Progress in lattice gauge theory

Two topics of lattice gauge theory are reviewed. They include string tension and β-function calculations by strong coupling Hamiltonian methods for SU(3) gauge fields in 3 + 1 dimensions, and a 1/N-expansion for discrete gauge and spin systems in all dimensions. The SU(3) calculations give solid evidence for the coexistence of quark confinement and asymptotic freedom in the renormalized continuum limit of the lattice theory. The crossover between weak and strong coupling behavior in the theory is seen to be a weak coupling but non-perturbative effect. Quantitative relationships between perturbative and non-perturbative renormalization schemes are obtained for the O(N) nonlinear sigma models in 1 + 1 dimensions as well as the range theory in 3 + 1 dimensions. Analysis of the strong coupling expansion of the β-function for gauge fields suggests that it has cuts in the complex 1/g²-plane. A toy model of such a cut structure which naturally explains the abruptness of the theory's crossover from weak to strong coupling is presented. The relation of these cuts to other approaches to gauge field dynamics is discussed briefly.The dynamics underlying first order phase transitions in a wide class of lattice gauge theories is exposed by considering a class of models-P(N) gauge theories - which are soluble in the N → ∞ limit and have non-trivial phase diagrams. The first order character of the phase transitions in Potts spin systems for N #62; 4 in 1 + 1 dimensions is explained in simple terms which generalizes to P(N) gauge systems in higher dimensions. The phase diagram of Ising lattice gauge theory coupled to matter fields is obtained in a $\text{1}\text{N}$ expansion. A one-plaquette model (1 time-0 space dimensions) with a first-order phase transitions in the N → ∞ limit is discussed.     

Minimum of oscillator strength of excitons in ultra-narrow GaAs/AlGaAs quantum wells:: Theory and experiment

A theoretical and experimental study of the exciton in ultra-narrow quantum wells (QWs) is performed. A crossover from strong (separate localization of electron and hole levels) to weak confinement (with localization of excitonic center of mass) is predicted to occur for decreasing thickness, and is characterized by a minimum of the oscillator strength per unit area. Cathodoluminescence measurements performed on a series of GaAs/Al_0.35Ga_0.65As QWs with thicknesses from one to eight monolayers show a minimum of the oscillator strength, in agreement with theory, and indicate that the crossover from strong to weak confinement occurs at a thickness of about three monolayers for this composition.     

Signals of confinement in Green functions of SU(2) Yang-Mills theory

It has been well established that the removal of center vortices from SU(2) lattice configurations results in the loss of confinement. The running coupling constant, gluon form factor, and ghost form factor are studied in the Landau gauge for the full and the vortex removed theory. In the latter case, a strong suppression of the running coupling constant and the gluon form factor at low momenta is observed, and the IR singularity of the ghost form factor disappears. Hence, the removal of the vortices generates a theory for which Zwanziger's horizon condition for confinement is no longer satisfied.     

Signature of a type-a glass transition and intrinsic confinement effects in a binary glass-forming system

We study dynamically highly asymmetric binary mixtures comprised of small methyl tetrahydrofuran (MTHF) molecules and polystyrene. Combined use of dielectric spectroscopy, ^{2}H nuclear magnetic resonance, incoherent quasielastic neutron scattering, and depolarized dynamic light scattering allows us to selectively probe the dynamics of the components in a broad dynamic range. It turns out that the mixtures exhibit two glass transitions in a wide concentration range although being fully miscible on a macroscopic scale. In between both glass transition temperatures, the dynamics of the small molecules show strong confinement effects, e.g., a crossover from Vogel-Fulcher to Arrhenius behavior of the time constants. Moreover, the dynamical behavior of small molecules close to the slow matrix is consistent with mode coupling theory predictions for a type-A glass transition, which was expected from recent theoretical and simulation studies in comparable systems.     

Asymptotically free SU(2) × SU(2) × SU(4) model of unified interaction

An asymptotically free SU(2) × SU(2) × SU(4) model of unified interaction is constructed. The gauge coupling constants are taken equal (in the order of magnitude) to the electromagnetic one. The strong interaction and the quark confinement is provided for by a gluonic mechanism. Some physical consequence of the model are briefly discussed.     

