Characterization of free particle dynamics in an idealized pilot-wave system

Matthew Durey and John Bush explore a class of dynamical systems with similarities to the walking-droplet system and various realist models of quantum dynamics. Their classical pilot-wave system consists of a vibrating particle propelled by the local slope of its self-generated, quasi-monochromatic wave field, which contains information about the particle’s prior motion.

The walking-droplet system represents the first-known example of a macroscopic pilot-wave system, 80 years after Louis de Broglie proposed such a system for microscopic particles. A 2005 experiment demonstrated that droplets can self-propel across the surface of a vibrating liquid through resonant interaction with their wave field. These “walkers” exhibit several features typically associated with quantum systems.

The advantage of Durey and Bush’s idealized framework lies within its simplicity, as it relies on only two dimensionless control parameters. The first, κ₀, prescribes the importance of particle inertia, while the second, Γ, defines the longevity of the pilot wave.

To identify regimes in which different stable dynamical states exist, Durey and Bush combined linear stability analysis with numerical simulation to evolve the generalized pilot-wave system. In doing so, they discovered a class of orbital motions in which a particle is strongly localized by its pilot-wave field. Beyond circular orbits corresponding to pilot-wave “spin states,” the results uncovered more complex orbits corresponding to precessing and wobbling spin states.

The classical pilot-wave system may also give insight into dynamics on the microscopic scale, such as a charged particle moving in response to its own electromagnetic field or an oscillating mass propelled by its gravitational wave field. The researchers hope further study will allow them to build a mathematical bridge between pilot-wave systems on the macroscopic and microscopic scales.

Source: “Classical pilot-wave dynamics: the free particle,” by Matthew Durey and John Bush, Chaos (2021). The article can be accessed at http://doi.org/10.1063/5.0039975 .