Anomalous dimension exponents on fractal structures for the Ising and three-state Potts model

We provide an overall picture of the magnetic critical behavior of the Ising and three-state Potts models on fractal structures. The results brought out from Monte Carlo simulations for several Hausdorff dimensions between 1 and 3 show that this behavior can be understood in the framework of weak universality. Moreover, the maxima of the susceptibility follow power laws in a very reliable way, which allows us to calculate the ratio of the exponents γ/ν and the anomalous dimension exponent η in a reliable way. At last, the evolution of these exponents with the Hausdorff dimension is discussed.     

An azo-isomerization-induced Freedericksz transition of a nematic liquid crystal

We observed an azo-isomerization-induced Freedericksz transition of the 5CB liquid crystal doped with 1% double-azo. In experiment, we found that the Freedericksz transition threshold occurred at optical intensity level of 0.3 mW/mm² for the 12.5 μm-thickness planar alignment doped 5CB, which is four orders of magnitude lower as that for the pure 5CB. Using optical phase retardation, we measured the relations between the Freedericksz transition threshold and the pump beam polarization. The maximum twist angle of liquid crystal molecules under different pump beam intensity is given. The experiment indicated that trans–cis isomerization plays an important role in the decrease of the Freedericksz transition threshold.     

Characteristic polynomials of random Hermitian matrices and Duistermaat–Heckman localisation on non-compact Kähler manifolds

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N×N random matrix taken from the Gaussian Unitary Ensemble (GUE). Deviating from the standard “supersymmetry” approach, we integrate out Grassmann variables at the early stage and circumvent the use of the Hubbard–Stratonovich transformation in the “bosonic” sector. The method, suggested recently by J.V. Fyodorov [Nucl. Phys. B 621 [PM] (2002) 643], is shown to be capable of calculation when reinforced with a generalisation of the Itzykson–Zuber integral to a non-compact integration manifold. We arrive to such a generalisation by discussing the Duistermaat–Heckman localisation principle for integrals over non-compact homogeneous Kähler manifolds. In the limit of large-N the asymptotic expression for the correlation function reproduces the result outlined earlier by A.V. Andreev and B.D. Simons [Phys. Rev. Lett. 75 (1995) 2304].     

Heavy flavour contributions to the deep inelastic scattering sum rules

We calculate the effect of the less singular terms at small x on the evolution of the coefficient function in φ³ theory in six dimensions, which result from a complete solution of the ladder equation. Scale-invariant next-to-leading order contributions are also studied. We show that the small-x approximation does not deliver the dominant contributions.     

Symmetry of the Riemann operator

Chaos quantization conditions, which relate the eigenvalues of a Hermitian operator (the Riemann operator) with the non-trivial zeros of the Riemann zeta function are considered, and their geometrical interpretation is discussed.     

Double-logarithmic asymptotics of the electromagnetic form factors of the electron and quark

The asymptotic behaviour of the electromagnetic form factors of the electron and quark is obtained in the double-logarithmic approximation for Sudakov kinematics, i.e., for the case that the value of the momentum transfer is much greater than the mass of the particle.     

The weak electroproduction of Σ in electron–proton scattering

We obtain differential cross sections for the reaction e⁻+p→Σ⁰+ν_e, for incident electron energies from 0.5 GeV to 6.0 GeV. This calculation is phenomenologically based and makes use of SU(3) and SU(2) relations. We obtain contributions of the individual form factors to the differential cross section and show that the vector current form factor dominates in the region of observability. We also obtain reaction rates for a standard set of conditions. Finally we compare this case with that for Λ production and discuss what might be learned from this reaction concerning the structure of the weak, strangeness changing, hadronic current.     

Summing the derivative expansion of the effective action

The derivative expansion of the effective action is a perturbative development in derivatives of the fields. The expansion breaks down when some of the derivatives are too large. We show how to sum exactly the first and second derivatives and treat perturbatively derivatives higher than second.     

Hyperon beta-decay and axial charges of the lambda in view of strongly distorted baryon wave-functions

Within the collective coordinate approach to chiral soliton models we suggest that breaking of SU(3) flavor symmetry mainly resides in the baryon wave-functions while the charge operators maintain a symmetric structure. Sizable symmetry breaking in the wave-functions is required to reproduce the observed spacing in the spectrum of the  baryons. The matrix elements of the flavor symmetric charge operators nevertheless yield g_A/g_V ratios for hyperon beta-decay which agree with the empirical data approximately as well as the successful F&D parameterization of the Cabibbo scheme. Demanding the strangeness component in the nucleon to vanish in the two flavor limit of the model, determines the structure of the singlet axial charge operator and yields the various quark flavor components of the axial charge of the Λ-hyperon. The suggested picture gains support from calculations in a realistic model using pion and vector meson degrees of freedom to build up the soliton.     