高频ECR离子源的最新进展

As they are first optimized for their ion losses,ECRISs are always under a fundamental compromise: having high losses and strong confinement at the same time.To help ECR ion source developers in the design or improvement of existing machines,general comments are presented in a review article being soon published. In this 160 pages contribution,fundamental aspects of ECRISs are presented,with a discussion of electron temperature and confinement and ion confinement.Then,as microwaves play a key role in these machines, a chapter presents major guidelines for microwave launching and coupling to ECR plasma.Moreover,once ECR plasma is created,understanding this plasma is important in ion sourcery;and a section is dedicated to plasma diagnostics with an emphasis on the determination of electron and ion density and temperature by vacuum ultraviolet(VUV)spectroscopy.Another chapter deals with the role of magnetic confinement and presents updated scaling laws.Next chapter presents different types of ECRISs designed according to the main parameters previously described.Finally,some industrial applications of ECRISs and ECR plasmas in general are presented like ion implantation and photon lithography.Some hints taken from this review article are presented in the following article.     

The classical Yang-Mills field of a quark source

The Coulomb solution of the classical Yang-Mills equations with external source is unstable for sufficiently strong coupling constant. We show that the Yang-Mills system has no other physically static, spherically symmetric solution. Some consequences for the quark confinement problem in non-abelian gauge theories are pointed out.     

Statistical theory of a quantum emitter strongly coupled to Anderson-localized modes

A statistical theory of the coupling between a quantum emitter and Anderson-localized cavity modes is presented based on a dyadic Green's function formalism. The probability of achieving the strong light-matter coupling regime is extracted for an experimentally realistic system composed of InAs quantum dots embedded in a disordered photonic crystal waveguide. We demonstrate that by engineering the relevant parameters that define the quality of light confinement, i.e., the light localization length and the loss length, strong coupling between a single quantum dot and an Anderson-localized cavity is within experimental reach. As a consequence, confining light by disorder provides a novel platform for quantum electrodynamics experiments.     

Strong coupling expansions for the mass gap in lattice gauge theories

We derive strong coupling expansions for the mass gap in euclidean lattice gauge theories in any space-time dimension. For gauge groups SU(2), SU(3), Z₂ and Z₃ the series are calculated up to order g^?16. They are used to get rough estimates for the lowest glueball mass in continuum SU(2) and SU(3) gauge theories, assuming a sudden crossover from strong to weak coupling behaviour in the lattice theory.     

Phase structure of QCD at high temperature with massive quarks and finite quark density: A Z(3) paradigm

The confinement/deconfinement phase transition in SU(3) lattice gauge theories at high temperatures is analogous to that of the Z(3) gauge theories. We study various Z(3) gauge-matter theories that result from replacing the gauge group SU(3) with its center Z(3). We include large-mass fermions in the Wilson formulation and allow a chemical potential. We show that in the limit of strong coupling and high temperature the (3 + 1)-dimensional theory becomes a three state, three-dimensional Potts model with uniform external fields of real and imaginary strengths related to the fermion mass and chemical potential. By studying the phase structure of the q = 3, d = 3 Potts model with external fields we argue that the confinement/deconfinement phase transition is first order, but highly sensitive to external fields, and that it does not occur at “strong coupling” in a Z(3) gauge theory if there is a light enough fermion present. We discuss the consequences of this result for QCD.     

Unusual thermodynamical and transport signatures of the BCS to bose-einstein crossover scenario below T(c)

In this paper we present predictions for thermodynamic and transport properties of a BCS to Bose-Einstein crossover theory, below T(c), which satisfies the reasonable constraints that it yields (i) the Leggett ground state and (ii) BCS theory at weak coupling and all temperatures T. The nature of the strong coupling limit is inferred, along with the behavior of the Knight shift, superfluid density, and specific heat. Comparisons with existing data on short coherence length superconductors, such as organic and high T(c) systems, are presented, which provide some support for the present picture.     

On the determination of the particle interaction potential in a dusty plasma from a pair correlation function

The effect of confinement on the pair correlation function of microparticles whose interaction is described by a screened Coulomb potential (Yukawa potential) has been investigated by the molecular dynamics simulations. The data are used to solve the inverse problem of the reconstruction of the particle interaction potential. It has been shown that such a reconstruction is likely impossible for a strongly nonideal system (with the coupling parameter Γ > 1). For systems with Γ ≤ 1, reconstruction is possible if confinement does not lead to the strong inhomogeneity of the system of microparticles.     

A phenomenological description of an incoherent Fermi liquid near optimal doping in high Tc cuprates

Marginal Fermi-liquid physics near optimal doping in high T(c) cuprates has been explained within two competing scenarios such as the spin-fluctuation theory based on an itinerant picture and the slave-particle approach based on a localized picture. In this study we propose an alternative scenario for the anomalous transport within the context of the slave-particle approach. Although the marginal Fermi-liquid phenomenology was interpreted previously within deconfinement of the compact gauge theory, referred to as the strange metal phase, we start from confinement, introducing the Polyakov loop parameter into an SU(2) gauge theory formulation of the t-J model. The Polyakov loop parameter gives rise to incoherent electrons through the confinement of spinons and holons, which result from huge imaginary parts of self-energy corrections for spinons and holons. This confinement scenario serves a novel mechanism for the marginal Fermi-liquid transport in the respect that the scattering source has nothing to do with symmetry breaking. Furthermore, the incoherent Fermi-liquid state evolves into the Fermi-liquid phase through crossover instead of an artificial second-order transition as temperature is lowered, where the crossover phenomenon does not result from the Anderson-Higgs mechanism but originates from an energy scale in the holon sector. We fit experimental data for the electrical resistivity around the optimal doping and find a reasonable match between our theory and the experiment.     

