Testing de Broglie's double solution in the mesoscopic regime

TL;DR

This paper explores solutions to a non-linear Schrödinger equation with self-focusing effects, aiming to test de Broglie's double solution theory in the mesoscopic regime through potential experimental verification.

Contribution

It introduces specific solutions combining pilot waves with solitons in a non-linear framework, proposing a method to experimentally observe de Broglie's double solution in mesoscopic systems.

Findings

Solutions show increased validity as soliton size decreases.

Proposes a Stern-Gerlach interferometer setup for experimental detection.

Discusses conditions under which the double solution could be observed.

Abstract

We present here solutions of a non-linear Schroedinger equation in presence of an arbitrary linear external potential. The non-linearity expresses a self-focusing interaction. These solutions are the product of the pilot wave with peaked solitons the velocity of which obeys the guidance equation derived by Louis de Broglie in 1926. The degree of validity of our approximations increases when the size of the soliton decreases and becomes negligible compared to the typical size over which the pilot wave varies. We discuss the possibility to reveal their existence by implementing a humpty-dumpty Stern-Gerlach interferometer in the mesoscopic regime.