Particles and Waves in Classical Dynamics

Rahil N. Valani, Anja C. Slim, David M. Paganin +2 more

A droplet bouncing on the surface of a vertically vibrating liquid bath can walk horizontally, guided by the waves it generates on each impact. This results in a self-propelled classical particle-wave entity. By using a one-dimensional theoretical pilot-wave model with a generalized wave form, we investigate the dynamics of this particle-wave entity. We employ different spatial wave forms to understand the role played by both wave oscillations and spatial wave decay in the walking dynamics. We observe steady walking motion as well as unsteady motions such as oscillating walking, self-trapped oscillations, and irregular walking. We explore the dynamical and statistical aspects of irregular walking and show an equivalence between the droplet dynamics and the Lorenz system, as well as making connections with the Langevin equation and deterministic diffusion.

Maciej Zworski

Henrik Carlsen, Osvaldo Goscinski

The dynamics of circular Rydberg wave packets for the hydrogen atom with particular emphasis on fractional and full revivals previously studied by Gaeta and Stroud [Phys. Rev. A 42, 6308 (1990)], is developed within the de Broglie-Bohm pilot-wave theory. The classical limit at high quantum numbers as described within the correspondence principle is compared with the classical limit of pilot-wave theory. By studying ensembles of particles it is found that pilot-wave theory is able to deliver a consistent picture of the particle dynamics even in the high-quantum-number limit, where classical and quantum features coexist.

Walter Dittrich, Martin Reuter

Jakob Viñas Solé

This paper examines the foundational implications of a trilogy demonstrating that particle-like behavior, effective forces, and guidance dynamics can emerge from classical wave systems through topological constraints. Particles are identified as phase singularities (topological defects), interactions arise from geometric phase distortions, and mass emerges from field reconfiguration costs. The work clarifies which quantum-like features (guidance equations, discrete charges) can arise classically from wave topology, and which genuinely quantum aspects (superposition, entanglement) require nonclassical principles. This perspective shifts emphasis from postulation to emergence, suggesting that some apparently fundamental features—particles, forces, quantization—may reflect universal patterns arising from wave dynamics and topological constraints in continuous media.

Walter Dittrich, Martin Reuter