Testing de Broglie’s double solution in the mesoscopic regime. (English) Zbl 1516.81006
Summary: We present here solutions of a non-linear Schrödinger 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.
MSC:
| 81P05 | General and philosophical questions in quantum theory |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35C08 | Soliton solutions |
| 81Q15 | Perturbation theories for operators and differential equations in quantum theory |
| 37C50 | Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
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