Faraday pilot-wave dynamics: modelling and computation

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Abstract

A millimetric droplet bouncing on the surface of a vibrating fluid bath can self-propel by virtue of a resonant interaction with its own wave field. This system represents the first known example of a pilot-wave system of the form envisaged by Louis de Broglie in his double-solution pilot-wave theory. We here develop a fluid model of pilot-wave hydrodynamics by coupling recent models of the droplet’s bouncing dynamics with a more realistic model of weakly viscous quasi-potential wave generation and evolution. The resulting model is the first to capture a number of features reported in experiment, including the rapid transient wave generated during impact, the Doppler effect and walker–walker interactions.

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Confinement of electrons to quantum corrals on a metal surface.

M F Crommie, C P Lutz, D M Eigler (1993)

A method for confining electrons to artificial structures at the nanometer lengthscale is presented. Surface state electrons on a copper(111) surface were confined to closed structures (corrals) defined by barriers built from iron adatoms. The barriers were assembled by individually positioning iron adatoms with the tip of a 4-kelvin scanning tunneling microscope (STM). A circular corral of radius 71.3 A was constructed in this way out of 48 iron adatoms. Tunneling spectroscopy performed inside of the corral revealed a series of discrete resonances, providing evidence for size quantization. STM images show that the corral's interior local density of states is dominated by the eigenstate density expected for an electron trapped in a round two-dimensional box.