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   pdfauthor={M. Winklmeier},
   pdftitle={Abstracts Escuela de Fisica Matematica 2013, Universidad de los Andes}]{hyperref}

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\begin{document}

\tableofcontents

\section{Tristam Bogart: tba}
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\section{Andr\'es Felipe Ducuara Garcia (Valle, Postgrado): Superactivation}
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\section{Servio Tullio P\'erez Merchancano: Puntos cu\'anticos acopladas y computaci\'on cu\'antica}
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\section{Florent Schaffhauser: Representaciones reales y cuaterni\'onicas de grupos de superficies}
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Representaciones reales y cuaterni\'onicas de grupos finitos, o m\'as generalmente de grupos de Lie compactos, forman una teor\'i­a matem\'atica bien establecida desde la primera mitad del siglo XX y est\'an relacionadas con la clasificaci\'on de part\'i­culas en el modelo est\'andar (``Fermions are real, bosons are quaternionic''). Por otro lado, se encuentran en matem\'aticas varias ecuaciones inspiradas de la teor\'ia ``gauge'' cl\'asica (por reducci\'on dimensional) y existen unas correspondencias entre soluciones de dichas ecuaciones y ciertas representaciones lineales del grupo fundamental de una superficie de Riemann. El prop\'osito de esta charla es explicar qu\'e son representaciones reales y cuaterni\'onicas de grupos de superficies y estudiar las simetr\'ias de las correspondientes soluciones de las ecuaciones de Yang-Mills 2-dimensionales.
\medskip

Real and quaternionic representations of surface groups.
\smallskip

Real and quaternionic representations of finite groups, or more generally of compact Lie groups, form a well-established theory since the first half of the twentieth century and are related to the classification of particles in the standard model (``Fermions are real, bosons are quaternionic''). On a different note, one finds in mathematics various equations derived from classical gauge theory (by dimensional reduction) and solutions to such equations are  in correspondence with certain linear representations of fundamental groups of Riemann surfaces. The goal of this talk is to explain what real and quaternionic representations of surface groups are and to study the symmetries of the corresponding solutions to the 2-dimensional Yang-Mills equations.
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\section{Andr\'es Schlief: Entanglement Spectrum in The Fractional Quantum Hall Effect}
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The study of the Fractional Quantum Hall Effect (FQHE) discovered in 1982 by Tsui,
Stormer and Gossard \cite{TSG} has been enlightening in various fields of physics.
Particularly, in the past two decades this effect has been of major interest for the study of highly correlated systems entanglement.
During this short communication I will present the concept of \emph{Entanglement Spectrum} and its application to the FQHE \cite{Li}.
In particular, I will present numerical results for Laughlin states in three different geometries and different Hilbert space partitions \cite{Li,Sterdyniak1, Sterdyniak2}.
A particular emphasis will be given in the interpretation of the entanglement spectra as a clear sign of the so-called \emph{Topological Order}\cite{Chen}.
In order to do this, the entanglement spectra will be used as numerical evidence of Haldane and Li's conjecture: The low-lying entanglement spectrum corresponds to the energy spectrum of the theory's edge modes described by a particular CFT \cite{Li, Sterdyniak1, Sterdyniak2}. 
\smallskip

{\bf Keywords}: Entanglement, Topological Order, Entanglement Spectrum

Modality:  Oral $\; \mid \;$ E-mail: \texttt{af.schlief225@uniandes.edu.co} 

\begin{thebibliography}{9}

\bibitem{Chen} X. Chen, Z. C. Gu, and X. G. Wen. 
\href{http://arxiv.org/abs/1004.3835}{arXiv:1004.3835v2 [con-mat.str-el]} (2010).

\bibitem{Lauchli} M. L\"auchli, E. J. Bergholtz, and M. Haque. 
\href{http://arXiv.org/abs/1003.5656v2}{arXiv:1003.5656v2 [con-mat.mes-hall]} (2010).

\bibitem{Li} H. Li \& F. D. M. Haldane. Phys. Rev. Lett. {\bf{101,}} 010504 (2008).

\bibitem{Sterdyniak1} A. Sterdyniak, A. Chandran, N. Regnault, B. A. Bernevig, and P. Bonderson. 
\href{http://arXiv.org/abs/1111.2810v2}{arXiv:1111.2810v2 [cond-mt.mes-hall]} (2011).

\bibitem{Sterdyniak2} R. Thomale, A. Sterdyniak, N. Regnault \& B. A Bernevig. Phys. Rev. Lett. {\bf{104,}} 180502 (2010).

\bibitem{TSG}  D. C. Tsui, H. L. Stormer, and A. C. Gossard. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett., 48(22):1559Ð1562, May 1982.
\end{thebibliography}

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\section{Cristian Susa (Valle, maestr\'ia, doctorado): Maximizing information flow between coupled qubits under dissipation}
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Quantum entanglement and, in general, quantum properties of physical systems have been studied for 
many years as important resources for quantum processing tasks and quantum information protocols. 
In this work, we study the information flow (as quantified by discord and entanglement of formation) in an optically-driven  bipartite qubit system 
(quantum emitters) coupled to a common dissipative environment. While 
the correlations between qubit systems have been widely studied in the literature, our interest is to gain
information about how each emitter is correlated to the environment. To this end, we use a 
monogamic relation which allows us to calculate the emitter-environment correlations without any prior  knowledge 
about the state of the environment at any time. We analyze the behavior of these correlations in terms 
of the inner properties of the emitters and the control parameters of the laser field. We show that a broader study involving the information flow  between the qubits and the environment gives new insights into the dynamics of the interqubit quantum correlations. These aspects increase our knowledge of the usefulness of the dissipative 
environment, and lead us to identify how to maximize the distribution of correlations between the qubits.\\
\\
{\bf Keywords}: Quantum entanglement,  discord, information, decoherence.
\\
\noindent 
{\bf Modality}:  Oral   
\\
\noindent 
{\bf  E-mail}:  \texttt{cristian.susa.q@correounivalle.edu.co}

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