Wilson fermions on the lattice—A study of the eigenvalue spectrum

We have studied the eigenvalues of the Wilson fermion matrix on various lattice sizes and for a range of coupling constants, β, in the quenched approximation. The implications for the phase structure of lattice QCD in the presence of Wilson fermions are discussed.     

A note on γ traces for the Wilson action in the continuum limit

In d=4 and d=2 dimensions we calculate averages of certain products of matrices with respect to closed lattice paths of length L. The approach to the asymptotic behaviour for large L is considered and found to be quite different in d=4 and d=2 dimensions.Institute für Theoretische Physik der Universität Hamburg, F.R.G.     

Some remarks on variable range hopping—in particular in the quantum Hall regime

An expression for the heat conductivity _xx is derived in the effective medium approximation. Mott type formulas are obtained for _xx and the Peltier coefficient _xx . Using percolation theory in a three-dimensional system the Wiedemann-Franz ratio was found to depend on the temperature like . The Mott type formulas were evaluated in a similar way for a two-dimensional system in the quantum Hall regime within the high-field percolation model. In contrast to previous calculations of the high field hopping conductivity _xx , the results are fully consistent with the experimental data on _xx and the density of states at the Fermi level. Finally, _xx is estimated which together with _xx and _xy =ie ²/h(i=0,1,2,...), determines both thermopower coefficients _xx and _xy .Dedicated to Professor W. Brenig on the occasion of his 60th birthday     

Effect of spin fluctuations on the superconducting phase of Hubbard fermions in the t-t′-t″-J* model

The effect of spin-fluctuation scattering processes on the region of the superconducting phase in strongly correlated electrons (Hubbard fermions) is investigated by the diagram technique for Hubbard operators. Modified Gor’kov equations in the form of an infinitely large system of integral equations are derived taking into account contributions of anomalous components $ P_{0\sigma ,\bar \sigma 0} The effect of spin-fluctuation scattering processes on the region of the superconducting phase in strongly correlated electrons (Hubbard fermions) is investigated by the diagram technique for Hubbard operators. Modified Gor’kov equations in the form of an infinitely large system of integral equations are derived taking into account contributions of anomalous components of strength operator . It is shown that spinfluctuation scattering processes in the one-loop approximation for the t-t′-t″-J* model taking into account long-range hoppings and three-center interactions are reflected by normal (P _{0σ, 0σ}) and anomalous () components of the strength operator. Three-center interactions result in different renormalizations of the kernels of the integral equations for the superconducting d phase in the expressions for the self-energy and strength operators. In this approximation for the d-type symmetry of the order parameter for the superconducting phase, the system of integral equations is reduced to a system of nonhomogeneous equations for amplitudes. The resultant dependences of critical temperature on the electron concentrations show that joint effect of long-range hoppings, three-center interactions, and spin-fluctuation processes leads to strong renormalization of the superconducting phase region. Original Russian Text ? V.V. Val’kov, A.A. Golovnya, 2008, published in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2008, Vol. 134, No. 6, pp. 1167–1180.     

Crumpled-to-tubule transition in anisotropic polymerized membranes: beyond the ϵ expansion

Anisotropic D-dimensional polymerized phantom membranes are investigated within a nonperturbative renormalization group framework. One focuses on the transition between a high-temperature, crumpled phase and a low-temperature, tubular phase where the membrane is flat along one direction and crumpled along the other ones. While the upper critical dimension--D(uc)=5/2--is close to D=2, the weak-coupling perturbative approach is qualitatively and quantitatively wrong. We show that our approach is free of the problems encountered within the perturbative framework and provides physically meaningful critical quantities.     

Effects of a rectangular aperture on the vectorial structure of a Gaussian beam in the far-field regime

With the help of the angular spectrum representation and the Gaussian function expansions of the hard-edge aperture function, the vectorial structure of a linearly polarized Gaussian beam (GB) diffracted by a rectangular aperture is analyzed in detail. It is found that the sizes of the energy flux density spots and the energy fluxes of the TE and TM terms depend on the aperture configuration and the polarization direction of the incident GB. The far fields may have smaller spots and larger energy fluxes for a GB diffracted by a rectangular aperture compared to that by a square aperture with the same beam intensity. And another potential application in information encoding and transmission for free-space communications is also proposed in addition to re-focusing to enhance the optical storage density. This encoding scheme has the benefit of easy implementation without modulating any properties of the light source.     

