Higher Order Approximation to the Hill Problem Dynamics about the Libration Points

An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture all the relevant periodic orbits originated from the libration points within a reasonable accuracy, the normalization is approached in complex variables. The validity of the solution extends to energy values considerably far away from that of the libration points and, therefore, can be used in the computation of Halo orbits as an alternative to the classical Lindstedt-Poincar\'e approach. Furthermore, the theory correctly predicts the existence of the two-lane bridge of periodic orbits linking the families of planar and vertical Lyapunov orbits.Comment: 28 pages, 8 figure

La poética de la analogía y del fragmento en la poesía de Govoni

The analogy’s and objects’s poetics, inheritated from D’Annunzio’s and Pascoli’s symbolism, meet in Govoni’s poetry. This poet manifests his own poetic identity through these both traditions but at the same time he is able “to cross” them in a personal way. At the first stage, the objects’s poetic, as fragment’s poetic, is expressed in the highest degree under the form of the “cataloghe-poem” and the “litany-poem”; then follows a more dynamic and free use of images which in a explicit way presents in the poem the effect of a totality. Finally, in the age of maturity, the pure analogy’s poetic imposes itself: the poem rises from a nucleus of images and its frame corresponds closely to the dynamism of the analogy. We examine in this essay specially the forms of the fragment’s poetic: the list of objects and the juxtaposition of images, and at the end we offer a series of considerations about the analogy’s poetic. Simultaneously we try to draw an itinerary of Govoni’s poetry and a portrait of his identity, how the sensorial function, which defines his personality, relates with other functions of the conscience, like sentiment, thought and intuition

Fine Structure of Open Shell Diatomic Molecules in Combined Electric and Magnetic Fields

We present a theoretical study of the impact of an electric field combined with a magnetic field on the rotational dynamics of open shell diatomic molecules. Within the rigid rotor approximation, we solve the time-independent Schr\"odinger equation including the fine-structure interactions and the \Lambda-doubling effects. We consider three sets of molecule specific parameters and several field regimes and investigate the interplay between the different interactions identifying the dominant one. The possibility of inducing couplings between the spin and rotational degrees of freedom is demonstrated.Comment: 11 pages, 16 figure

Steady-state phase diagram of a driven QED-cavity array with cross-Kerr nonlinearities

We study the properties of an array of QED-cavities coupled by nonlinear elements in the presence of photon leakage and driven by a coherent source. The main effect of the nonlinear couplings is to provide an effective cross-Kerr interaction between nearest-neighbor cavities. Additionally, correlated photon hopping between neighboring cavities arises. We provide a detailed mean-field analysis of the steady-state phase diagram as a function of the system parameters, the leakage, and the external driving, and show the emergence of a number of different quantum phases. A photon crystal associated to a spatial modulation of the photon blockade appears. The steady state can also display oscillating behavior and bistability. In some regions the crystalline ordering may coexist with the oscillating behavior. Furthermore we study the effect of short-range quantum fluctuations by employing a cluster mean-field analysis. Focusing on the corrections to the photon crystal boundaries, we show that, apart for some quantitative differences, the cluster mean field supports the findings of the simple single-site analysis. In the last part of the paper we concentrate on the possibility to build up the class of arrays introduced here, by means of superconducting circuits of existing technology. We consider a realistic choice of the parameters for this specific implementation and discuss some properties of the steady-state phase diagram.Comment: 11 pages, 12 figure

Photon solid phases in driven arrays of nonlinearly coupled cavities

We introduce and study the properties of an array of QED cavities coupled by nonlinear elements, in the presence of photon leakage and driven by a coherent source. The nonlinear couplings lead to photon hopping and to nearest-neighbor Kerr terms. By tuning the system parameters, the steady state of the array can exhibit a photon crystal associated with a periodic modulation of the photon blockade. In some cases, the crystalline ordering may coexist with phase synchronization. The class of cavity arrays we consider can be built with superconducting circuits of existing technology.Comment: 8 pages, 8 figures. Published versio

Los mitos y Jung

En su autobiografía Recuerdos, sueños, pensamientos, Jung, al explicar la dinámica de su obra, señala el momento crucial en el que se le plantea como exigencia ineludible el conocimiento y el estudio de los mitos. Se trata del momento que precede y prepara la escritura de su obra Símbolos de transformación, publicada en 1912. Es el momento en que su relación con Freud entra en crisis, crisis que desemboca en ruptura precisamente con la publicación de ese libro, cuyos contenidos se desmarcan claramente de la doctrina de Freud. En ese tiempo que precede a 1912, la relación de Jung y de Freud es muy intensa. Hacen juntos en 1909 un viaje a EE.UU., que duró siete semanas y Jung narra cómo, estando juntos todos los días, analizaban mutuamente sus sueños

Some definable types that cannot be amalgamated

We exhibit a theory where definable types lack the amalgamation property.Comment: 4 page

The domination monoid in henselian valued fields

We study the domination monoid in various classes of structures arising from the model theory of henselian valuations, including RV-expansions of henselian valued fields of residue characteristic 0 (and, more generally, of benign valued fields), p-adically closed fields, monotone D-henselian differential valued fields with many constants, regular ordered abelian groups, and pure short exact sequences of abelian structures. We obtain Ax-Kochen-Ershov type reductions to suitable fully embedded families of sorts in quite general settings, and full computations in concrete ones.Comment: 35 pages. Minor revisio