Pseudoquatum Features of Parametrically Driven Classical Fluids (1710.01686v2)

Abstract: Recent experiments on walking droplets suggest an underlying connection between fluid dynamics and the quantum mechanics. Such experiments may be used to support the de Broglie-Bohm pilot-wave theory. In this paper we show that many quantum-like features of hydrodynamic excitations can be explained in the framework of the parametrically driven nonlinear Schr\"{o}dinger equation (DNLSE). It is shown that the nonlinear Schr\"{o}dinger equation (NLSE) describes the pseudoquantum features of a given pseudoparticle in the Sagdeev pseudopotential just as the ordinary linear Schr\"{o}dinger equation (LSE) describes the quantum nature of real particles. The NLSE is shown to reduce to nonlinear Hamilton-Jacobi equation (NHJE) for the phase function of the complex wavefunction. The origin of the wave-particle dual-character in both LSE and NLSE is explained and basic similarities between the two models is highlighted. It is shown that many more pseudoquantum effects (yet to be explored) such as pseudoentanglement, self-interference effect and quantization of pseudoparticle energy are inherent features of classical fluids. Current investigation suggests that emergence of the quantum nature of fluids is independent from dynamics of the bouncing droplets or their interactions with the surface waves instantaneously created by them. In contrast to previous suggestions, it is remarked that intrinsically nonlinear collective excitations of a fluid can drive any particle even a pseudoparticle to behave quantum mechanically. These collective interactions in hydrodynamic model confirm the important nonlocal character (which is a key aspect of the de Broglie-Bohm pilot-wave theory) of all the pseudoquantum phenomena. The recent hydrodynamic quantum analog experiments and extensive new theoretical models may hopefully enable physicists to unlock the decade long hidden mystery of the quantum weirdness.