Pressure effects on Dirac fermions in α-(BEDT-TTF)?I?

We investigate the pressure effect on the layered Dirac fermion system, which is realized in quasi-two-dimensional organic compound α-(BEDT-TTF)?I?. The trajectory of the contact points is investigated using the tight-binding model with the transfer integrals determined by x-ray diffraction experiments. Vanishing of the Dirac fermion spectrum, opening of the gap, and pressure dependence of interlayer magnetoresistance are discussed.     

Exploration of the Townsend regime by discharge light emission in a gas discharge deviceExploration of the Townsend regime by discharge light emission in a gas discharge deviceExploration of the Townsend regime by discharge light emission in a gas discharge deviceExploration of the Townsend regime by discharge light emission in a gas discharge deviceExploration of the Townsend regime by discharge light emission in a gas discharge device

The Townsend discharge mechanism has been explored in a planar microelectronic gas discharge device （MGDD） with different applied voltages U and interelectrode distance d under various pressures in air. The anode and the cathode of the MGDD are formed by a transparent SnO2 covered glass and a GaAs semiconductor, respectively. In the experiments, the discharge is found to be unstable just below the breakdown voltage Ub, whereas the discharge passes through a homo- geneous stable Townsend mode beyond the breakdown voltage. The measurements are made by an electrical circuit and a CCD camera by recording the currents and light emission （LE） intensities. The intensity profiles, which are converted from the 3D light emission images along the semiconductor diameter, have been analysed for different system parameters. Dif- ferent instantaneous conductivity ~t regimes are found below and beyond the Townsend region. These regimes govern the current and spatio-temporal LE stabilities in the plasma system. It has been proven that the stable LE region increases up to 550 Torr as a function of pressure for small d. If the active area of the semiconductor becomes larger and the interlectrode distance d becomes smaller, the stable LE region stays nearly constant with pressure.     

Anisotropic conductance of Pb–induced chain structures on Si(557) in the monolayer regime

We present data of a study of four-point conductance of adsorbed Pb films on Si(557) in the thickness range between 0.6 up to several monolayers (ML) at various annealing stages. These measurements are combined with tunneling microscopy (STM). Onset of conductance is found close to the percolation limit. Pb layers annealed to room temperature are characterized by activated contributions to conductance up to 3 ML, a purely metallic temperature dependence at thicker layers, and an anisotropy of at most a factor of 2. On the contrary, annealing to 640 K, leaving only the first monolayer on the Si(557) surface results in extremely high surface state conductance which is quasi one–dimensional below a critical temperature of Tc=78 K, associated with an order–disorder phase transition. Induced by a 10-fold superperiodicity along the Pb chains and their lateral ordering, the system switches from low to high conductance anisotropy, with a metal–insulator transition in the direction perpendicular to the chain structure, while in the direction along the chains conductance with a 1/T + const. temperature dependence was found.     

A practical second-order electromagnetic model in the quasi-specular regime based on the curvature of a ‘good-conducting’ scattering surface

Abstract

This letter presents an approximate second-order electromagnetic model where polarization coefficients are surface dependent up to the curvature order in the quasi-specular regime. The scattering surface is considered ‘good-conducting’ as opposed to the case for our previous derivation where perfect conductivity was assumed. The model reproduces dynamically, depending on the properties of the scattering surface, the tangent-plane (Kirchhoff) or the first-order small-perturbation (Bragg) limits. The convergence is assumed to be ensured by the surface curvature alone. This second-order model is shown to be consistent with the small-slope approximation of Voronovich (SSA-1+SSA-2) for perfectly conducting surfaces. Our model differs from SSA-1 + SSA-2 in its dielectric expression, to correct for a full convergence toward the tangent-plane limit under the ‘good-conducting’ approximation. This new second-order formulation is simple because it involves a single integral over the scattering surface and therefore it is suitable for a vast array of analytical and numerical applications in quasi-specular applications.     

Analytic approach to the MSSM mass spectrum in the large tan β regime

In various unified extensions of the Minimal Supersymmetric Standard Model, the Yukawa couplings of the third generation are predicted to be of the same order. As a result, low energy measured mass ratios require large ratios of the standard model Higgs vacuum expectation values, corresponding to a large value of the parameter tan β. We present analytic solutions for the Yukawa couplings and the Higgs and third generation squark masses, in the case of large top and bottom Yukawa couplings. We examine regions of these Yukawas which give predictions for the top mass compatible with the present experimentally determined top mass and provide useful approximate formulae for the scalars. We discuss the implications on the radiative symmetry breaking mechanism and derive constraints on the undetermined initial conditions of the scalars.     

