THE VARIATIONAL CALCULATION OF MASS GAP IN 2+1 DIMENSIONAL SU(2) LGT

A variational calculation of the mass gap in 2+1 dimensional SU(2) lattice gauge theory by using a Hamiltonian which possesses exact ground state and correct continuum limit is made.In the range 1.3≤1/g²≤7,a good scaling behaviour am=2.28g² is obtained,which is in agreement with weak-coupling perturbation theory and the results obtained by another Hamiltonian which does not possess correct continuum limit.     

A strong-coupling expansion for fermion field theories and the large-N limit of the gross-neveu model

An expansion in the fermion propagator is formulated for the N-species Gross-Neveu model in the large-N limit. Different regularisation schemes may be adopted and we compare two. We find that a continuum momentum cut-off is easiest to work with and automatically avoids spurious fermionic states which afflict a naive lattice formulation. Chiral symmetry is broken at zeroth order and the resulting expansion is inverse powers of g²N simplifies considerably for large N. In this limit the strong-coupling expansion may be summed to all orders. Extrapolation techniques, like Padé approximants, are not needed. Using a momentum cut-off we recover all the exact results previously derived by summing weak-coupling expansions.     

Caustics in a simpleSU(2) lattice gauge theory model

This paper describes the beginning of an attempt to study the weak coupling limit of lattice gauge theories, using the Hamiltonian formulation and the semiclassical approximation. The topics are caustics and the behavior of the ground state wave function in the vicinity of caustics. For two very simpleSU(2) models (one plaquette, two plaquettes) we demonstrate the existence of caustics, determine their locations and study the peaking behavior of the ground state wave function on them in the limitg ²→0.     

Plaquette expansion study of compact U(1) lattice gauge theory in (2 + 1) dimensions

The plaquette expansion is applied to compact U(1) lattice gauge theory in (2 + 1) dimensions to high order: 1/N ⁸ for the ground state energy density and 1/N ⁷ for the anti-symmetric or photon mass gap, where N is defined as the number of plaquettes. Evidence of scaling in the photon mass gap is observed for low order (≤ 1/N ⁴) for inverse coupling values β = 0. 7 to 1. 25 with scaling behaviour given by the weak-coupling formula: M ²/β = exp(-5. 01β + 5. 82) in good agreement with other studies. Higher order results appear to diverge from the scaling slope past the transition point portenting the prospect that the strong coupling trial state in this region gives vise to an asymtotic series in 1/N for the photon mass gap.     

(p,t) Reactions on odd-a nuclei and the weak-coupling core-excitation model

Excited $\text{7}\text{2}{}^{\mathrm{?}}$ states to which enhanced L = 0 (p, t) transitions are observed have been identified in ⁴¹Ca at 2958 keV and in ⁵⁷Co at 2611 keV. A comparison of these (p, t) transitions with those to the 0⁺ states in ⁴⁰Ca at 3353 keV and in ⁵⁸Ni at 2940 keV leads to the conclusion that these states are obtained by weak-coupling of a $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ particle and hole, respectively, to the excited 0⁺ states of the doubly even cores. It is suggested that these cases are examples of a rather general weak-coupling phenomenon.     

Calculation of the glueball mass spectrum ofSU (2) andSU (3) non-abelian lattice gauge theories II:SU (3)

We calculate the glueball mass spectrum in theSU (3) lattice regularized gauge theory. We find fourlight glueballs: the 0⁺⁺, 2⁺⁺, 0^?+ and, most interestingly from the experimental point of view, the oddball 1^?+. We calculate the 0⁺⁺ and 2⁺⁺ masses over a range of β values and find thatboth states conform to continuum renormalization group behaviour to a very significant degree. The question of metastable states and temperature is addressed in detail. Finally we discuss and resolve contrary claims in the recent literature.     

SU(2) Lattice gauge theory in (2+1)D

Cluster expansion methods are applied to theSU(2) lattice gauge model in (2+1) dimensions. Strong-coupling series are calculated for the vacuum energy per site, the axial string tension, and the scalar mass gap; while ELCE approximants are used to estimate the string tension beyond its roughening transition. The simple scaling behaviour expected of this super-renormalizable theory is clearly seen, and we estimate that in the continuum limit the string tension σ～(0.14±0.01)g ⁴, while the mass gapM _s ～(2.2±0.25)g ². More accurate Monte Carlo simulations are needed to check the universality between the Hamiltonian and Euclidean versions of this model.     

Strings in the CP2N−1 model

The CP₂^N?1 model is discussed using strings as collective variables in the hamiltonian formulation. The large N limit is obtained as a semiclassical approximation. The mass gap and β-function are computed. In the limit N → ∞, it is shown that the singlet spectrum contains both bound states and scattering states whose energies and wave functions are calculated.     

