Another focus is demonstrating how the temporal nonlocality of the droplet dynamics, as results from the persistence of its pilot wave field, may give rise to behavior that appears to be spatially nonlocal. Particular attention is given to enumerating the dynamical mechanisms responsible for the emergence of robust, structured statistical behavior. ![]() We here review the experimental studies of the walker system, and the hierarchy of theoretical models developed to rationalize its behavior. A more optimistic stance is that it suggests the manner in which quantum mechanics might be completed through a theoretical description of particle trajectories. ![]() At a minimum, it extends the range of classical systems to include quantum-like statistics in a number of settings. The fact that this hydrodynamic pilot-wave system exhibits many features typically associated with the microscopic, quantum realm raises a number of intriguing questions. Moreover, it represents the first macroscopic realization of a form of dynamics proposed for quantum particles by Louis de Broglie in the 1920s. It provides a means of visualizing a particle as an excitation of a field, a common notion in quantum field theory. The walking droplet system discovered by Yves Couder and Emmanuel Fort presents an example of a vibrating particle self-propelling through a resonant interaction with its own wave field. The non-Hermitian theory overturns the understanding of optical trapping and binding, and unveils the critical role played by non-Hermiticity and exceptional points, paving the way for large-scale manipulation. Our conclusion does not contradict with the observation of large optically-bound cluster in a fluid, where the ambient damping can take away the excess energy and restore the stability. As such, optical forces alone fail to bind a large cluster. Surprisingly, unstable complex eigenvalues are prevalent for clusters with ~10 or more particles, and in the many-particle limit, their presence is inevitable. Contrary to conventional systems, the operator governing time evolution is real and asymmetric (i.e., non-Hermitian), which inevitably yield complex eigenvalues when driven beyond the exceptional points, where light pumps in energy that eventually “melts” the light-bound structures. With incoming illumination and radiative losses, optical forces are inherently nonconservative, thus non-Hermitian. Intense light traps and binds small particles, offering unique control to the microscopic world.
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