Spatial structures and localization of vacuum entanglement in the linear harmonic chain

We study the structure of vacuum entanglement for two complimentary segments of a linear harmonic chain, applying the modewise decomposition of entangled gaussian states discussed in \cite {modewise}. We find that the resulting entangled mode shape hierarchy shows a distinctive layered structure with well defined relations between the depth of the modes, their characteristic wavelength, and their entanglement contribution. We re-derive in the strong coupling (diverging correlation length) regime, the logarithmic dependence of entanglement on the segment size predicted by conformal field theory for the boson universality class, and discuss its relation with the mode structure. We conjecture that the persistence of vacuum entanglement between arbitrarily separated finite size regions is connected with the localization of the highest frequency innermost modes.Comment: 23 pages, 19 figures, RevTex4. High resolution figures available upon request. New References adde

Geometric Phase and Modulo Relations for Probability Amplitudes as Functions on Complex Parameter Spaces

We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form \amp{\psi_f}{\psi}, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions involving the U(1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space ${\cal R} = {\mathbb C}P^n$, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.Comment: 11 pages, 1 figure, revtex

Un cambio en la narrativa: Over the Garden Wall como reconstrucción literaria de La Divina Comedia de Dante

Literature remains a field that serves TV creators and critics as a model both for influence and comparison. The continuity claimed by Thomas Doherty between the most recent TV narrative form with the serialised novels of Dickens or Wharton is not limited to the form itself but to its content as well. Such is the case of the TV animated miniseries Over the Garden Wall, created by Patrick McHale in 2014, whose combination of Victorian fairy-tale imagery and aesthetics, as well as its reliance on literary allusion incarnates this paradigm. Within its narrative there can be found an array of literary references that range from the classics to children’s fables, as well as allusions to history and to different mythologies; an intertextual character that is featured in TV as much as in literary texts from all eras, binding the two forms together. Among the numerous texts referenced in this tale of tales, however, there is one that stands out: Dante Alighieri’s Divine Comedy. This article scrutinises the relationship between Over the Garden Wall and Dante’s Comedy, understanding the show’s protagonist, Wirt, and his quest as a replication of Dante and his descent through Hell. The main claim is that by doing so, Over the Garden Wall also highlights how Campbell’s narrative paradigm, applicable as it is to forms of media other than literature, evinces the narrative continuity, which exists between TV and the written text.La literatura sigue siendo un campo que sirve a creadores y críticos de televisión como modelo tanto de influencia como de comparación. La continuidad reivindicada por Thomas Doherty entre narrativa televisiva más reciente y las novelas serializadas de Dickens o Wharton no se limita a la forma en sí, sino también a su contenido. Tal es el caso de la miniserie de animación televisiva Over the Garden Wall, creada por Patrick McHale en 2014, cuya combinación de imaginario de cuentos de hadas y estética victoriana, así como su dependencia de la alusión literaria, encarna este paradigma. Dentro de su narrativa se pueden encontrar un abanico de referencias literarias que van desde los clásicos hasta las fábulas infantiles, pasando por alusiones a la historia y a diferentes mitologías; un personaje intertextual que aparece tanto en la televisión como en los textos literarios de todas las épocas, uniendo ambas formas. Entre los numerosos textos a los que se hace referencia en esta serie animada, hay uno que se destaca: La Divina Comedia de Dante Alighieri. Este artículo analiza la relación entre Over the Garden Wall y La Divina Comedia, entendiendo al protagonista del programa, Wirt, y su búsqueda, como una réplica de Dante y su des-censo al infierno. La afirmación principal es que, al hacerlo, Over the Garden Wall muestra cómo el paradigma narrativo de Campbell es aplicable a otros medios distintos de la literatura y evidencia la continuidad narrativa que existe entre la televisión y el texto escrito