THE MASS GAP IN 2+1 DIMENSIONAL SU(2) LATTICE GAUGE THEORY

A variational calculation of the mass gap in 2+1 dimensional SU(2) lattice gauge theory by using a Hamiltonian with the ground state being exactly known is made.In the range 0≤1/g²≤7,a good scaling behaviour am=2.28g² is obtained,which is in agreement with weak-coupling perturbation theory.     

Optical spectra of (CdF2)0.9(InF3)0.1 semiconductor solid solutions

The differences in the optical spectra of CdF₂:In semiconductors with bistable DX centers (concentrated (CdF₂)_0.9(InF₃)_0.1 solid solutions) and “standard” samples with a lower impurity concentration used to record holograms are discussed. In contrast to the standard samples, in which complete decay of two-electron DX states and transfer of electrons to shallow donor levels may occur at low temperatures, long-term irradiation of a (CdF₂)_0.9(InF₃)_0.1 solid solution by UV or visible light leads to decay of no more than 20% deep centers. The experimental data and estimates of the statistical distribution of electrons over energy levels in this crystal give the total electron concentration, neutral donor concentration, and concentration of deep two-electron centers to be ～5 × 10¹⁸ cm^?3, ～9 × 10¹⁷ cm^?3, and more than 1 × 10²⁰ cm^?3, respectively. These estimates show that the majority of impurity ions are located in clusters and can form only deep two-electron states in CdF₂ crystals with a high indium content. In this case, In³⁺ ions in a limited concentration (In³⁺ (～9 × 10¹⁷ cm^?3) are statistically distributed in the “unperturbed” CdF₂ lattice and, as in low-concentrated samples, form DX centers, which possess both shallow hydrogen-like and deep two-electron states.     

A field-theoretic study of the Regge-eikonal model. II

A previous study of the Regge-eikonal model in φ³ is extended to QED. First we define a reggeon amplitude that is built up by tower diagrams, and then study multiregge exchange by use of Gribov's reggeon calculus. The situation is essentially the same as in φ³: The eikonal approximation is the true high-energy and weak coupling limit (s → ∞, α ln s = fixed), but it breaks down outside of the weak-coupling limit. This confirms that the eikonal approximation as a model for Regge-cuts is not justifiable by field-theoretic arguments because of the neglect of inelastic intermediate states.     

Investigation the effect of lattice angle on the band structure in 3D phononic crystals with rhombohedral(II) lattice

In this paper, the propagation of acoustic waves in the phononic crystals (PC) of 3D with rhombohedral(II) lattice is studied theoretically. The PC are constituted of nickel spheres embedded in epoxy. The calculations of the band structure and density of states are performed with the plane wave expansion method in the irreducible part of the Brillouin zone (BZ). In this study, we analyze the dependence of the band structures inside (the complete band gap width) and outside the complete band gap (negative refraction of acoustic wave) on the lattice angle in the irreducible part of the first BZ. Also the effect of lattice angle has been analyzed on the band structure of the ( \( \bar{1}10 \) ) and (122) planes. Then, the equifrequency surface is calculated for the high symmetry point in the [111] and [100] directions. The results show that the maximum width of AEBG (0.022) in the irreducible part of the BZ of RHL2 is formed for (105^°) and no AEBG is found for γ > 150^°. Also, the maximum of the first and second AEBG width are 0.1076 and 0.0523 for γ = 133^° in the ( \( \bar{1}10 \) ) plane and the maximum of the first and second AEBG width are 0.1446 and 0.0998 for γ = 113^° in the (122) plane. In addition, we have found that frequencies in which negative refraction occurs is constant for all lattice angles.     

Electronic structure and lattice dynamics of Li2Ni(WO4)2

We combined spectroscopic ellipsometry and Raman scattering measurements to explore the electronic structure and lattice dynamics in Li₂Ni(WO₄)₂. The optical absorption spectrum of Li₂Ni(WO₄)₂ measured at room temperature presents a direct optical band gap at 2.25 eV and two bands near 5.2 and 6.0 eV, which are attributed to charge-transfer transitions from oxygen 2p states to nickel 3d or tungsten 5p states. The Raman scattering spectrum of Li₂Ni(WO₄)₂ measured at room temperature presents seventeen phonon modes at approximately 112, 143, 193, 222, 267, 283, 312, 352, 387, 418, 451, 476, 554, 617, 754, 792, and 914 cm⁻¹. When the temperature is decreased to 20 K, the frequency, linewidth, and normalized intensity of all phonon modes exhibited almost no temperature dependence. Upon cooling across 13 K, which is the antiferromagnetic phase transition temperature, the oxygen octahedra stretching mode at 914 cm⁻¹ exhibited a softening and an increase in intensity, thus suggesting a coupling between the magnetic and lattice degrees of freedom. The spin-phonon coupling constant was estimated to be 0.94 mRy/Ų, indicating a weak spin-phonon interaction in Li₂Ni(WO₄)₂.     

