Two-Dimensional Supersymmetric Quantum Mechanics: Two Fixed Centers of Force

The problem of building supersymmetry in the quantum mechanics of two Coulombian centers of force is analyzed. It is shown that there are essentially two ways of proceeding. The spectral problems of the SUSY (scalar) Hamiltonians are quite similar and become tantamount to solving entangled families of Razavy and Whittaker-Hill equations in the first approach. When the two centers have the same strength, the Whittaker-Hill equations reduce to Mathieu equations. In the second approach, the spectral problems are much more difficult to solve but one can still find the zero-energy ground states.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Solitary Waves in Massive Nonlinear S^N-Sigma Models

The solitary waves of massive (1+1)-dimensional nonlinear S^N-sigma models are unveiled. It is shown that the solitary waves in these systems are in one-to-one correspondence with the separatrix trajectories in the repulsive N-dimensional Neumann mechanical problem. There are topological (heteroclinic trajectories) and non-topological (homoclinic trajectories) kinks. The stability of some embedded sine-Gordon kinks is discussed by means of the direct estimation of the spectra of the second-order fluctuation operators around them, whereas the instability of other topological and non-topological kinks is established applying the Morse index theorem

State determination: an iterative algorithm

An iterative algorithm for state determination is presented that uses as physical input the probability distributions for the eigenvalues of two or more observables in an unknown state $\Phi$. Starting form an arbitrary state $\Psi_{0}$, a succession of states $\Psi_{n}$ is obtained that converges to $\Phi$ or to a Pauli partner. This algorithm for state reconstruction is efficient and robust as is seen in the numerical tests presented and is a useful tool not only for state determination but also for the study of Pauli partners. Its main ingredient is the Physical Imposition Operator that changes any state to have the same physical properties, with respect to an observable, of another state.Comment: 11 pages 3 figure

Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts

Spectral heat kernel/zeta function regularization procedures are employed in this paper to control the divergences arising from vacuum fluctuations of Bogomolnyi-Prasad-Sommerfield vortices in the Abelian Higgs model. Zero modes of vortex fluctuations are the source of difficulties appearing when the standard Gilkey-de Witt expansion is performed. A modified GdW expansion is developed to diminish the impact of the infrared divergences due to the vortex zero modes. With this new technique at our disposal we compute the one-loop vortex mass shift in the planar AHM and the quantum corrections to the string tension of the magnetic flux tubes living in three dimensions. In both cases it is observed that weak repulsive forces surge between these classically non interacting topological defects caused by vacuum quantum fluctuations.Comment: 25 pages, 2 figure

El género en construcciones tempranas de autoría, 1447-1518

The notion and construction of authorship has been reinterpreted and shaped throughout history. In the Iberian world, the rise of authorial self-consciousness begins to manifest in the early thirteenth century, thanks to the gradual rise of vernacular languages as literary languages, which afforded a new understanding of the writer’s craft and place in society. The establishment of decrees within the sixteenth-century book trade reshaped it by making it compulsory to register on the work certain bibliographical details. The turn of the seventeenth century, furthermore, witnessed a rapid commercialization of the literary product — despite remaining rooted in a system of patronage, literary production began to give way to the active role of printer-publishers and booksellers. Writing for publication was a complex venture for most aspiring authors, to be sure. Nevertheless, pre-modern literary careers continue to be qualified, chiefly upon gender grounds. This essay, therefore, will reflect on the role of gender in early constructions of female authorship within Iberian book history, using a critical stance informed by new approaches to the field. It is hoped that it will help to provoke more nuanced discussions on the role of women as cultural producers within the pre-modern Iberian literary field.La noción y construcción de autoría ha sido reinterpretada y moldeada a través de la historia. En el mundo ibérico, el surgimiento de la conciencia autorial comienza a manifestarse a principios del siglo XIII por la elevación de las lenguas vernáculas como lenguas literarias, que hizo posible un nuevo discurso sobre el quehacer literario y su lugar en la sociedad. El establecimiento de decretos dentro del mercado libresco del siglo XVI la remodeló al hacer obligatorio el registro de ciertos datos bibliográficos en la obra misma. El siglo XVII, asimismo, fue testigo de la rápida comercialización del producto literario — los impresores-editores y vendedores de libros comenzaron a asumir un papel más activo en la producción literaria, pese a seguir arraigada al sistema de mecenazgo. Escribir para la publicación, sin duda, constituía una operación compleja para muchos. No obstante, la carrera del autor pre-moderno suele calificarse, generalmente, por razones de género. Este ensayo reflexiona sobre el papel del género en construcciones tempranas de autoría femenina dentro de la historia del libro ibérico, usando para ello nuevos enfoques con Christine de Pizan y Teresa de Cartagena. El objetivo es reivindicar el temprano estatus de la mujer como autora en el campo literario ibérico