Soluções localizadas em modelos de campos relativísticos e em condensados de Bose-Einstein
Data
2010-07-09
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Universidade Federal de Goiás
Resumo
This work combines some of the results obtained on the study of solitons in
relativistic fields and Bose-Einstein condensates. By using a first order formalism
to solve the equations of motion of relativistic fields, introduced previously by our
group, we construct several classes of lump solutions described by a single real
scalar field. We show how these solutions can be controlled depending on a single
parameter in the field potential. In condensed matter the solutions of the lump
type correspond to bright solitons, very studied in the context of nonlinear crystals,
fiber optics, Bose-Einstein condensates, etc. In all these cases, such solutions are
obtained via a nonlinear Schr¨odinger equation, responsible for describing the propagation
of pulses in optical fibers or crystals, or the atomic density in condensates.
In this sense, our main goal is to study the soliton and breather modulations via
nonlinear Schrodinger equation. We concentrate on the Bose-Einstein condensate
in which the modulation of atomic density can be accomplished through the Feshbach
resonance. We study cases where the nonlinearity is described by terms cubic,
cubic and quintic, and purely quintic in the nonlinear Schr¨odinger equation. Also,
situations where two interacting condensates in which the nonlinear Schr¨odinger
equations are coupled, breather modulations, and the study of the soliton behavior
under influence of chaotic, random and non-periodic perturbations in the nonlinearity
of the system. In many cases we consider the condensate trapped in the cigarshaped
configuration, i.e., with freedom in only one spatial dimension. Numerical
simulations are performed to verify the stability of the solutions.
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Citação
CARDOSO, Wesley Bueno. Localized solutions in models of relativistic fields and
Bose-Einstein condensates. 2010. 112 f. Tese (Doutorado em Ciencias Exatas e da Terra) - Universidade Federal de Goiás, Goiânia, 2010.