periodic vibrational modes, or Floquet forms (FFs), are allowed that are located in independent stability stripes in the modulation parameter space. Reducing the FFs to their periodic eigenfunctions, one can transform the original equation of motion to a dimensionless Schrödinger stationary wave equation with a harmonic potential. This transformation allows for an analytical prediction of the stability stripes and the modal shapes of the vibrating mass. These results shed new light on the stability of linear dynamical systems, analytical solutions of Mathieu equations and on the relations between Initial and Boundary Value Problems.

physics.class-ph↗

arXiv2017

Bending transition in the penetration of a flexible intruder in a 2D dense granular medium

We study the quasi-static penetration of a flexible beam in a two-dimensional dense granular medium lying on an horizontal plate. Rather than a buckling-like behavior we observe a transition between a regime of crack-like penetration in which the fiber only shows small fluctuations around a stable straight geometry and a bending regime in which the fiber fully bends and advances through series of loading/unloading steps. We show that the shape reconfiguration of the fiber is controlled by a single non dimensional parameter: L/Lc, the ratio of the length of the flexible beam L to Lc, a bending elasto-granular length scale that depends on the rigidity of the fiber and on the departure from the jamming packing fraction of the granular medium. We show moreover that the dynamics of the bending transition in the course of the penetration experiment is gradual and is accompanied by a symmetry breaking of the granular packing fraction in the vicinity of the fiber. Together with the progressive bending of the fiber, a cavity grows downstream of the fiber and the accumulation of grains upstream of the fiber leads to the development of a jammed cluster of grains. We discuss our experimental results in the framework of a simple model of bending-induced compaction and we show that the rate of the bending transition only depends on the control parameter L/Lc.

cond-mat.soft↗

arXiv2017

Buckling of an elastic ridge: competition between wrinkles and creases

We investigate the elastic buckling of a triangular prism made of a soft elastomer. A face of the prism is bonded to a stiff slab that imposes an average axial compression. We observe two possible buckling modes which are localized along the free ridge. For ridge angles $ϕ$ below a critical value $ϕ^\star\approx 90^\circ$ experiments reveal an extended sinusoidal mode, while for $ϕ$ above $ϕ^\star$ we observe a series of creases progressively invading the lateral faces starting from the ridge. A numerical linear stability analysis is set up using the finite-element method and correctly predicts the sinusoidal mode for $ϕ\leq ϕ^\star$, as well as the associated critical strain $ε_{\mathrm{c}}(ϕ)$. The experimental transition at $ϕ^\star$ is found to occur when this critical strain $ε_{\mathrm{c}}(ϕ)$ attains the value $ε_{\mathrm{c}}(ϕ^\star) = 0.44$ corresponding to the threshold of the sub-critical surface creasing instability. Previous analyses have focused on elastic crease patterns appearing on planar surfaces, where the role of scale-invariance has been emphasized; our analysis of the elastic ridge provides a different perspective, and reveals that scale-invariance is not a sufficient condition for localization.

physics.class-ph↗