Effects of spontaneous symmetry break in the origin of non-analytic behavior of entanglement at quantum phase transitions

We present an example where Spontaneous Symmetry Breaking may effect not only the behavior of the entanglement at Quantum Phase Transitions, but also the origin of the non-analyticity. In particular, in the XXZ model, we study the non analyticities in the concurrence between two spins, which was claimed to be accidental, since it had its origin in the optimization involved in the concurrence definition. We show that when one takes in account the effect of the Spontaneous Symmetry Breaking, even tough the values of the entanglement measure does not change, the origin the the non-analytical behavior changes: it is not due to the optimization process anymore and in this sense it is a "natural" non-analyticity. This is a much more subtle influence of the Spontaneous Symmetry Breaking not noticed before. However the non-analytical behavior still suggests a second order quantum phase transition and not the first order that occurs and we explain why. We also show that the value of entanglement between one site and the rest of the chain does change when taking into account the Spontaneous Symmetry Breaking.Comment: a brief report, comments welcome. Text improved after referee suggestion

Bell inequalities and entanglement at quantum phase transition in the XXZ Model

Entanglement and violation of Bell inequalities are aspects of quantum nonlocality that have been often confused in the past. It is now known that this equivalence is only true for pure states. Even though almost all the studies of quantum correlations at quantum phase transitions deal only with entanglement, we here argue that Bell inequalities can also reveal a general quantum phase transition. This is also shown for a particular case of two spin-1/2 particles in an infinite one-dimensional chain described by the XXZ model. In this case, the Bell inequality is able to signal not only the first-order phase transition, but also the infinite-order Kosterlitz-Thouless quantum phase transition, which cannot be revealed either by the energy of the system nor by the bipartite entanglement. We also show that although the nearest-neighbor spins are entangled, they, unexpectedly, never violate the Bell inequality. This indicates that the type of entanglement which is relevant for quantum phase transition is not trivial, i.e., it cannot be revealed by the Bell inequality.Comment: Published version. English improved and Sec. II shortened, after referee suggestions. 7 pages, 6 figure

On the global convergent of an inexact quasi-Newton conditional gradient method for constrained nonlinear systems

In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global convergence analysis of the proposed method is established under suitable conditions, and some preliminary numerical experiments are given to illustrate its performance

Convergence of the Gauss-Newton method for a special class of systems of equations under a majorant condition

In this paper, we study the Gauss-Newton method for a special class of systems of nonlinear equation. Under the hypothesis that the derivative of the function under consideration satisfies a majorant condition, semi-local convergence analysis is presented. In this analysis the conditions and proof of convergence are simplified by using a simple majorant condition to define regions where the Gauss-Newton sequence is "well behaved". Moreover, special cases of the general theory are presented as applications

A characterization of singular packing subspaces with an application to limit-periodic operators

A new characterization of the singular packing subspaces of general bounded self-adjoint operators is presented, which is used to show that the set of operators whose spectral measures have upper packing dimension equal to one is a $G_\delta$ (in suitable metric spaces). As an application, it is proven that, generically (in space of continuous sampling functions), spectral measures of the limit-periodic Schr\"odinger operators have upper packing dimensions equal to one. Consequently, in a generic set, these operators are quasiballistic.Comment: Accepted for publication in Forum Mathematicu

Asymptotic Quantum Search and a Quantum Algorithm for Calculation of a Lower Bound of the Probability of Finding a Diophantine Equation That Accepts Integer Solutions

Several mathematical problems can be modeled as a search in a database. An example is the problem of finding the minimum of a function. Quantum algorithms for solving this problem have been proposed and all of them use the quantum search algorithm as a subroutine and several intermediate measurements are realized. In this work, it is proposed a new quantum algorithm for finding the minimum of a function in which quantum search is not used as a subroutine and only one measurement is needed. This is also named asymptotic quantum search. As an example, we propose a quantum algorithm based on asymptotic quantum search and quantum counting able to calculate a lower bound of the probability of finding a Diophantine equation with integer solution.Comment: Eleven pages, two figures. A complexity analysis is include

An Inexact Newton-like conditional gradient method for constrained nonlinear systems

In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of the new method as well as results on its rate are established by using a general majorant condition. Two applications of such condition are provided: one is for functions whose the derivative satisfies Holder-like condition and the other is for functions that satisfies a Smale condition, which includes a substantial class of analytic functions. Some preliminaries numerical experiments illustrating the applicability of the proposed method for medium and large problems are also presented

Performance Assessment of WhatsApp and IMO on Android Operating System (Lollipop and KitKat) during VoIP calls using 3G or WiFi

This paper assesses the performance of mobile messaging and VoIP connections. We investigate the CPU usage of WhatsApp and IMO under different scenarios. This analysis also enabled a comparison of the performance of these applications on two Android operating system (OS) versions: KitKat or Lollipop. Two models of smartphones were considered, viz. Galaxy Note 4 and Galaxy S4. The applications behavior was statistically investigated for both sending and receiving VoIP calls. Connections have been examined over 3G and WiFi. The handset model plays a decisive role in CPU usage of the application. t-tests showed that IMO has a better performance that WhatsApp whatever be the Android at a significance level 1%, on Galaxy Note 4. In contrast, WhatsApp requires less CPU than IMO on Galaxy S4 whatever be the OS and access (3G/WiFi). Galaxy Note 4 using WiFi always outperformed S4 in terms of processing efficiency.Comment: 8 pages, Number of floats/tables/figures:

The Fourier-Like and Hartley-Like Wavelet Analysis Based on Hilbert Transforms

In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet functions and is named as the Fourier-Like and Hartley-Like wavelet analysis. A Hilbert transform analysis on the wavelet theory is also included.Comment: 7 pages, 10 figures, Anais do XXII Simp\'osio Brasileiro de Telecomunica\c{c}\~oes, Campinas, 200

On the spectral Hausdorff dimension of 1D discrete Schr\"odinger operators under power decaying perturbations

We show that spectral Hausdorff dimensional properties of discrete Schr\"oodinger operators with (1) Sturmian potentials of bounded density and (2) a class of sparse potentials are preserved under suitable polynomial decaying perturbations, when the spectrum of these perturbed operators have some singular continuous component.Comment: To appear in Osaka Journal of Mathematic