On the generating function of weight multiplicities for the representations of the Lie algebra C2C_2

We use the generating function of the characters of $C_2$ to obtain a generating function for the multiplicities of the weights entering in the irreducible representations of that simple Lie algebra. From this generating function we derive some recurrence relations among the multiplicities and a simple graphical recipe to compute them.Comment: arXiv admin note: text overlap with arXiv:1304.720

Coherently manipulating flying qubits in a quantum wire with a magnetic impurity

e study the effect of a magnetic impurity with spin-half on a single propagating electron in a one-dimensional model system via the tight-binding approach. Due to the spin-dependent interaction, the scattering channel for the flying qubit is split, and its transmission spectrum is obtained. It is found that, the spin orientation of the impurity plays the role as a spin state filter for a flying qubit.Comment: 6 pages, 5 figure

Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories

We study the electric flux tubes that undertake color confinement in N=2 supersymmetric Yang-Mills theories softly broken down to N=1 by perturbing with the first two Casimir operators. The relevant Abelian Higgs model is not the standard one due to the presence of an off-diagonal coupling among different magnetic U(1) factors. We perform a preliminary study of this model at a qualitative level. BPS vortices are explicitely obtained for particular values of the soft breaking parameters. Generically however, even in the ultrastrong scaling limit, vortices are not critical but live in a "hybrid" type II phase. Also, ratios among string tensions are seen to follow no simple pattern. We examine the situation at the half Higgsed vacua and find evidence for solutions with the behaviour of superconducting strings. In some cases they are solutions to BPS equations.Comment: 15 pages, 1 figure, revtex; v2: typos corrected, final versio

Explicit computation of low-lying eigenfunctions for the quantum trigonometric Calogero-Sutherland model related to the exceptional algebra E7

Preprint[EN]In the previous paper http://hdl.handle.net/10366/121330 we have studied the characters and Clebsch-Gordan series for the exceptional Lie algebra E7 by relating them to the quantum trigonometric Calogero-Sutherland Hamiltonian with coupling constant K=1. Now we extend that approach to the case of general K. [ES] En el artículo anterior http://hdl.handle.net/10366/121330 hemos estudiado los personajes y series de Clebsch-Gordan para el álgebra de Lie excepcional E7 por ellos en relación cotn el quantum hamiltoniano trigonométrico Calogero-Sutherland con constante de acoplamiento K = 1. Ahora extendemos este enfoque al caso del general K

Low Energy Vortex Dynamics in Abelian Higgs Systems.

The low energy dynamics of the vortices of the Abelian Chern-Simons-Higgs system is investigated from the adiabatic approach. The difficulties involved in treating the field evolution as motion on the moduli space in this system are shown. Another two generalized Abelian Higgs systems are discusssed with respect to their vortex dynamics at the adiabatic limit. The method works well and we find bound states in the first model and scattering at right angles in the second system. 1 Introduction. Since their discovery by Nielsen and Olesen [1], the vortex solutions present in the Abelian Higgs Model have been used, beyond their original purpose as vehicles of the strong forces, in a variety of contexts. They have been found useful, for example, to describe cosmic strings; also, because the energy of static configurations in the AHM can be interpreted as the Ginzburg-Landau theory for superconducting materials, these topological solutions correspond to the magnetic flux tubes appearing in ..

Irreducible Characters and Clebsch-Gordan Series for the Exceptional Algebra E6: An Approach through the Quantum Calogero-Sutherland Model

Preprint[EN] We re-express the quantum Calogero-Sutherland model for the Lie algebra E_6 and the particular value of the coupling constant (\kappa=1) by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to develop a systematic procedure to obtain all the Clebsch-Gordan series required to perform the change of variables. We describe how the resulting quantum Hamiltonian operator can be used to compute more characters and Clebsch-Gordan series for this exceptional algebra. [ES]Hemos vuelto a expresar el modelo cuántico Calogero-Sutherland para el álgebra de Lie E_6 y el valor particular de la constante de acoplamiento (\kappa=1) utilizando los caracteres irreducibles fundamentales del álgebra como variables dinámicas. Para ello, es necesario desarrollar un procedimiento sistemático para obtener toda la serie de Clebsch-Gordan, necesario para realizar el cambio de variables. Se describe cómo el operador hamiltoniano cuántico resultante se puede utilizar para calcular más caracteres y series Clebsch-Gordan para este álgebra excepcional

A perturbative approach to the quantum elliptic Calogero-Sutherland model

Preprint[EN]We solve perturbatively the quantum elliptic Calogero-Sutherland model in the regime in which the quotient between the real and imaginary semiperiods of the Weierstrass ${\cal P}$ function is small. [ES]Resolvemos perturbativamente el modelo cuántico elíptico Calogero-Sutherland en el régimen en el que el cociente, entre los semiperiodos real e imaginario de la función Weierstrass ${\cal P}$, es pequeño