Hydrodynamic Quantum Analogs: Frontiers

A millimetric droplet may walk across the surface of a vibrating liquid bath, propelled through a resonant interaction with its own guiding or "pilot" wave. Remarkably, these walking droplets exhibit many features previously thought to be exclusive to the microscopic, quantum realm. Consequently, since their discovery twenty years ago, they have provided the basis for the field of hydrodynamic quantum analogs. The walking droplet system is a concrete, macroscopic realization of wave-particle duality, and has a number of common features with the pilot-wave theory originally suggested by Louis de Broglie in the 1920s. Its success as a quantum analog provides new support for de Broglie's theory, and has prompted a revisitation of quantum pilot-wave theories. This grant will support an exploration of the potential and limitations of the walking-droplet system as a quantum analog; thus, it will promote the progress of science through redefining the boundary between classical and quantum phenomena. The intellectual merit of the project is that, in so doing, it will both question and inform the philosophical foundations of quantum physics. The project will be directed towards an integrated experimental and theoretical investigation of hydrodynamic quantum analogs. The first component will leverage recent advances in our understanding of non-resonant effects in pilot-wave hydrodynamics in order to assess the importance of ponderomotive effects in a number of new and established hydrodynamic quantum analogs. The second component will be an exploration of a new theoretical model of three-dimensional pilot-wave dynamics, with a view to analogizing a number of canonical quantum systems dominated by spin. The third component will be directed towards rationalizing the striking similarity between the wave field of walking droplets and the quantum wave function of exciton-polaritons, as arise when light flows past a defect with a commensurate frequency. These three components will be augmented by the ongoing discovery and exploration of new hydrodynamic quantum analogs. The research lies at the intersection of dynamical systems theory, stochastic mechanics, fluid mechanics and quantum theory. Particular attention will be given to comparing the pilot-wave theories and stochastic models of the hydrodynamic system with those developed for their quantum counterparts. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.