Detection of entanglement between collective spins

Entanglement between individual spins can be detected by using thermodynamics quantities as entanglement witnesses. This applies to collective spins also, provided that their internal degrees of freedom are frozen, as in the limit of weakly-coupled nanomagnets. Here, we extend such approach to the detection of entanglement between subsystems of a spin cluster, beyond such weak-coupling limit. The resulting inequalities are violated in spin clusters with different geometries, thus allowing the detection of zero- and finite-temperature entanglement. Under relevant and experimentally verifiable conditions, all the required expectation values can be traced back to correlation functions of individual spins, that are now made selectively available by four-dimensional inelastic neutron scattering

Integrable dispersionless PDEs arising as commutation condition of pairs of vector fields

We review some results about the theory of integrable dispersionless PDEs arising as commutation condition of pairs of one-parameter families of vector fields, developed by the authors during the last years. We review, in particular, the formal aspects of a novel Inverse Spectral Transform including, as inverse problem, a nonlinear Riemann - Hilbert (NRH) problem, allowing one i) to solve the Cauchy problem for the target PDE; ii) to construct classes of RH spectral data for which the NRH problem is exactly solvable; iii) to construct the longtime behavior of the solutions of such PDE; iv) to establish if a localized initial datum breaks at finite time. We also comment on the existence of recursion operators and Backl\"und - Darboux transformations for integrable dispersionless PDEs.Comment: 17 pages, 1 figure. Written rendition of the talk presented by one of the authors (PMS) at the PMNP 2013 Conference, in a special session dedicated to the memory of S. V. Manakov. To appear in the Proceedings of the Conference PMNP 2013, IOP Conference Serie

On the solutions of the dKP equation: nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

We make use of the nonlinear Riemann Hilbert problem of the dispersionless Kadomtsev Petviashvili equation, i) to construct the longtime behaviour of the solutions of its Cauchy problem; ii) to characterize a class of implicit solutions; iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking.Comment: 33 pages, 10 figures, few formulas update

The Cauchy Problem on the Plane for the Dispersionless Kadomtsev - Petviashvili Equation

We construct the formal solution of the Cauchy problem for the dispersionless Kadomtsev - Petviashvili equation as application of the Inverse Scattering Transform for the vector field corresponding to a Newtonian particle in a time-dependent potential. This is in full analogy with the Cauchy problem for the Kadomtsev - Petviashvili equation, associated with the Inverse Scattering Transform of the time dependent Schroedinger operator for a quantum particle in a time-dependent potential.Comment: 10 pages, submitted to JETP Letter

Incremental context creation and its effects on semantic query precision

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-10543-2_19Proceedings of 4th International Conference on Semantic and Digital Media Technologies, SAMT 2009 Graz, Austria, December 2-4, 2009We briefly describe the results of an experimental study on the incremental creation of context out of the results of targeted queries, and discuss the increase in retrieval precision that results from the incremental enrichment of context.This work was supported in part by Consejería de Educación, Comunidad Autónoma de Madrid, under the grant CCG08-UAM/TIC/4303, Búsqueda basada en contexto como alternativa semántica al modelo ontológico. Simone Santini was in part supported by the Ramón y Cajal initiative of the Ministero de educación y ciencia. Alexandra Dumitrescu was in part supported by the European Social Fund, Universidad Autónoma de Madrid

Initial-Boundary Value Problems for Linear and Soliton PDEs

Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based on the elimination of the unknown boundary values by proper restrictions of the functional space and of the spectral variable complex domain. Illustrative examples include the linear Schroedinger equation on compact and semicompact n-dimensional domains and the nonlinear Schroedinger equation on the semiline.Comment: 18 pages, LATEX, submitted to the proccedings of NEEDS 2001 - Special Issue, to be published in the Journal of Theoretical and Mathematical Physic