An $\mathsf{\epsilon}$-expansion for small-world networks

I construct a well-defined expansion in for diffusion processes on small-world networks. The technique permits one to calculate the average over disorder of moments of the Greens function, and is used to calculate the average Greens function and fluctuations to first non-leading order in , giving results which agree with numerics. This technique is also applicable to other problems of diffusion in random media.Received: 28 July 2004, Published online: 14 December 2004PACS: 89.75.Hc Networks and genealogical trees 64.60.Ak Renormalization-group studies of phase transitions     

Ab initio phonon dispersion relations of $\mathsf{\alpha}$-Ga

We present the ab initio phonon dispersion relations of -Ga. The calculations are carried out within density functional perturbation theory by using either norm-conserving pseudopotential and 4s and 4p electrons in the valence or ultrasoft pseudopotential and 3d electrons in the valence as well. The inclusion of 3d electrons in the valence turned out to be necessary to better reproduce the experimental frequencies of the stretching modes of the Ga₂ dimers present in the -Ga structure.Received: 29 July 2003, Published online: 19 November 2003PACS: 63.20.Dj Phonon states and bands, normal modes, and phonon dispersion - 71.15.Nc Total energy and cohesive energy calculations - 71.15.Mb Density functional theory, local density approximation, gradient and other corrections     

Ion trap nuclear resonance on $\mathsf{^{151}Eu^ + }$

Laser-microwave double resonance techniques applied to a cloud of a natural mixture of Eu ⁺ isotopes confined in a Penning trap has been used to induce and detect nuclear Zeeman transitions. In spite of the complex level structure of Eu ⁺ and overlapping spectra from the two isotopes five different transitions could be observed from which the nuclear magnetic moment can be derived. We obtain for ¹⁵¹ Eu ⁺ g _I = 1.377 34(6) demonstrating the potential for high accuracy of the technique. The experiment can be considered as a feasibility test that precise spectroscopy data using the ion storage technique can be obtained of very complex ions and under unfavourable conditions.Received: 13 June 2003, Published online: 12 August 2003PACS: 32.60. + i Zeeman and Stark effects - 32.10.Dk Electric and magnetic moments, polarizability     

The 2-site Hubbard and $\mathsf{t}$-$\mathsf{J}$ models

The fermionic and bosonic sectors of the 2-site Hubbard model have been exactly solved by means of the equation of motion and Greens function formalism. The exact solution of the t-J model has been also reported to investigate the low-energy dynamics. We have successfully searched for the exact eigenoperators, and the corresponding eigenenergies, having in mind the possibility to use them as an operatorial basis on the lattice. Many local, single-particle, thermodynamical and response properties have been studied as functions of the external parameters and compared between the two models and with some numerical and exact results. It has been shown that the 2-site Hubbard model already contains the most relevant energy scales of the Hubbard model: the local Coulomb interaction U and the spin-exchange one . As a consequence of this, for some relevant properties (kinetic energy, double occupancy, energy, specific heat and entropy) and as regards the metal-insulator transition issue, it has resulted possible to almost exactly mime the behavior of larger systems, sometimes using a higher temperature to get a comparable level spacing. The 2-site models have been also used as toy models to test the efficiency of the Greens function formalism for composite operators. The capability to reproduce the exact solutions, obtained by the exact diagonalization technique, gives a firm ground to the approximate treatments based on this formalism.Received: 16 July 2003, Published online: 30 January 2004PACS: 71.10.-w Theories and models of many-electron systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.)     

Application of large deviation theory to the mean-field $\boldsymbol{\varphi}^\mathsf{4}$-model

A large deviation technique is used to calculate the microcanonical entropy function s(v,m) of the mean-field ϕ⁴-model as a function of the potential energy v and the magnetization m. As in the canonical ensemble, a continuous phase transition is found. An analytical expression is obtained for the critical energy v_c(J) as a function of the coupling parameter J.     