抛物量子点中极化子的温度依赖性

根据Pekar类型变分法在电子与声子强耦合的条件下计算了抛物量子点中强耦合极化子的基态能量.讨论了电子-声子耦合强度,量子点受限长度对基态能量的影响,同时引进温度参数并讨论了其对基态能量的影响,结果得出在低温的条件下,耦合强度和受限长度对基态的能量影响起主要作用;在高温的条件下,温度对基态的能量影响起主要作用,而耦合强度与受限长度的影响很小.     

Density-functional theory of inhomogeneous electron systems in thin quantum wires

Motivated by current interest in strongly correlated quasi-one-dimensional (1D) Luttinger liquids subject to axial confinement, we present a novel density-functional study of few-electron systems confined by power-low external potentials inside a short portion of a thin quantum wire. The theory employs the 1D homogeneous Coulomb liquid as the reference system for a Kohn-Sham treatment and transfers the Luttinger ground-state correlations to the inhomogeneous electron system by means of a suitable local-density approximation (LDA) to the exchange-correlation energy functional. We show that such 1D-adapted LDA is appropriate for fluid-like states at weak coupling, but fails to account for the transition to a “Wigner molecules” regime of electron localization as observed in thin quantum wires at very strong coupling. A detailed analyzes is given for the two-electron problem under axial harmonic confinement.     

Analysis of coupling in the semi-cylindrical surface plasmonic couplers

In this paper, we have investigated the performance of a nano-optical directional coupler based on gap plasmon waveguides. The coupler consists of two waveguides having a localized coupled plasmon propagating between two semi-cylindrical surfaces. It is clear that the wave number and correspondingly light confinement in the waveguides are the most effective parameters in coupling strength and coupling length. Some expected and unexpected dependencies of the coupling length on the structure parameters are shown. Simulation results of the coupler obtained by the compact-2D finite-difference time-domain (FDTD) method comply with those derived by an analytic method with the aid of the finite-element frequency-domain (FEFD) software package of COMSOL. The considered structures, because of their small coupling length and dimensions are appropriate for use in optical integrated circuits.     

SU(4) Fermi liquid state and spin filtering in a double quantum dot system

We study a symmetrical double quantum dot (DD) system with strong capacitive interdot coupling using renormalization group methods. The dots are attached to separate leads, and there can be a weak tunneling between them. In the regime where there is a single electron on the DD the low-energy behavior is characterized by an SU(4)-symmetric Fermi liquid theory with entangled spin and charge Kondo correlations and a phase shift pi/4. Application of an external magnetic field gives rise to a large magnetoconductance and a crossover to a purely charge Kondo state in the charge sector with SU(2) symmetry. In a four-lead setup we find perfectly spin-polarized transmission.     

Lattice Yang-Mills theory at nonzero temperature and the confinement problem

We discuss finite temperature lattice Yang-Mills theory with special attention to the confinement problem. The relationship between the confinement criteria of Wilson, Polyakov, and 't Hooft is clarified by establishing a string of inequalities between the corresponding string tensions. The close connection between finite temperature Yang-Mills models and spin models is exploited to obtain new and rather sharp upper bounds for the critical coupling constant above which there is confinement. This same analogy also allows us to establish infrared bounds for the gauge models that yield a lower bound for this critical coupling and thereby show the existence of a weak coupling regime without confinement at nonzero temperature in three or more space dimensions. Finally we discuss extension of our results to other forms of the lattice action, the Hamiltonian lattice models of Kogut and Susskind and 't Hooft'sN → ∞ limit.     

Examining the crossover from the hadronic to partonic phase in QCD

A mechanism, consistent with color confinement, for the transition between perturbative and physical vacua during the gradual crossover from the hadronic to partonic phase is proposed. The essence of this mechanism is the appearance and growing up of a kind of grape-shape perturbative vacuum inside the physical one. A percolation model based on simple dynamics for parton delocalization is constructed to exhibit this mechanism. The crossover from hadronic matter to sQGP (strongly coupled quark-gluon plasma) as well as the transition from sQGP to weakly coupled quark-gluon plasma with increasing temperature is successfully described by using this model.