Quark-antiquark potential in QCD

The potential energy of colour sources as a function of their separation is computed up to two loops; the renormalization group equations it satisfies are derived. This enable us to obtain β(g) to O(g⁵) and recover its known value. The solution of this Callan-Symanzik equation to O(g⁵) leads to a colour-confining potential. A qualitative argument is given to reject it as an artifact of the approximation used.     

Continuum limit improved lattice action for pure Yang-Mills theory (II)

Wilson loops are calculated to one-loop order using lattice actions including 6-link loops. The static potential is extracted and its small-a expansion performed using coefficients determined at tree level. The Λ-parameter for Symanzik's improved action is thereby obtained and constraints placed on the coefficients appearing in the action at order g².     

Wilson loops on 324 lattices and theSU(3) potential

Wilson loops are calculated on 32⁴ lattices in the coupling regime 6/g ²=6.3–6.9. Determination of the string tension from these loops with a method based on string model calculations shows a string tension that does not seem to scale. This is probably due to the amount of statistics. It points to difficulties in obtaining accurate physical results for coupling values above 6.6. Suggestions to improve this situation are made.     

A connection between ν-dimensional Yang-Mills theory and (ν−1)-dimensional,non-linear σ-models

We study non-linear σ-models and Yang-Mills theory. Yang-Mills theory on the ν-dimensional lattice ? ^v can be obtained as an integral of a product over all values of one coordinate of non-linear σ-models on ? ^v?1 in random external gauge fields. This exhibits two possible mechanisms for confinement of static quarks one of which is that clustering of certain two-point functions of those σ-models implies confinement of static quarks in the corresponding Yang-Mills theory. Clustering is proven for all one-dimensional σ-models, for theU(n) ×U(n) σ-models,n=1, 2, 3, ..., in two dimensions, and for the SU(2) × SU(2) σ-models for a large range of couplingsg ² ? O(ν). Arguments pertinent to the construction of the continuum limit are discussed. A representation of the expectation of Wilson loops in terms of expectations of random surfaces bounded by the loops is derived when the gauge group is SU(2),U(n) or O(n),n=1, 2, 3, ..., and connections to the theory of dual strings are sketched.     

Orientational effect of the dynamical interaction of circular dislocation loops with a moving edge dislocation

The glide of an edge dislocation in a crystal containing circular dislocation loops is studied theoretically. An analytical expression is obtained for the drag force exerted on a dislocation by various types of dislocation loops, and it is shown that this force depends significantly on the orientation of the Burgers vector of immobile dislocation loops with respect to the gliding dislocation line. The F _‖/F _⊥ ratio of the drag force for the parallel orientation of the Burgers vectors of the loops with respect to the gliding dislocation line (F _‖) and the drag force for the perpendicular orientation (F _⊥) is equal to K(v/c)², where v is the velocity of the dislocation; c is the velocity of acoustic waves in the crystal; and K is a dimensionless coefficient, whose value is of the order of the ratio of the concentrations of dislocation loops with parallel and perpendicular orientations of the Burgers vector.     

Conductance of finite systems and scaling in localization theory

The conductance of finite systems plays a central role in the scaling theory of localization (Abrahams et al., Phys. Rev. Lett. 42, 673 (1979)). Usually it is defined by the Landauer-type formulas, which remain open the following questions: (a) exclusion of the contact resistance in the many-channel case; (b) correspondence of the Landauer conductance with internal properties of the system; (c) relation with the diffusion coefficient D(??, q) of an infinite system. The answers to these questions are obtained below in the framework of two approaches: (1) self-consistent theory of localization by Vollhardt and Wölfle, and (2) quantum mechanical analysis based on the shell model. Both approaches lead to the same definition for the conductance of a finite system, closely related to the Thouless definition. In the framework of the self-consistent theory, the relations of finite-size scaling are derived and the Gell-Mann-Low functions ??(g) for space dimensions d = 1, 2, 3 are calculated. In contrast to the previous attempt by Vollhardt and Wölfle (1982), the metallic and localized phase are considered from the same standpoint, and the conductance of a finite system has no singularity at the critical point. In the 2D case, the expansion of ??(g) in 1/g coincides with results of the ??-model approach on the two-loop level and depends on the renormalization scheme in higher loops; the use of dimensional regularization for transition to dimension d = 2 + ?? looks incompatible with the physical essence of the problem. The results are compared with numerical and physical experiments. A situation in higher dimensions and the conditions for observation of the localization law ??(??) ?? ?i?? for conductivity are discussed.     

