Multifractal Properties of Aperiodic Ising Model: role of geometric fluctuations

The role of the geometric fluctuations on the multifractal properties of the local magnetization of aperiodic ferromagnetic Ising models on hierachical lattices is investigated. The geometric fluctuations are introduced by generalized Fibonacci sequences. The local magnetization is evaluated via an exact recurrent procedure encompassing a real space renormalization group decimation. The symmetries of the local magnetization patterns induced by the aperiodic couplings is found to be strongly (weakly) different, with respect to the ones of the corresponding homogeneous systems, when the geometric fluctuations are relevant (irrelevant) to change the critical properties of the system. At the criticality, the measure defined by the local magnetization is found to exhibit a non-trivial F(alpha) spectra being shifted to higher values of alpha when relevant geometric fluctuations are considered. The critical exponents are found to be related with some special points of the F(alpha) function and agree with previous results obtained by the quite distinct transfer matrix approach.Comment: 10 pages, 7 figures, 3 Tables, 17 reference

Many-body system with a four-parameter family of point interactions in one dimension

We consider a four-parameter family of point interactions in one dimension. This family is a generalization of the usual $\delta$-function potential. We examine a system consisting of many particles of equal masses that are interacting pairwise through such a generalized point interaction. We follow McGuire who obtained exact solutions for the system when the interaction is the $\delta$-function potential. We find exact bound states with the four-parameter family. For the scattering problem, however, we have not been so successful. This is because, as we point out, the condition of no diffraction that is crucial in McGuire's method is not satisfied except when the four-parameter family is essentially reduced to the $\delta$-function potential.Comment: 8 pages, 4 figure

Assessing the Prosody of Non-Native Speakers of English: Measures and Feature Sets

In this paper, we describe a new database with audio recordings of non-native (L2) speakers of English, and the perceptual evaluation experiment conducted with native English speakers for assessing the prosody of each recording. These annotations are then used to compute the gold standard using different methods, and a series of regression experiments is conducted to evaluate their impact on the performance of a regression model predicting the degree of Abstract naturalness of L2 speech. Further, we compare the relevance of different feature groups modelling prosody in general (without speech tempo), speech rate and pauses modelling speech tempo (fluency), voice quality, and a variety of spectral features. We also discuss the impact of various fusion strategies on performance.Overall, our results demonstrate that the prosody of non-native speakers of English as L2 can be reliably assessed using supra- segmental audio features; prosodic features seem to be the most important ones

The time-dependent Schrödinger equation: the need for the Hamiltonian to be self-adjoint

We present some simple arguments to show that quantum mechanics operators are required to be self-adjoint. We emphasize that the very definition of a self-adjoint operator includes the prescription of a certain domain of the operator. We then use these concepts to revisit the solutions of the time-dependent Schroedinger equation of some well-known simple problems - the infinite square well, the finite square well, and the harmonic oscillator. We show that these elementary illustrations can be enriched by using more general boundary conditions, which are still compatible with self-adjointness. In particular, we show that a puzzling problem associated with the Hydrogen atom in one dimension can be clarified by applying the correct requirements of self-adjointness. We then come to Stone\'s theorem, which is the main topic of this paper, and which is shown to relate the usual definitions of a self-adjoint operator to the possibility of constructing well-defined solutions of the time-dependent Schrödinger equation.Conselho Nacional de Desenvolvimento Cientí fico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Quantum phase transitions in alternating spin-(1/2, 5/2) Heisenberg chains

The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for magnetic susceptibility, magnetization and specific heat are obtained through the finite-temperature Lanczos method with the aim in describing available experimental data, as well as comparison with theoretical results from the semiclassical approximation and the low-temperature susceptibility expansion derived from Takahashi's modified spin-wave theory. In particular, we study in detail the temperature vs. magnetic field phase diagram of the spin-1/2 spin-5/2 chain, in which several low-temperature quantum phases are identified: the Luttinger Liquid phase, the ferrimagnetic plateau and the fully polarized one, and the respective quantum critical points and crossover lines

Dirac and Majorana heavy neutrinos at LEP II

The possibility of detecting single heavy Dirac and Majorana neutrinos at LEP II is investigated for heavy neutrino masses in the range $M_N=(\sqrt s/2, \sqrt s)$. We study the process $e^+e^- \longrightarrow \nu_{\ell} \ell q_i \bar q_j$ as a clear signature for heavy neutrinos. Numerical estimates for cross sections and distributions for the signal and the background are calculated and a Monte Carlo reconstruction of final state particles after hadronization is presented.Comment: 4 pages, 8 figure