In this paper we consider a nonlinear Schr ̈odinger equation with a cubic nonlinearity and a multi-dimensional double well potential. In the semiclassical limit the problem of the existence of stationary solutions simply reduces to the analysis of a finite dimensional Hamiltonian system which exhibits different behaviour depending on the dimension. In particular, in dimension 1 the symmetric stationary solution shows a standard pitchfork bifurcation effect, while in dimensions 2 and 3 new asymmetrical solutions associated with saddle points occur. These last solutions are localized on a single well and this fact is related to the phase transition effect observed in Bose–Einstein condensates in periodical lattices.
Stationary solutions to the multi-dimensional Gross–Pitaevskii equation with double-well potential / Sacchetti, Andrea. - In: NONLINEARITY. - ISSN 0951-7715. - STAMPA. - 27(2014), pp. 2643-2662. [10.1088/0951-7715/27/11/2643]
Data di pubblicazione: | 2014 | |
Titolo: | Stationary solutions to the multi-dimensional Gross–Pitaevskii equation with double-well potential | |
Autore/i: | Sacchetti, Andrea | |
Autore/i UNIMORE: | ||
Digital Object Identifier (DOI): | http://dx.doi.org/10.1088/0951-7715/27/11/2643 | |
Rivista: | ||
Volume: | 27 | |
Pagina iniziale: | 2643 | |
Pagina finale: | 2662 | |
Codice identificativo ISI: | WOS:000343931400002 | |
Codice identificativo Scopus: | 2-s2.0-84908066935 | |
Citazione: | Stationary solutions to the multi-dimensional Gross–Pitaevskii equation with double-well potential / Sacchetti, Andrea. - In: NONLINEARITY. - ISSN 0951-7715. - STAMPA. - 27(2014), pp. 2643-2662. [10.1088/0951-7715/27/11/2643] | |
Tipologia | Articolo su rivista |
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arxiv_52.pdf | Pre-print dell'autore (bozza pre referaggio) | Open Access Visualizza/Apri |
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