Effect of illumination on magnetization and microwave absorption of La1−xCaxMnO3 (x<0.2) films

Light-induced changes of the hysteresis loops of magnetization and microwave absorption are investigated in low-doped La_1−xCa_xMnO₃ (x<0.2) thin films. The width of the hysteresis loops decreases clearly under illumination with visible or near-infrared light at temperatures below 50 K. The microwave conductivity has a minimum value at magnetic fields corresponding to the magnetization reversal and is shifted towards weaker fields under illumination. These effects show complex nonexponential time evolution and dependence on strength of the magnetic field. The results can be explained by assuming that small ferromagnetic metallic regions exist within the insulating ferromagnetic phase of the sample, and that these regions are expanded by optically induced charge transfer between Jahn–Teller split e_g states of neighboring Mn³⁺ ions. Decrease of the Mn³⁺ XPS core level spectrum is observed in the samples under illumination with a HeNe laser.     

A nonperturbative solution to the Dyson-Schwinger-equations of QCD

This is the first of two papers in which we discuss a nonperturbatively modified solution to the Euclidean Dyson-Schwinger equations for the 7 superficially divergent proper verticesΓ of QCD. It takes the formΣ _n g ²ⁿ Γ( ⁿ ) where eachΓ( ⁿ ) approaches its perturbative form at large momenta. At lower momenta, it differs from that form by an additional non-analyticg ² dependence through a dynamical mass scaleb, proportional toΛ _qcd and associated with a pole dependence on the momentum invariants. In the zeroth-order two-point functions, these nonperturbative modifications amount to a generalized Schwinger mechanism, leading to propagators without particle poles. The termsΓ(⁰), representing the Feynman rules of the modified iterative solution, can become self-consistent in the DS equations through a mechanism of “nonperturbative logarithms” which we explain. The mechanism is tied to the presence of divergent loops, and thus represents a pure quantum effect, similar to quantum anomalies. It restricts formation of nonperturbativeΓ(⁰)'s to the 7 primitively divergent vertices, thus escaping the infinite nature of the DS hierarchy. In a given loop order, the self-consistency problem reduces to a finite set of algebraic equations.     

Minor magnetization loops in two-dimensional dipolar Ising model

The two-dimensional dipolar Ising model is investigated for the relaxation and dynamics of minor magnetization loops. Monte Carlo simulations show that in a stripe phase an exponential decrease can be found for the magnetization maxima of the loops, M∼exp(−αN_l) where N_l is the number of loops. We discuss the limits of this behavior and its relation to the equilibrium phase diagram of the model.     

Renormalization point invariance,twisted fans,and critical exponents at finite ϵ in the reggeon calculus.

A procedure for calculating critical exponents directly at finite ? is proposed. It relies on the invariance of the critical exponents at the critical coupling g^c of the full theory with respect to finite changes in the renormalization point. This is expressed as the coincidence of curves at the point β = 0 in the plane of β versus a critical exponent parametrically described by the renormalized coupling for various values of the renormalization point (the “twisted fan”). If more than one critical exponent is present the fan is a set of curves in a multidimensional space with the twist at β = 0 and the exact values of the critical exponents. In perturbative approximations, an approximate invariance may result whether or not a zero of β exists to that order. We show that in the one and two loop approximations to the Reggeon calculus this approximate invariance does occur. The values of the critical exponents at the approximate twists show remarkable stability properties. We obtain σ_tot ≈ (lns)^?γ where ?γ ≈ 0.11 and 0.17 for one and two loops respectively.     

Summing divergent perturbative series in a strong coupling limit. The Gell-Mann-Low function of the ϕ4 theory

An algorithm is proposed for determining asymptotics of the sum of a perturbative series in the strong coupling limit using given values of the expansion coefficients. Application of the algorithm is illustrated, methods for estimating errors are developed, and an optimization procedure is described. Applied to the ?⁴ theory, the algorithm yields the Gell-Mann-Low function asymptotics of the type β(g)≈7.4g ^0.96 for large g. The fact that the exponent is close to unity can be interpreted as a manifestation of the logarithmic branching of the type β(g)～g (lng)^?γ (with γ≈0.14), which is confirmed by independent evidence. In any case, the ?⁴ theory is self-consistent. The procedure of summing perturbative series with arbitrary values of the expansion parameter is discussed.     

Oxygen hole centers in coesite,a high pressure phase of SiO2

Electron spin resonance (ESR) spectra have been measured for coesite synthesized under high pressure condition from natural quartz and irradiated by γ-rays at 77K. The prominent signals detected at 77 K have an anisotropicg-factor of orthorhombic symmetry,g ₁=2.0015,g ₂=2.0055 andg ₃=2.065 and are ascribed to an oxygen related hole center in coesite. The observed signal atg _‖=2.0033 andg _⊥=2.0085 might be related with an O- or O₂-type hole center.     