\Lambda, \bar{\Lambda} polarization and spin transfer in lepton deep-inelastic scattering

The flavor and helicity distributions of the and hyperons for both valence and sea quarks are calculated in a perturbative QCD (pQCD) based model. We relate these quark distributions to the fragmentation functions of and , and calculate the z-dependence of the longitudinal spin transfer to and in lepton deep-inelastic scattering (DIS). It is shown that the spin transfer to the is compatible with the first HERMES results at DESY, and further tests are suggested. We also make predictions for the z-dependence of the and longitudinal polarizations in neutrino (antineutrino) DIS processes. We investigate the sea contribution to the fragmentation functions, and we test a possible scenario where the sea quarks in (or the sea antiquarks in ) are negatively polarized, whereas the sea antiquarks in the (or the sea quarks in ) are positively polarized. The asymmetry of the polarized fragmentation functions of the sea quarks and antiquarks to and provides a way to understand the different behavior between the and spin transfers observed in the recent E665 experiment at FNAL. Received: 5 April 2000 / Published online: 26 July 2000     

Self-focusing effects in a nematic liquid crystal at 10.6 $\mathsf{\mu}$m

E7 is a room temperature nematic liquid crystal that presents both a high temperature nematic-to-isotropic transition and a high positive dielectric anisotropy. The optical characteristics of this liquid crystal have been widely investigated in the visible region of the spectrum, while less experiments have been performed in the middle infrared spectral region, where, nevertheless, potential applications are important. We investigate the self-focusing of a middle infrared laser beam when it passes through a film of E7. We also take into account the heating of the liquid crystal film caused by the partial absorption of the laser light by means of a thermographic technique. A theoretical interpretation of the self-focusing phenomenon is given in terms of the reorientation of the molecules with respect to their unperturbed direction and an estimation of the average value of the elastic constants of the liquid crystal is given by fitting the experimental data with the theoretical model.Received: 16 April 2003PACS: 42.70.Df Liquid crystals - 42.65.-k Nonlinear optics - 42.55.Lt Gas lasers including excimer and metal-vapor lasers     

On PPT States in ${\cal C}^K \otimes {\cal C}^M\otimes {\cal C}^N$ Composite Quantum Systems

We study the general representations of positive partial transpose (PPT) states in ${\cal C}^K \otimes {\cal C}^M \otimes {\cal C}^N$. For the PPT states with rank-N a canonical form is obtained, from which a sufficient separability condition is presented.     

Gain-assisted giant Kerr nonlinearity in a ${\sf \Lambda}$-type system with two-folded lower levels

We propose a four-level Λ scheme with a one-mode active Raman gain core and two-folded lower levels to obtain new linear and nonlinear optical responses. We show that this scheme is fundamentally different from that based on electromagnetically induced transparency (EIT). Firstly, it is gain-assisted and thus capable of eliminating all attenuation of probe field. Furthermore, due to the quantum interference effect introduced by a coupling field a gain doublet appears in gain spectrum, and hence the distortion of the probe field during propagation can be effectively avoided. In addition, in such system a large and rapidly responding Kerr nonlinearity can be produced, which is much (more than 10 times) larger than that obtained in the EIT-based scheme with the same energy-level configuration.     

A statistical mechanics model of isotropic turbulence well-defined within the context of the $\mathsf{\epsilon}$ expansion

A statistical mechanics model of isotropic turbulence that renormalizes the effects of turbulent stresses into a velocity-gradient-dependent random force term is introduced. The model is well-defined within the context of the renormalization group expansion, as the effective expansion parameter is . The Kolmogorov constant and N parameter of turbulence are of order unity, in accord with experimental results. Nontrivial intermittency corrections to the single-time structure functions are calculated as a controlled expansion in .Received: 20 December 2002, Published online: 23 July 2003PACS:   47.27.Ak Fundamentals - 47.27.Gs Isotropic turbulence; homogeneous turbulence - 05.10.Cc Renormalization group methods     

Longitudinal $\bar{\Lambda}_0$ polarization in heavy-ion collisions as a probe for QGP formation

We present an analysis of the longitudinal polarization in ultrarelativistic heavy-ion collisions. The polarization of s coming from the decay chain exhibits a very well differentiated behavior depending on the production region of the primordial s. This effect reflects the different values of the ratio in the QGP region, where nucleon-nucleon interactions take place in a hot and dense environment, and the peripherical region, in which ordinary nucleon-nucleon interactions occur. An increase in the longitudinal polarization signals a strangeness enhancement which is thought of as a property of the QGP phase.Received: 21 September 2004, Revised: 25 October 2004, Published online: 17 December 2004