Proton structure functions in an infinite resonance O(4, 2) model

The proton electromagnetic inelastic structure functions have been explicitly evaluated in a noncompact O(4, 2) model for the spectrum of hadronic states, using the Barut-Corrigan-Kleinert infinite component wave equation. The resulting structure functions exhibit nontrivial scaling behavior in the Bjorken limit and give qualitative agreement with observation. They also satisfy exactly the Callan-Gross relation.     

The (p, 2p) reaction for slightly deformed nuclei

A perturbation approach for the calculation of (p, 2p) angular correlations for slightly deformed nuclei is developed using the formalism of the distorted wave t-matrix approximation (DWTA) in the static limit where approximations that incorporate absorption and focussing effects are used for the spin-orbit independent optical-model waves. Using a finite-range off-shell t-matrix that fits p-p scattering at 90° to approximate the p-p interaction inside the nucleus, a zero-order calculation is performed and normalized to ¹⁹F(p, 2p)¹⁸O angular correlation data at 42.7 MeV. A rms study is undertaken in order to parametrize the bound-state and the sensitivity of the shape of the angular correlation to the rms value is observed. The deformation of the bound-state is introduced using normalized perturbation theory and calculations with various values of the deformation parameter β for prolate and oblate deformations are performed and the results are compared. The shape of the (p, 2p) angular correlation is shown to be highly sensitive to the degree of deformation and is consistent with the shape dependence of the correlation to the rms value of the bound-state wave function.     

The thermodynamics of SU(3) lattice gauge theory with a light isodoublet of quarks

Using hybrid differential equations with stochastic pseudo-fermion fields, we simulated SU(3) lattice gauge theory with a light isodoublet of quarks on a 4 × 8³ lattice. The bare quark mass is 0.0125 in lattice units which corresponds to 7.75 MeV if the finite temperature chiral transition occurs at T_c=155 MeV as suggested by phenomenology. The transition is first order and metastable states are found over a narrow range in temperature. Results for 4⁴ lattices are also presented for 2 and 3 light flavors.     

Infrared conductivity from spin and charge density waves: (TMTSF) 2X

Infrared conductivity from an incommensurate spin density wave occurs due to even-order charge density wave harmonics which interact with the host lattice. Phonon states within the density-wave-induced energy gap for single-particle excitations lead to conductivity much different from that of an incommensurate charge density wave including counter-ion ordering. The conductivity expected for relaxed and quenched states of (TMTSF)₂ClO₄ is discussed.     

A study of the 84Kr(α, 2nγ)86Sr reaction

Decay properties of levels of ⁸⁶Sr populated by the 28 MeV ⁸⁴Kr(α, 2nγ) reaction have been studied by in-beam γ-ray spectroscopy. The observation of several new levels with $\text{J ≧ 6}$ allows a detailed comparison of the 2p-2n structures of ⁸⁶Sr with those of neighboring N = 48 nuclei. The results are discussed in terms of the weak-coupling model.     

A study of the nucleus 107Ag in the core-excitation model with the (p,t) and (τ, d) reactions

The ¹⁰⁷Ag residual nucleus was studied in the core-excitation model using the (p, t) and (τ, d) reactions. The L, J, π of levels between 0.0 and 2.25 MeV was deduced from the combined reactions. The octupole state observed at 2.19 MeV in other experiments was resolved in (p, t) into a triplet of states at 2.182, 2.203 and 2.229 MeV; octupole strength was observed in (p, t) over a range from 1.144 to 2.229 MeV. Core-excitation wave functions for the quadrupole 2⁺ and 2'⁺ vibration doublets of ¹⁰⁷Ag were constructed using electromagnetic data. These wave functions, combined with data from the ¹⁰⁸Pd(p, t) core reaction, effectively reproduced the ¹⁰⁹Ag(p, t) differential cross sections to these states. The ground-state L = 0 transfer in (p, t) to ¹⁰⁷Ag was only 0.752±0.113 as strong as the corresponding transfer to ¹⁰⁶pd. this is an unexpectedly large blocking effect for an unpaired proton to exert upon a neutron-transfer reaction. An apparent dependence of the (p, t) angular distributions to states of ¹⁰⁷Ag built upon the same core excitation was observed, depending upon the J of the final state.