Scaling limit of a non-relativistic model

I calculate the structure function for scattering from the two-body bound state in its lowest level in a non-relativistic model of confined scalar ``quarks'' of masses $m_A$ and $m_B$. The scaling limit in $x={\bf q}^2/2(m_A+m_B)q^0$ exists and is non-vanishing only for the values $x=m_A/(m_A+m_B)$ and $x=m_B/(m_A+m_B)$ which correspond to the fractions of the momentum of the two-body system carried by each of the ``quarks.'' In the scaling limit, the interference from scattering off of the two ``quarks'' vanishes. Thus the scaling limit of this model agrees with the parton picture.Comment: 10 pages, 3 figures not included, in LaTex, UMD 92-22

Pentaquark state in pole-dominated QCD sum rules

We propose a new approach in QCD sum rules applied for exotic hadrons with a number of quarks, exemplifying the pentaquark Theta^{+} (I=0,J=1/2) in the Borel sum rule. Our approach enables reliable extraction of the pentaquark properties from the sum rule with good stability in a remarkably wide Borel window. The appearance of its valid window originates from a favorable setup of the correlation functions with the aid of it chirality of the interpolating fields on the analogy of the Weinberg sum rule for the vector currents. Our setup leads to large suppression of the continuum contributions which have spoiled the Borel stability in the previous analyses, and consequently enhances importance of the higher-dimensional contributions of the OPE, which are indispensable for investigating the pentaquark properties. Implementing the OPE analysis up to dimension 15, we find that the sum rules for the chiral-even and odd parts independently give the Theta^{+} mass of 1.68 pm 0.22 GeV with uncertainties of the condensate values. Our sum rule indeed gives rather flat Borel curves almost independent of the continuum thresholds both for the mass and pole residue. Finally, we also discuss possible isolation of the observed states from the KN scattering state on view of chiral symmetry.Comment: 8 pages, 7 figure

Experimental demonstration of Aharonov-Casher interference in a Josephson junction circuit

A neutral quantum particle with magnetic moment encircling a static electric charge acquires a quantum mechanical phase (Aharonov-Casher effect). In superconducting electronics the neutral particle becomes a fluxon that moves around superconducting islands connected by Josephson junctions. The full understanding of this effect in systems of many junctions is crucial for the design of novel quantum circuits. Here we present measurements and quantitative analysis of fluxon interference patterns in a six Josephson junction chain. In this multi-junction circuit the fluxon can encircle any combination of charges on five superconducting islands, resulting in a complex pattern. We compare the experimental results with predictions of a simplified model that treats fluxons as independent excitations and with the results of the full diagonalization of the quantum problem. Our results demonstrate the accuracy of the fluxon interference description and the quantum coherence of these arrays

Tunable disorder in a crystal of cold polar molecules

In the present work, we demonstrate the possibility of controlling by an external field the dynamics of collective excitations (excitons) of molecules on an optical lattice. We show that a suitably chosen two-species mixture of ultracold polar molecules loaded on an optical lattice forms a phononless crystal, where exciton-impurity interactions can be controlled by applying an external electric field. This can be used for the controlled creation of many-body entangled states of ultracold molecules and the time-domain quantum simulation of disorder-induced localization and delocalization of quantum particles

QCD radiative and power corrections and Generalized GDH sum rules

We extend the earlier suggested QCD-motivated model for the $Q^2$-dependence of the generalized Gerasimov-Drell-Hearn (GDH) sum rule which assumes the smooth dependence of the structure function $g_T$, while the sharp dependence is due to the $g_2$ contribution and is described by the elastic part of the Burkhardt-Cottingham sum rule. The model successfully predicts the low crossing point for the proton GDH integral, but is at variance with the recent very accurate JLAB data. We show that, at this level of accuracy, one should include the previously neglected radiative and power QCD corrections, as boundary values for the model. We stress that the GDH integral, when measured with such a high accuracy achieved by the recent JLAB data, is very sensitive to QCD power corrections. We estimate the value of these power corrections from the JLAB data at $Q^2 \sim 1 {GeV}^2$. The inclusion of all QCD corrections leads to a good description of proton, neutron and deuteron data at all $Q^2$.Comment: 10 pages, 4 figures (to be published in Physical Review D

Axial anomaly: the modern status

The modern status of the problem of axial anomaly in QED and QCD is reviewed. Two methods of the derivation of the axial anomaly are presented: 1) by splitting of coordinates in the expression for the axial current and 2) by calculation of triangle diagrams, where the anomaly arises from the surface terms in momentum space. It is demonstrated, that the equivalent formulation of the anomaly can be given, as a sum rule for the structure function in dispersion representation of three point function of AVV interaction. It is argued, that such integral representation of the anomaly has some advantages in the case of description of the anomaly by contribution of hadronic states in QCD. The validity of the t'Hooft consistency condition is discussed. Few examples of the physical application of the axial anomaly are given.Comment: 17 pages, 3 figures, to be published in International Journal of Modern Physics A, few minor correction were done, two references were adde

The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems

Open quantum systems are, in general, described by a density matrix that is evolving under transformations belonging to a dynamical semigroup. They can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space of dimension $2$. First, we find final fixed states (called pointers) of an evolution of an open system, and we then obtain a general solution to the FGKLS equation and confirm that it converges to a pointer. After this, we check that the solution has physical meaning, i.e., it is Hermitian, positive and has trace equal to $1$, and find a moment of time starting from which the FGKLS equation can be used - the range of applicability of the semigroup symmetry. Next, we study the behavior of a solution for a weak interaction with an environment and make a distinction between interacting and non-interacting cases. Finally, we prove that there cannot exist oscillating solutions to the FGKLS equation, which would resemble the behavior of a closed quantum system.Comment: 27 p.

Entropy-driven phase transition in a polydisperse hard-rods lattice system

We study a system of rods on the 2d square lattice, with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N=2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals

Bosonic model with Z3Z_3 fractionalization

Bosonic model with unfrustrated hopping and short-range repulsive interaction is constructed that realizes $Z_3$ fractionalized insulator phase in two dimensions and in zero magnetic field. Such phase is characterized as having gapped charged excitations that carry fractional electrical charge 1/3 and also gapped $Z_3$ vortices above the topologically ordered ground state.Comment: 7 pages, 3 figure