Entanglement in continuous variable systems: Recent advances and current perspectives

We review the theory of continuous-variable entanglement with special emphasis on foundational aspects, conceptual structures, and mathematical methods. Much attention is devoted to the discussion of separability criteria and entanglement properties of Gaussian states, for their great practical relevance in applications to quantum optics and quantum information, as well as for the very clean framework that they allow for the study of the structure of nonlocal correlations. We give a self-contained introduction to phase-space and symplectic methods in the study of Gaussian states of infinite-dimensional bosonic systems. We review the most important results on the separability and distillability of Gaussian states and discuss the main properties of bipartite entanglement. These include the extremal entanglement, minimal and maximal, of two-mode mixed Gaussian states, the ordering of two-mode Gaussian states according to different measures of entanglement, the unitary (reversible) localization, and the scaling of bipartite entanglement in multimode Gaussian states. We then discuss recent advances in the understanding of entanglement sharing in multimode Gaussian states, including the proof of the monogamy inequality of distributed entanglement for all Gaussian states, and its consequences for the characterization of multipartite entanglement. We finally review recent advances and discuss possible perspectives on the qualification and quantification of entanglement in non Gaussian states, a field of research that is to a large extent yet to be explored.Comment: 61 pages, 7 figures, 3 tables; Published as Topical Review in J. Phys. A, Special Issue on Quantum Information, Communication, Computation and Cryptography (v3: few typos corrected

Is acting prosocially beneficial for the credit market?

This article argues that behaving prosocially implies more transparent information during the negotiation process of a financial contract and more cooperation among the parties to respect the terms of the contract. For this reason this work considers interest rate on loans and insolvency rate functions of prosocial behaviour along with the traditional socio-economic and financial collaterals. The context of study is Italy and the analysis is developed at a cross-regional level. We collect data from the two reports on “Relatives and Safety Net” produced by the Italian Centre Bureau of Statistics (ISTAT) in 1998 and 2003 and from the reports on “Regional Economics” produced by the Bank of Italy in the same years. A two-period panel model shows two interesting outcomes. Firstly, regions with a higher proportion of prosocial individuals report lower interest rates on loans and insolvency rates. Secondly, when we include the efficiency of legal enforcement, evidence supports the idea that a more efficient legal framework can act as a more reliable transmission mechanism of institutional norms and facilitate the internalisation of social norms

Cellular Automaton for Realistic Modelling of Landslides

A numerical model is developed for the simulation of debris flow in landslides over a complex three dimensional topography. The model is based on a lattice, in which debris can be transferred among nearest neighbors according to established empirical relationships for granular flows. The model is then validated by comparing a simulation with reported field data. Our model is in fact a realistic elaboration of simpler ``sandpile automata'', which have in recent years been studied as supposedly paradigmatic of ``self-organized criticality''. Statistics and scaling properties of the simulation are examined, and show that the model has an intermittent behavior.Comment: Revised version (gramatical and writing style cleanup mainly). Accepted for publication by Nonlinear Processes in Geophysics. 16 pages, 98Kb uuencoded compressed dvi file (that's the way life is easiest). Big (6Mb) postscript figures available upon request from [email protected] / [email protected]

A conjectural generating function for numbers of curves on surfaces

I give a conjectural generating function for the numbers of $\delta$-nodal curves in a linear system of dimension $\delta$ on an algebraic surface. It reproduces the results of Vainsencher for the case $\delta\le 6$ and Kleiman-Piene for the case $\delta\le 8$. The numbers of curves are expressed in terms of five universal power series, three of which I give explicitly as quasimodular forms. This gives in particular the numbers of curves of arbitrary genus on a K3 surface and an abelian surface in terms of quasimodular forms, generalizing the formula of Yau-Zaslow for rational curves on K3 surfaces. The coefficients of the other two power series can be determined by comparing with the recursive formulas of Caporaso-Harris for the Severi degrees in $\P_2$. We verify the conjecture for genus 2 curves on an abelian surface. We also discuss a link of this problem with Hilbert schemes of points.Comment: amslatex 13 page

On a filtered multiplicative basis of group algebras

Let $K$ be a field of characteristic $p$ and $G$ a nonabelian metacyclic finite $p$-group. We give an explicit list of all metacyclic $p$-groups $G$, such that the group algebra $KG$ over a field of characteristic $p$ has a filtered multiplicative $K$-basis. We also present an example of a non-metacyclic 2-group $G$, such that the group algebra $KG$ over any field of characteristic 2 has a filtered multiplicative $K$-basis.Comment: 10 pages, AMS-Te

X-ray and optical observations of three clusters of galaxies: Abell 901, Abell 1437, and Abell 3570

We analyse three clusters of galaxies, Abell 901 (z=0.17), Abell 1437 (z=0.13) and Abell 3570 (z=0.037). They have low to intermediate X-ray fluxes and an irregular morphology in the ROSAT All-Sky Survey (RASS). These clusters are chosen to test the abilities and limitations of the RASS in terms of cluster fluxes and cluster morphologies. Therefore some ``worst'' cases are used here. X-ray observations with the ROSAT/HRI and optical spectroscopic observations are carried out. The ROSAT/HRI observations, which have a much better spatial resolution than the RASS, reveal in two of the three cases a significantly different morphology than seen in the RASS. The reasons are point sources which could not be resolved in the RASS and were therefore confused with the cluster emission. For A3570 we could confirm the relaxed state of the cluster by the optical determination of a small velocity dispersion. In the cluster with the lowest flux (Abell 901) the countrate measurement is strongly affected by point sources, in the two other cases the countrate measurements of the RASS are reliable, i.e. they are reproduced by the ROSAT/HRI measurement. We conclude that for clusters with a flux of a few times 10^{-12} erg/cm^2/s or smaller, which show at the same time a non-relaxed morphology, the flux measurement of the RASS can be seriously affected by fore- or background sources. We point out that an all-sky survey of a second ABRIXAS mission would provide a much clearer source distinction for low-flux clusters and thus a much improved countrate determination.Comment: 8 pages (incl. 6 figures), accepted for publication in A&A (Suppl.

Extension of the Brinkman-Rice picture and the Mott transition

In order to explain the metal-Mott-insulator transition, the Brinkman-Rice (BR) picture is extended. In the case of less than one as well as one electron per atom, the on-site Coulomb repulsion is given by U={kappa}{rho}^2U_c by averaging the electron charge per atom over all atomic sites, where {kappa} is the correlation strength of U, {rho} is the band filling factor, and U_c is the critical on-site Coulomb energy. The effective mass of a quasiparticle is found to be m*/m=1/{1-{kappa}^2{rho}^4} for 0<{kappa}{rho}^2<1 and seems to follow the heat capacity data of Sr_{1-x}La_xTiO_3 and YBa_2Cu_3O_{7-delta} at {kappa}=1 and 0<{kappa}{rho}^2<1. The Mott transition of the first order occurs at {kappa}{rho}^2=1 and a band-type metal-insulator transition takes place at {kappa}{rho}^2=0. This Mott transition is compared with that in the d=infinity Hubbard model. The effective mass for 2D-DOS instead of the vHs can be used for the mechanism of high T_c superconductivity.Comment: RevTex, Physica C, Vol. 341-348, 259-260 (2000