TEDE Communidade:
https://tedebc.ufma.br/jspui/handle/tede/tede/706
2019-10-31T20:15:23ZDinâmica de sólitons vetoriais em condensados de Bose-Einstein com interação spin-órbita
https://tedebc.ufma.br/jspui/handle/tede/tede/2879
Título: Dinâmica de sólitons vetoriais em condensados de Bose-Einstein com interação spin-órbita
Autor: FLORIAN, Cesar Antonio Ibañez
Primeiro orientador: CASTRO, Luis Rafael Benito
Abstract: Nowadays, the experimental realization of a Bose-Einstein condensate (BEC) of atoms
with spin-orbit interaction (SOC) has aroused a new interest in studying the intriguing
and interesting properties of the system. For example, a BEC of 87Rb atoms (with atomic
hyper ne state f = 1) trapped in cigar form (quasi-one-dimensional) can be subjected to
an external magnetic eld, which causes the Zeeman e ect on the states of its constituent
atoms. Then, through of an arrangement of Raman-type laser and a certain frequency
of the lasers, it is possible to induce a transition between the sub-levels mf = 1 and
mf = 0, thus leading to spin-orbita coupling, between the hyper ne sub-levels, and a
mixture of states for each sub-level. In this dissertation, we study several dynamics of the bright-bright vector soliton, in (1 + 1) space-time dimensions, which are created in a BEC of two internal state atoms, with and without spin-orbit coupling, governed by two equations of Gross-Pitaevskii coupled. To solve the coupled equations, we employed the variational approximation, being used recently for this type of system. In both cases, with and without spin-orbit coupling, we present exact analytical solutions, which solve the equations of motion with di erent polynomial potentials. From the analytical solutions, we study the precession of the system pseudo-spin vector S = 1=2, the unbalance of the pseudo-spin Sz of the soliton, the phase di erence between the soliton components (internal dynamics of soliton), in addition, we also study the movement of the center of mass of the system, and the evolution of the linear momentum of the system (external dynamics of the soliton). We explicitly show the in uence of external potential on the pseudo-spin precission of the system. Finally, we study numerically the stability conditions of the bright-bright soliton solutions, obtained in this work, under small disturbances in their initial condition.
Instituição: Universidade Federal do Maranhão
Tipo do documento: Dissertação2019-03-08T00:00:00ZEletrodinâmica de Maxwell modificada por termo CPT-par de altas derivadas e violação da simetria de Lorentz
https://tedebc.ufma.br/jspui/handle/tede/tede/2842
Título: Eletrodinâmica de Maxwell modificada por termo CPT-par de altas derivadas e violação da simetria de Lorentz
Autor: SANTOS, Letícia Lisboa dos
Primeiro orientador: FERREIRA JUNIOR, Manoel Messias
Abstract: The Standard Model Extension (MPE), proposed in 1998 by Kostelecky and Colladay, shares several properties of the Standard Model already known, such as renormalizability, energy and momentum conservation and gauge symmetry, but does not preserve the Lorentz symmetry, with possibility of violating CPT symmetry as well. The gauge sector of the MPE contains a CPT-even term and a CPT-odd one. The object of study in this dissertation is only the CPT-even one, represented by the tensor (kF )κλµν , which contains 19 independent components. In the third chapter, we present a review of Maxwell’s electrodynamics modified by the non birefringent CPT-even term, being the tensor (kF )κλµν reduced to the symmetric tensor, Dαλ. The parameterization of this tensor is given by (CαBλ + CλBα) /2, where Bα and Cλ are two 4-vectors.
In the fourth chapter, as a prototype of electromagnetic theory with high derivatives, we study the Podolsky electrodynamics, analyzing some of its main features. We analyze the equations of motion for the potential, finding the solution for the electrostatic potential by means of the Green´s method. Then, we calculate the Feynman´s propagator, whose poles provide the dispersion relations of the theory, and allow to assess its causality, stability and unitarity.
In the fifth chapter of this dissertation, we examined an electrodynamics with high order derivatives, containing a term of type ∂σFσβ∂λFλαDβα, where Dβα is a Lorentz symmetry violation tensor, symmetric and CPT-par. This term may or may not contain the Podolsky term, associated with the trace of Dνµ tensor. Using an appropriate parameterization, Dνµ = 1/2 (CνBµ + CµBν) , we calculate the Feynman propagator, achieving the dispersion relations of this theory, and examining the causality of several sectors. We finish presenting the classical solutions for this theory obtained by the Green´s method.
Instituição: Universidade Federal do Maranhão
Tipo do documento: Dissertação2016-10-17T00:00:00ZSólitons BPS no modelo CP(2) acoplado minimamente com a ação de Maxwell-Chern-Simons
https://tedebc.ufma.br/jspui/handle/tede/tede/2840
Título: Sólitons BPS no modelo CP(2) acoplado minimamente com a ação de Maxwell-Chern-Simons
Autor: GUTIERREZ, Neyver Henry Gonzalez
Primeiro orientador: SIFUENTES, Rodolfo Alván Casana
Abstract: The dissertation addresses the study of radial symmetry s olitons in (2+1)-dimensions in
a model in which the CP(2)- eld interacts minimally with an Abelian gauge eld ruled by
the Maxwell-Chern-Simons term. The implementation of the Bogomol'nyi-Prasad-Sommer eld
(BPS) formalism makes possible to nd rst-order di erential equations (BPS equations) whose solutions (BPS states) minimize the total energy of the system. The potential which generates BPS solitons is obtained through a simple but e ective methodology will be shown in detail. The magnetic ux and the total BPS energy are directly proportional to the winding numberg characterizing the non-trivial topology of the solutions, i.e., they are quantized. The analysis of the behavior of the solutions at the boundaries (at the origin and in nite) is performed by solving the linearized BPS equations. Finally, the complete solutions are obtained numerically and the respective pro les are presented which we comment on their main properties.
Instituição: Universidade Federal do Maranhão
Tipo do documento: Dissertação2019-04-25T00:00:00ZVórtices BPS no modelo de Maxwell- CP(2) com estrutura interna
https://tedebc.ufma.br/jspui/handle/tede/tede/2810
Título: Vórtices BPS no modelo de Maxwell- CP(2) com estrutura interna
Autor: ANDRADE, João Luís Brandão
Primeiro orientador: SANTOS, Carlos Eduardo da Hora
Abstract: In this dissertation, I present the original BPS vortices (Bogomol'nyi-Prasad-Sommer)eld)
inherent in a gauge model Maxwell-CP(2) from the general scenario CP (N-1) (in which
N = 3, with N corresponding to the number of components of the CP (2) field), when subjected
to the presence of an additional, real and neutral scalar field. Then, focusing on radially symmetrical
structures, we construct a first-order structure for the model, using the Bogomol'nyi
procedure. From the minimization of the total energy, we obtain general expressions for the
minimum energy of the model, whose value has an extra contribution due to the presence of the
neutral field, and for the respective first order equations (BPS equations), in which both the
minimum energy while the BPS equations depend directly on the functional structure of the
dielectric function. The introduction of the scalar field, which interacts with the electromagnetic
sector via an unusual dielectric function, produces significant modifications in the shape
of the resulting BPS vortices, such changes being understood as the manifestation of internal
structures originated by the presence of the additional neutral field.
Instituição: Universidade Federal do Maranhão
Tipo do documento: Dissertação2019-04-23T00:00:00Z