Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Author:
Papaioannou Μaria
Supervisors info:
κ.Ιωάννης Στρατής, καθηγητής στη Σχολή Θετικών Επιστημών, Τμήμα Μαθηματικών
Original Title:
Σολιτόνια σε συμπυκνώματα Bose-Einstein
Translated title:
Solitons in Bose- Einstein condensate
Summary:
The aim of this thesis is to introduce the reader to physical notions and mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein condensates (BECs). Upon introducing the general framework, we present the Gross-Pitaevskii (GP) equation, through the mean field theory and its form from 3D to 1D. The GP equation (1D) is the nonlinear Schrödinger equation (NLS). The solutions of the NLS equation are the black, white and grey solitons, that can be observed in the phase space. We also discuss the hydrodynamic approach of the NLS equation through the equations of continuity. With this approach, we present the transformation from NLS to KdV (via the Boussinesq equation) and from NLS to KdV, through the perturbation theory. Special attention is paid to the ground state in presence of the potential: we study the solitons' solutions that behave like particles and obey the second law of Newton.
Main subject category:
Science
Other subject categories:
Mathematics
Physics
Keywords:
solitons, waves, nonlinear Schrödinger equation, Gross–Pitaevskii equation, mean field theory, Korteweg–de Vries equation, black, white and grey solitons in the phase space
