Master Thesis Online
Solitons in Bose-Einstein condensates
Heuchamps, Alexandre 
Promotor(s) :
Schlagheck, Peter
;
Vanderheyden, Benoît
Date of defense : 9-Sep-2019/10-Sep-2019 • Permalink : http://hdl.handle.net/2268.2/8366
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| Title : | Solitons in Bose-Einstein condensates |
| Translated title : | [fr] Solitons dans les condensats de Bose-Einstein |
| Author : | Heuchamps, Alexandre
|
| Date of defense : | 9-Sep-2019/10-Sep-2019 |
| Advisor(s) : | Schlagheck, Peter
Vanderheyden, Benoît
|
| Committee's member(s) : | Martin, John
Gilet, Tristan
|
| Language : | English |
| Number of pages : | 71 |
| Discipline(s) : | Engineering, computing & technology > Multidisciplinary, general & others |
| Institution(s) : | Université de Liège, Liège, Belgique |
| Degree: | Master en ingénieur civil physicien, à finalité approfondie |
| Faculty: | Master thesis of the Faculté des Sciences appliquées |
Abstract
[en] This work is aimed to study, both in an analytic and a numerical way, solitons in Bose-Einstein condensates. To reach that goal, a detour through the general theory of Bose-Einstein condensates in a mean-field picture is needed. Once the concepts established, the study of the solitons themselves can be undertaken. In this work, these structures are studied in the framework of the Gross-Pitaevskii equation, which is a mean-field approximation. Numerically, the discretization in time is performed through a spectral method, whereas the space discretization is done through finite difference. Even if the code that was developped is able to fit the analytic result for a free Schrödinger equation (for a sufficiently small timestep), the analytic solution of the full Gross-Pitaevskii equation cannot be fitted over long periods of time, even with a small timestep, which indicates that more elaborated numerical techniques have to be used.
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