Quartic oscillator potential in the γ-rigid regime of the collective geometrical model

A prolate γ-rigid version of the Bohr-Mottelson Hamiltonian with a quartic anharmonic oscillator potential in β collective shape variable is used to describe the spectra for a variety of vibrational-like nuclei. Speculating the exact separation between the two Euler angles and the β variable, one arrives at a differential Schrödinger equation with a quartic anharmonic oscillator potential and a centrifugal-like barrier. The corresponding eigenvalue is approximated by an analytical formula depending only on a single parameter up to an overall scaling factor. The applicability of the model is discussed in connection to the existence interval of the free parameter, which is limited by the accuracy of the approximation, and by comparison with the predictions of the related X(3) and X(3)-β ² models. The model is applied to qualitatively describe the spectra for nine nuclei which exhibit near-vibrational features.     

Exotic fermions in Kadyshevsky’s theory and the possibility to detect them

As it is known, the principal research interest of V.G. Kadyshevsky was the development of a geometric approach to quantum field theory with a constraint imposed on the mass spectrum of elementary particles. Non-Hermitian operators arising in this case seemed to be a major obstacle to the development of a consistent theory. These issues have been resolved recently, and the introduction of the pseudo-Hermitian algebraic approach to the construction of quantum theory was a major advance in this physical research. The central point of such theories is the construction of PT-symmetric non-Hermitian Hamiltonians with real eigenvalues. It is important to note that both purely theoretical and experimental studies (e.g., in non-Hermitian optics) are found among the many published papers on this subject. Therefore, we believe that the development of pseudo-Hermitian relativistic quantum theory with a maximal mass may provide favorable opportunities to discuss the possible experimental verification of theoretical results obtained in this field. Kadyshevsky himself regarded the hypothesis of existence of new particles, which he called exotic fermions, as an important prediction of his theory. The possibility of discovery of exotic neutrinos in precision experiments on the determination of the neutrino mass is discussed in the present study.     

Implication of Tsallis entropy in the Thomas–Fermi model for self-gravitating fermions

The Thomas–Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the q$q$-statistics  . Starting from the q$q$-deformation of the Fermi–Dirac distribution function, a generalized Thomas–Fermi equation is derived. It is shown that the Tsallis entropy   preserves a scaling property of this equation. The q$q$-statistical   approach to Jeans’ instability in a system of self-gravitating fermions is also addressed. The dependence of the Jeans’ wavenumber (or the Jeans length) on the parameter q$q$ is traced. It is found that the q$q$-statistics makes the Fermionic system unstable at scales shorter than the standard Jeans length.     

Superintegrability in Two Dimensions and the Racah–Wilson Algebra

The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere is cast in the framework of the Racah problem for the \({\mathfrak{su}(1,1)}\) algebra. The Hamiltonian of the 3-parameter system and the generators of its quadratic symmetry algebra are seen to correspond to the total and intermediate Casimir operators of the combination of three \({\mathfrak{su}(1,1)}\) algebras, respectively. The construction makes explicit the isomorphism between the Racah–Wilson algebra, which is the fundamental algebraic structure behind the Racah problem for \({\mathfrak{su}(1, 1)}\) , and the invariance algebra of the generic 3-parameter system. It also provides an explanation for the occurrence of the Racah polynomials as overlap coefficients in this context. The irreducible representations of the Racah–Wilson algebra are reviewed as well as their connection with the Askey scheme of classical orthogonal polynomials.     

Thermoelectric properties of the interacting two dimensional electron gas in the diffusion regime?

We demonstrate that kinetic coefficients related to thermoelectric properties of the two dimensional electron gas in the diffusive regime are strongly influenced by electron-electron interaction. As an example we consider the thermoelectric coefficients of the diluted two-dimensional electron gas in Si(100) MOSFET’s in the presence of charged-impurity scattering. We find that the screening anomaly at q = 2k _F, also responsible for Friedel oscillations, leads at low electron densities to a large change in the thermoelectric coefficient for the thermopower.     

“Volume trapping” of protons in the channeling regime in a bent crystal

A computer analysis of the “volume trapping” effect for 1 GeV protons in the planar channeling regime in a bent Si crystal has been performed. The dependences of the trapping efficiency on the beam incidence angle and the bending radius of the crystal have been obtained.