Entanglement from density measurements: analytical density-functional for the entanglement of strongly correlated fermions

We derive an analytical density functional for the single-site entanglement of the one-dimensional homogeneous Hubbard model, by means of an approximation to the linear entropy. We show that this very simple density functional reproduces quantitatively the exact results. We then use this functional as input for a local density approximation to the single-site entanglement of inhomogeneous systems. We illustrate the power of this approach in a harmonically confined system, which could simulate recent experiments with ultracold atoms in optical lattices as well as in a superlattice and in an impurity system. The impressive quantitative agreement with numerical calculations -- which includes reproducing subtle signatures of the particle density stages -- shows that our density-functional can provide entanglement calculations for actual experiments via density measurements. Next we use our functional to calculate the entanglement in disordered systems. We find that, at contrast with the expectation that disorder destroys the entanglement, there exist regimes for which the entanglement remains almost unaffected by the presence of disordered impurities.Comment: 6 pages, 3 figure

Hubbard model as an approximation to the entanglement in nanostructures

We investigate how well the one-dimensional Hubbard model describes the entanglement of particles trapped in a string of quantum wells. We calculate the average single-site entanglement for two particles interacting via a contact interaction and consider the effect of varying the interaction strength and the interwell distance. We compare the results with the ones obtained within the one-dimensional Hubbard model with on-site interaction. We suggest an upper bound for the average single-site entanglement for two electrons in M wells and discuss analytical limits for very large repulsive and attractive interactions. We investigate how the interplay between interaction and potential shape in the quantum-well system dictates the position and size of the entanglement maxima and the agreement with the theoretical limits. Finally, we calculate the spatial entanglement for the quantum-well system and compare it to its average single-site entanglement

Weighted-indexed semi-Markov models for modeling financial returns

In this paper we propose a new stochastic model based on a generalization of semi-Markov chains to study the high frequency price dynamics of traded stocks. We assume that the financial returns are described by a weighted indexed semi-Markov chain model. We show, through Monte Carlo simulations, that the model is able to reproduce important stylized facts of financial time series as the first passage time distributions and the persistence of volatility. The model is applied to data from Italian and German stock market from first of January 2007 until end of December 2010.Comment: arXiv admin note: substantial text overlap with arXiv:1109.425

Massive Cosmologies

We explore the cosmological solutions of a recently proposed extension of General Relativity with a Lorentz-invariant mass term. We show that the same constraint that removes the Boulware-Deser ghost in this theory also prohibits the existence of homogeneous and isotropic cosmological solutions. Nevertheless, within domains of the size of inverse graviton mass we find approximately homogeneous and isotropic solutions that can well describe the past and present of the Universe. At energy densities above a certain crossover value, these solutions approximate the standard FRW evolution with great accuracy. As the Universe evolves and density drops below the crossover value the inhomogeneities become more and more pronounced. In the low density regime each domain of the size of the inverse graviton mass has essentially non-FRW cosmology. This scenario imposes an upper bound on the graviton mass, which we roughly estimate to be an order of magnitude below the present-day value of the Hubble parameter. The bound becomes especially restrictive if one utilizes an exact self-accelerated solution that this theory offers. Although the above are robust predictions of massive gravity with an explicit mass term, we point out that if the mass parameter emerges from some additional scalar field condensation, the constraint no longer forbids the homogeneous and isotropic cosmologies. In the latter case, there will exist an extra light scalar field at cosmological scales, which is screened by the Vainshtein mechanism at shorter distances.Comment: 21 page

Continuum elasticity theory of edge excitations in a two-dimensional electron liquid with finite range interactions

We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with the following simplifying assumptions: (i) The system is {\it macroscopically} homogeneous and isotropic in the half-plane delimited by the edge (ii) The electron-electron interaction is of finite range due to screening by external electrodes (iii) The system is nearly incompressible. At sufficiently small wave vector $q$ we find a universal dispersion curve $\omega \sim q$ independent of the shear modulus. At larger wave vectors the dispersion can change its form in a manner dependent on the comparison of various length scales. We obtain analytical formulas for the dispersion and damping of the modes in various physical regimes.Comment: 3 figure

Quantum mechanics in metric space: wave functions and their densities

Hilbert space combines the properties of two fundamentally different types of mathematical spaces: vector space and metric space. While the vector-space aspects of Hilbert space, such as formation of linear combinations of state vectors, are routinely used in quantum mechanics, the metric-space aspects of Hilbert space are much less exploited. Here we show that a suitable metric stratifies Fock space into concentric spheres. Maximum and minimum distances between wave functions are derived and geometrically interpreted in terms of this metric. Unlike the usual Hilbert-space analysis, our results apply also to the reduced space of only ground-state wave functions and to that of particle densities, each of which forms a metric space but not a Hilbert space. The Hohenberg-Kohn mapping between densities and ground-state wave functions, which is highly complex and nonlocal in coordinate description, is found, for three different model systems, to be very simple in metric space, where it is represented by a monotonic mapping of vicinities onto vicinities. Surprisingly, it is also found to be nearly linear over a wide range of parameters

Low Power Analog Design in Scaled Technologies

In this paper an overview on the main issues in analog IC design in scaled CMOS technology is presented. Decreasing the length of MOS channel and the gate oxide has led to undoubted advantages in terms of chip area, speed and power consumption (mainly exploited in the digital parts). Besides, some drawbacks are introduced in term of power leakage and reliability. Moreover, the scaled technology lower supply voltage requirement has led analog designers to find new circuital solution to guarantee the required performance

Stima della pericolosità sismica in termini di intensità macrosismica in Italia: due metodologie di calcolo a confronto

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PSR J1016-5857: a young radio pulsar with possible supernova remnant, X-ray, and gamma-ray associations

We report the discovery of a young and energetic pulsar in the Parkes multibeam survey of the Galactic plane. PSR J1016-5857 has a rotation period of 107 ms and period derivative of 8e-14, implying a characteristic age of 21 kyr and spin-down luminosity of 2.6e36 erg/s. The pulsar is located just outside, and possibly interacting with, the shell supernova remnant G284.3-1.8. Archival X-ray data show a source near the pulsar position which is consistent with emission from a pulsar wind nebula. The pulsar is also located inside the error box of the unidentified EGRET source 3EG J1013-5915, for which it represents a plausible counterpart.Comment: 5 pages, 3 included figures, accepted for publication by ApJ Letter

Nuova formulazione delle procedure per la stima dell’intensità macrosismica da dati epicentrali o da risentimenti in zone vicine

Vengono presentate nuove relazioni empiriche, definite per il territorio italiano, per la stima dell’intensità in un dato sito a partire da informazioni epicentrali o relative a località vicine. Queste relazioni, espresse in forma probabilistica e quindi direttamente utilizzabili per la stima della pericolosità sismica, condividono la stessa formalizzazione e la medesima base informativa. In particolare, sono state seguite tre diverse strategie: le prime due hanno portato alla definizione di una relazione di attenuazione per la stima dell’intensità al sito da dati epicentrali utilizzando una forma parametrica rispettivamente Gaussiana e Binomiale; la terza analisi è stata invece mirata a definire le modalità di “correzione” del valore locale di intensità, dedotto dalle informazioni epicentrali, con dati di risentimenti osservati in località vicine al sito in esame