Modified Wandzura-Wilczek Relation with the Nachtmann Variable

If one retains M^2/Q^2 terms in the kinematics, the Nachtmann variable \xi seems to be more appropriate to describe deep inelastic lepton-nucleon scattering. Up to the first power of M^2/Q^2, a modified Wandzura-Wilczek relation with respect to \xi was derived. Kinematical correction factors are given as functions of \xi and Q^2. A comparison of the modified g_2^WW(\xi) and original g_2^WW(x) with the most recent g_2 data is shown.Comment: 10 pages, 3 figures, revised version with minor correction

Magnetic Properties of J-J-J' Quantum Heisenberg Chains with Spin S=1/2, 1, 3/2 and 2 in a Magnetic Field

By means of the density matrix renormalization group (DMRG) method, the magnetic properties of the J-J-J$^{\prime}$ quantum Heisenberg chains with spin $S=1/2$, 1, 3/2 and 2 in the ground states are investigated in the presence of a magnetic field. Two different cases are considered: (a) when $J$ is antiferromagnetic and $J^{\prime}$ is ferromagnetic (i.e. the AF-AF-F chain), the system is a ferrimagnet. The plateaus of the magnetization are observed. It is found that the width of the plateaus decreases with increasing the ferromagnetic coupling, and disappears when $$ passes over a critical value. The saturated field is observed to be independent of the ferromagnetic coupling; (b) when $J$ is ferromagnetic and $J^{\prime}$ is antiferromagnetic (i.e. the F-F-AF chain), the system becomes an antiferromagnet. The plateaus of the magnetization are also seen. The width of the plateaus decreases with decreasing the antiferromagnetic coupling, and disappears when $J^{\prime}/J$ passes over a critical value. Though the ground state properties are quite different, the magnetization plateaus in both cases tend to disappear when the ferromagnetic coupling becomes more dominant. Besides, no fundamental difference between the systems with spin half-integer and integer has been found.Comment: 8 pages, 9 figures, to be published in J. Phys.: Condens. Matte

Quark Orbital Angular Momentum in the Baryon

Analytical and numerical results, for the orbital and spin content carried by different quark flavors in the baryons, are given in the chiral quark model with symmetry breaking. The reduction of the quark spin, due to the spin dilution in the chiral splitting processes, is transferred into the orbital motion of quarks and antiquarks. The orbital angular momentum for each quark flavor in the proton as a function of the partition factor $\kappa$ and the chiral splitting probability $a$ is shown. The cancellation between the spin and orbital contributions in the spin sum rule and in the baryon magnetic moments is discussed.Comment: 26 pages, 3 figures, revised version with minor eq. no and ref. no. corrections. Discussion on the $\Lambda$ spin and a new ref. are adde

Pattern-Based Analysis of Time Series: Estimation

While Internet of Things (IoT) devices and sensors create continuous streams of information, Big Data infrastructures are deemed to handle the influx of data in real-time. One type of such a continuous stream of information is time series data. Due to the richness of information in time series and inadequacy of summary statistics to encapsulate structures and patterns in such data, development of new approaches to learn time series is of interest. In this paper, we propose a novel method, called pattern tree, to learn patterns in the times-series using a binary-structured tree. While a pattern tree can be used for many purposes such as lossless compression, prediction and anomaly detection, in this paper we focus on its application in time series estimation and forecasting. In comparison to other methods, our proposed pattern tree method improves the mean squared error of estimation

General Localization Lengths for Two Interacting Particles in a Disordered Chain

The propagation of an interacting particle pair in a disordered chain is characterized by a set of localization lengths which we define. The localization lengths are computed by a new decimation algorithm and provide a more comprehensive picture of the two-particle propagation. We find that the interaction delocalizes predominantly the center-of-mass motion of the pair and use our approach to propose a consistent interpretation of the discrepancies between previous numerical results.Comment: 4 pages, 2 epsi figure

Localized to extended states transition for two interacting particles in a two-dimensional random potential

We show by a numerical procedure that a short-range interaction $u$ induces extended two-particle states in a two-dimensional random potential. Our procedure treats the interaction as a perturbation and solve Dyson's equation exactly in the subspace of doubly occupied sites. We consider long bars of several widths and extract the macroscopic localization and correlation lengths by an scaling analysis of the renormalized decay length of the bars. For $u=1$, the critical disorder found is $W_{\rm c}=9.3\pm 0.2$, and the critical exponent $\nu=2.4\pm 0.5$. For two non-interacting particles we do not find any transition and the localization length is roughly half the one-particle value, as expected.Comment: 4 two-column pages, 4 eps figures, Revtex, to be published in Europhys. Let