The vacuum energy of QED with four-fermion interaction

We consider quantum electrodynamics in the quenched approximation including a four-fermion interaction with coupling constantg. The effective potential at stationary points is computed as a function of the coupling constants α andg and an ultraviolet cutoff Λ, showing a minimum of energy in the (α,g) plane for α=α _c =π/3 andg=∞. When we go to the continuum limit (Λ→∞), keeping finite the dynamical mass, the minimum of energy moves to (α=0,g=1), which correspond to a point where the theory is trivial.     

On theg-value shift and intersystem crossing in photo-excited radical-triplet systems

The electron paramagnetic resonance (EPR) signals of photoexcited quartet (Q₁) states for zinc(II) tetra-tert-butyl-phthalocyanine (ZnPc) ligated by 3- and 4-(N-nitronyl-nitroxide) pyridine radicals (3-NOPy, 4-NOPy) were observed in toluene solution at room temperature by means of X-band (9.4 GHz) time-resolved EPR (TREPR) spectroscopy. Theg values of Q₁ in the ZnPc-3-NOPy and ZnPc-4-NOPy complexes were found to beg=2.0025 andg=2.0036, respectively. The obtainedg value (2.0036) for ZnPc-4-NOPy is in good agreement with the value (g=2.0037) of the Q₁ state calculated under the strong-exchange limit. Theg value (2.0025) is just an average of the Q₁ and D₁ (g=2.0013) states for ZnPc-3-NOPy. Theg value of Q₁ for zinc(II) meso-tetraphenylporphine (ZnTPP) ligated by 3-NOPy showed a slight shift (g=2.0027) at X-band and no shift (g=2.0031) at W-band from the calculatedg value (g=2.0031) (J. Fujisawa, Y. Iwasaki, Y. Ohba, S. Yamauchi, K. Koga, S. Karasawa, M. Fuhs, K. Möbius, S. Weber, Appl. Magn. Reson. 21, 483–493, 2001). These changes in theg value were found to originate from an averaging of the TREPR spectra over the Q₁ and photoexcited doublet (D₁) states via a fast intersystem crossing (ISC) process. The ISC rates between these two states were estimated by means of numerical calculations with the modified Bloch equations as 1.2·10⁸ and 6·10⁷ s^?1 for the ZnTPP-3-NOPy complex at the X- and W-bands, respectively. The lower limit of the ISC rate was obtained as 10⁹s^?1 for the ZnPc-3-NOPy complex and the higher limit was found to be 3.1·10⁸ s^?1 for the ZnPc-4-NOPy complex.     

Kinetics of isothermal nucleation in a supercooled iron melt

An isothermal kinetic diagram for the beginning of homogeneous nucleation is constructed using the molecular-dynamics model of an instantaneously supercooled iron melt near the icosahedral percolation transition temperature identified with the glass transition temperature T _g . This diagram is compared with the theoretical one calculated using quantitative information obtained by analyzing the kinetics of the initial stage of growth of supercritical nuclei at temperatures higher than T _g . A satisfactory coincidence of the theoretical curve with computer simulation data at temperatures higher than T _g and substantial disagreement with these data below T _g , where crystallization is necessarily preceded by the formation of an icosahedral percolation cluster, demonstrate the substantive influence of an icosahedral substructure on the nucleation rate predicted by the classical theory.     

Deconvolution of partial pair correlation functions of an n component system using n diffraction experiments

A proof of the relation g_iig_jj = g_ijg_ji is given. This relation gives an additional $\text{n(n ? 1)}\text{2}$ equation for use in deconvoluting partial pair correlation functions from experimental diffraction data. Formulae for g₁₁, g₁₂, g₂₂ for a binary alloy system are explicitly derived.     

Threshold conditions and bound states for locally periodic delta potentials

We present a systematic study of the conditions for the generation of threshold energy eigen states and also the energy spectrum generated by two types of locally periodic delta potentials each having the same strength λV and separation distance parameter a: (a) sum of N attractive potentials and (b) sum of pairs of attractive and repulsive potentials. Using the dimensionless parameter g = λV a in case (a) the values of g = g _n , n = 1, 2, …, N at which threshold energy bound state gets generated are shown to be the roots of Nth order polynomial D ₁(N, g) in g. We present an algebraic recursive procedure to evaluate the polynomial D ₁(N, g) for any given N. This method obviates the need for the tedious mathematical analysis described in our earlier work to generate D ₁(N, g). A similar study is presented for case (b). Using the properties of D ₁(N, g) we establish that in case (a) the critical minimum value of g which guarantees the generation of the maximum possible number of bound states is g = 4. The corresponding result for case (b) is g = 2. A typical set of numerical results showing the pattern of variation of g _n as a function of n and several interesting features of the energy spectrum for different values of g and N are also described.