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Pré-Publication, Document De Travail Année : 2016

Generalized guidance equation for peaked quantum solitons: the single particle case

Thomas Durt

Résumé

We study certain non-linear generalisations of the Schrödinger equation which admit static solitonic 2 solutions in absence of external potential acting on the particle. We consider a class of solutions that can be written as a product of a solution of the linear Schrödinger equation with a peaked quantum soliton, in a regime where the size of the soliton is quite smaller than the typical scale of variation of the linear wave. In the non-relativistic limit, the solitons obey a generalized de Broglie-Bohm (dB-B) guidance equation. In first approximation, this guidance equation reduces to the dB-B guidance equation according to which they move at the so-called de Broglie-Bohm velocity along the hydrodynamical flow lines of the linear Schrödinger wave. If we consider a spinorial electronic wave function a la Dirac, its barycentre is predicted to move exactly in accordance with the dB-B guidance equation.
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hal-01271531 , version 1 (09-02-2016)

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Thomas Durt. Generalized guidance equation for peaked quantum solitons: the single particle case. 2016. ⟨hal-01271531⟩
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