Entanglement in fermionic chains with finite range coupling and broken symmetries

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Renyi entropy of a partial observation to a subsystem consisting of $X$ contiguous sites in the limit of large $X$. The present work generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A striking new feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size of $X$. This logarithmic behaviour originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyse the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long range pairing.Comment: 27 pages, 5 figure

On the M\"obius transformation in the entanglement entropy of fermionic chains

There is an intimate relation between entanglement entropy and Riemann surfaces. This fact is explicitly noticed for the case of quadratic fermionic Hamiltonians with finite range couplings. After recollecting this fact, we make a comprehensive analysis of the action of the M\"obius transformations on the Riemann surface. We are then able to uncover the origin of some symmetries and dualities of the entanglement entropy already noticed recently in the literature. These results give further support for the use of entanglement entropy to analyse phase transition.Comment: 29 pages, 5 figures. Final version published in JSTAT. Two new figures. Some comments and references added. Typos correcte

Variation in Bandwidths Among Solutions to Shaped Beam Synthesis Problems Concerning Linear Arrays of Parallel Dipoles

The problem of synthesizing a linear array generating a shaped beam pattern with M filled s has 2M alternative solutions. In this study we examined their bandwidths as regards compliance with pattern quality or input impedance requirements in the presence and absence of a backing ground plane. Placing a ground plane behind the antenna almost doubles sidelobe level bandwidth

Analysis, Synthesis, and Diagnostics of Antenna Arrays through Complex-Valued Neural Networks

This is the peer reviewed version of the following article: Julio C. Brégains; Francisco Ares "Analysis, synthesis, and diagnostics of antenna arrays through complex-valued neural networks", Microwave and Optical Technology Letters, 1512 - 1515 Volume: 48, Issue: 8, Aug. 2006, which has been published in final form at DOI: 10.1002/mop.21706. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving[Abstract] It is shown in this paper that when artificial neural networks are extended to be complex valued, they can be incorporated as a very powerful and effective tool in the analysis, synthesis, and diagnostics of antenna arrays

Optimal cellular mobility for synchronization arising from the gradual recovery of intercellular interactions

Cell movement and intercellular signaling occur simultaneously during the development of tissues, but little is known about how movement affects signaling. Previous theoretical studies have shown that faster moving cells favor synchronization across a population of locally coupled genetic oscillators. An important assumption in these studies is that cells can immediately interact with their new neighbors after arriving at a new location. However, intercellular interactions in cellular systems may need some time to become fully established. How movement affects synchronization in this situation has not been examined. Here we develop a coupled phase oscillator model in which we consider cell movement and the gradual recovery of intercellular coupling experienced by a cell after movement, characterized by a moving rate and a coupling recovery rate respectively. We find (1) an optimal moving rate for synchronization, and (2) a critical moving rate above which achieving synchronization is not possible. These results indicate that the extent to which movement enhances synchrony is limited by a gradual recovery of coupling. These findings suggest that the ratio of time scales of movement and signaling recovery is critical for information transfer between moving cells.Comment: 18 single column pages + 1 table + 5 figures + Supporting Informatio

Orthogonality catastrophe and fractional exclusion statistics

We show that the N-particle Sutherland model with inverse-square and harmonic interactions exhibits orthogonality catastrophe. For a fixed value of the harmonic coupling, the overlap of the N-body ground state wave functions with two different values of the inverse-square interaction term goes to zero in the thermodynamic limit. When the two values of the inverse-square coupling differ by an infinitesimal amount, the wave function overlap shows an exponential suppression. This is qualitatively different from the usual power law suppression observed in the Anderson''s orthogonality catastrophe. We also obtain an analytic expression for the wave function overlaps for an arbitrary set of couplings, whose properties are analyzed numerically. The quasiparticles constituting the ground state wave functions of the Sutherland model are known to obey fractional exclusion statistics. Our analysis indicates that the orthogonality catastrophe may be valid in systems with more general kinds of statistics than just the fermionic type

A WiMAX Conformal Broad-Beam Antenna

[Abstract] The numerical model of a very simple conformal antenna, prepared to work in the 3.4 to 3.6 GHz WiMAX range, is presented. The pattern radiated by the proposed antenna displays high gain and excellent linear polarization within the broad coverage zone.Xunta de Galicia; 09TIC008105PRXunta de Galicia; 07TIC002206PRMinisterio de Ciencia e Innovación; TEC2007-68020-C04-01Ministerio de Ciencia e Innovación; TEC2008-04485Ministerio de Ciencia e Innovación; CSD2008-00010

Visualizing the 3D Polar Power Patterns and Excitations of Planar Arrays with Matlab

[Abstrac] This paper discusses the use of Matlab to create three-dimensional polar plots of the power patterns of planar arrays together with 3D plots of the amplitudes and phases of their excitations. A few lines of Matlab M-code suffice to create complex plots

Effects of Measurement Distance on Measurements of Symmetrically Shaped Patterns Generated by Line Sources

[Abstract] Symmetrically shaped patterns, generated by real continuous linear apertures derived from Taylor distributions, resemble Taylor sum patterns in regard to the distance-dependence of their sidelobe heights. Their ripple shows negligible near-field degradation. If the aperture distribution is complex, however, the ripple and sidelobe levels show previously unreported degradation behavior, including a lowering of the first sidelobe level