arXiv subjects

Roberto D'Agosta

Publications and source records attributed to Roberto D'Agosta.

39 records · Page 3Linked to original sources

arXiv2001

States without linear counterpart in Bose-Einstein condensates

We show the existence of stationary solutions of a 1-D Gross-Pitaevskii equation in presence of a multi-well external potential that do not reduce to any of the eigenfunctions of the associated Schroedinger problem. These solutions, which in the limit of strong nonlinearity have the form of chains of dark or bright solitons located near the extrema of the potential, represent macroscopically excited states of a Bose-Einstein condensate and are in principle experimentally observable.

cond-mat↗

arXiv2001

Stationary states of Bose-Einstein condensates in single- and multi-well trapping potentials

The stationary solutions of the Gross-Pitaevskii equation can be divided in two classes: those which reduce, in the limit of vanishing nonlinearity, to the eigenfunctions of the associated Schrödinger equation and those which do not have linear counterpart. Analytical and numerical results support an existence condition for the solutions of the first class in terms of the ratio between their proper frequency and the corresponding linear eigenvalue. For one-dimensional confined systems, we show that solutions without linear counterpart do exist in presence of a multi-well external potential. These solutions, which in the limit of strong nonlinearity have the form of chains of dark or bright solitons located near the extrema of the potential, represent macroscopically excited states of a Bose-Einstein condensate and are in principle experimentally observable.

cond-mat.stat-mech↗

arXiv2000

Stationary states of the Gross-Pitaevskii equation with linear counterpart

We study the stationary solutions of the Gross-Pitaevskii equation that reduce, in the limit of vanishing non-linearity, to the eigenfunctions of the associated Schrödinger equation. By providing analytical and numerical support, we conjecture an existence condition for these solutions in terms of the ratio between their proper frequency (chemical potential) and the corresponding linear eigenvalue. We also give approximate expressions for the stationary solutions which become exact in the opposite limit of strong non-linearity. For one-dimensional systems these solutions have the form of a chain of dark or bright solitons depending on the sign of the non-linearity. We demonstrate that in the case of negative non-linearity (attractive interaction) the norm of the solutions is always bounded for dimensions greater than one.

cond-mat↗