Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model

We generalize the Matrix Product States method using the chiral vertex operators of Conformal Field Theory and apply it to study the ground states of the XXZ spin chain, the J1-J2 model and random Heisenberg models. We compute the overlap with the exact wave functions, spin-spin correlators and the Renyi entropy, showing that critical systems can be described by this method. For rotational invariant ansatzs we construct an inhomogenous extension of the Haldane-Shastry model with long range exchange interactions.Comment: 5 pages, 4 figures, 1 reference adde

An integration of partial evaluation in a generic abstract interpretation framework

Information generated by abstract interpreters has long been used to perform program specialization. Additionally, if the abstract interpreter generates a multivariant analysis, it is also possible to perform múltiple specialization. Information about valúes of variables is propagated by simulating program execution and performing fixpoint computations for recursive calis. In contrast, traditional partial evaluators (mainly) use unfolding for both propagating valúes of variables and transforming the program. It is known that abstract interpretation is a better technique for propagating success valúes than unfolding. However, the program transformations induced by unfolding may lead to important optimizations which are not directly achievable in the existing frameworks for múltiple specialization based on abstract interpretation. The aim of this work is to devise a specialization framework which integrates the better information propagation of abstract interpretation with the powerful program transformations performed by partial evaluation, and which can be implemented via small modifications to existing generic abstract interpreters. With this aim, we will relate top-down abstract interpretation with traditional concepts in partial evaluation and sketch how the sophisticated techniques developed for controlling partial evaluation can be adapted to the proposed specialization framework. We conclude that there can be both practical and conceptual advantages in the proposed integration of partial evaluation and abstract interpretation

Angular Inflation from Supergravity

We study supergravity inflationary models where inflation is produced along the angular direction. For this we express the scalar component of a chiral superfield in terms of the radial and the angular components. We then express the supergravity potential in a form particularly simple for calculations involving polynomial expressions for the superpotential and Kahler potential. We show for a simple Polonyi model the angular direction may give rise to a stage of inflation when the radial field is fixed to its minimum. We obtain analytical expressions for all the relevant inflationary quantities and discuss the possibility of supersymmetry breaking in the radial direction while inflating by the angular component.Comment: 7 pages, one figure. Final version. Title changed, two figures droppe

Identidad profesional y conocimiento matemático para la enseñanza de maestros en formación

En este estudio se pretende obtener una mayor comprensión sobre la identidad profesional en formación de estudiantes para maestro y las implicaciones para los programas de formación del profesorado. Se indaga sobre las reflexiones realizadas por estudiantes para maestro de educación primaria concernientes a sus experiencias relativas a la enseñanza y aprendizaje de las matemáticas y a conocimientos que estiman necesarios para enseñar matemáticas. Los resultados obtenidos revelan los aspectos que estos estudiantes destacan como elementos constitutivos de la identidad profesional del maestro haciendo mención a los componentes propios del proceso de enseñanza y aprendizaje de las matemáticas. Se propone una aproximación de la caracterización de la identidad profesional a través del conocimiento matemático para la enseñanza

Hysteretic nonequilibrium Ising-Bloch transition

We show that a parametrically driven cubic-quintic complex Ginzburg-Landau equation exhibits a hysteretic nonequilibrium Ising-Bloch transition for large enough quintic nonlinearity. These results help to understand the recent experimental observation of this pheomenon [A. Esteban-Martin et al., Phys. Rev. Lett. 94, 223903 (2005)].Comment: 3 pages + six figure

Phase-locking of a Nonlinear Optical Cavity via Rocking: Transmuting Vortices into Phase Patterns

We report experimental observation of the conversion of a phase-invariant nonlinear system into a phase-locked one via the mechanism of rocking [G. J. de Valcarcel and K. Staliunas, Phys. Rev. E 67, 026604 (2003)]. This conversion results in that vortices of the phase-invariant system are being replaced by phase patterns such as domain walls. The experiment is carried out on a photorefractive oscillator in two-wave mixing configuration.A model for the experimental device is given that reproduces the observed behavior.Comment: 9 pages and 4 figure

Towards Integrating Partial Evaluation in a Specialization Framework based on Generic Abstract Interpretation

Abstract is not availabl

Squeezing spectra from s-ordered quasiprobability distributions. Application to dispersive optical bistability

It is well known that the squeezing spectrum of the field exiting a nonlinear cavity can be directly obtained from the fluctuation spectrum of normally ordered products of creation and annihilation operators of the cavity mode. In this article we show that the output field squeezing spectrum can be derived also by combining the fluctuation spectra of any pair of s-ordered products of creation and annihilation operators. The interesting result is that the spectrum obtained in this way from the linearized Langevin equations is exact, and this occurs in spite of the fact that no s-ordered quasiprobability distribution verifies a true Fokker-Planck equation, i.e., the Langevin equations used for deriving the squeezing spectrum are not exact. The (linearized) intracavity squeezing obtained from any s-ordered distribution is also exact. These results are exemplified in the problem of dispersive optical bistability.Comment: 15 pages, no figures, to be published in Journal of Modern Optic