Binding energy of an exciton bound to ionized donors in quantum dots

Binding energies for an exciton (X) trapped in the two-dimensional quantum dot by a positive ion located on the z axis at a distance d from the dot plane are calculated by using the method of few-body physics. This configuration is called a barrier (D⁺,X) center. The dependence of the binding energy of the ground state of the barrier (D⁺,X) center on the dot radius for a few values of the distance d between the fixed positive ion on the z axis and the dot plane is obtained. We find that when d<0.2nm the barrier (D⁺,X) center does not form a bound state.     

Unitary representations of superconformal algebra

superconformal algebra is algebra with two Virasoro operators. The Kac determinant is calculated and the complete list of unitary representations is determined. Two types of extensions of algebra are discussed. A new approach to construction of algebras from rational conformal field theories is proposed.     

Magnetization plateau in the S=1/2 XXZ spin chain with period 3 magnetic field

We investigate the S=1/2 XXZ spin chain with period 3 magnetic field term. The magnetization plateau-nonplateau transition at m=±1/6 is expected to be of the Berezinski–Kosterlitz–Thouless type from the bosonization argument. By examining the level crossing of low-lying excitations numerically, we precisely determine the plateau phase diagram.     

Revisiting the role of correlation coefficient to distinguish chaos from noise

The correlation coefficient vs. prediction time profile has been widely used to distinguish chaos from noise. The correlation coefficient remains initially high, gradually decreasing as prediction time increases for chaos and remains low for all prediction time for noise. We here show that for some chaotic series with dominant embedded cyclical component(s), when modelled through a newly developed scheme of periodic decomposition, will yield high correlation coefficient even for long prediction time intervals, thus leading to a wrong assessment of inherent chaoticity. But if this profile of correlation coefficient vs. prediction horizon is compared with the profile obtained from the surrogate series, correct interpretations about the underlying dynamics are very much likely. Received 8 March 1999     

Excited TBA equations II: massless flow from tricritical to critical Ising model

We consider the massless tricritical Ising model perturbed by the thermal operator _1,3 in a cylindrical geometry and apply integrable boundary conditions, labelled by the Kac labels (r,s), that are natural off-critical perturbations of known conformal boundary conditions. We derive massless thermodynamic Bethe ansatz (TBA) equations for all excitations by solving, in the continuum scaling limit, the TBA functional equation satisfied by the double-row transfer matrices of the A₄ lattice model of Andrews, Baxter and Forrester (ABF) in Regime IV. The resulting TBA equations describe the massless renormalization group flow from the tricritical to critical Ising model. As in the massive case of Part I, the excitations are completely classified in terms of (m,n) systems but the string content changes by one of three mechanisms along the flow. Using generalized q-Vandermonde identities, we show that this leads to a flow from tricritical to critical Ising characters. The excited TBA equations are solved numerically to follow the continuous flows from the UV to the IR conformal fixed points.     

Note on the massive Rarita-Schwinger field in the AdS/CFT correspondence

We consider a massive Rarita-Schwinger field on the Anti-de Sitter space and solve the corresponding equations of motion. We show that appropriate boundary terms calculated on-shell give two-point correlation functions for spin-3/2 fields of the conformal field theory on the boundary. The relation between Rarita-Schwinger field masses and conformal dimensions of corresponding operators is established.     

Equilibrium of a gravitating plasma in a dipolar magnetic field

The equilibria of plasma in a dipolar magnetic field under the gravitational influence of a massive body (a star or black hole) and a self gravitating plasma are considered. Analytical solutions are found that can be useful for understanding the physics of plasma flows in accretion disks and star formation.     

Fixed-t partial wave analysis of πN scattering

The last full Karlsruhe PW analysis of πN scattering was finished ca. 20 years ago. After that a huge pile of new accurate πN scattering data has emerged, with which the old analysis is not completely compatible. We are making a highly modernized version of the old analysis to all (recent and old) data, aiming to pay particular attention to the discrepancies between different data sets and to the handling of the experimental errors as well as to the electromagnetic corrections and the effects of isospin breaking.     

Greater understanding of the hydrogen atom: RTT-integrability and Yangian symmetry

We show that the hydrogen atom possesses Yangian symmetry and integrability in terms of the RTT relation. A possible experimental test of the physical effect of Yangian is proposed.     

Medium effects in coherent pion photo- and electroproduction on He and C

Coherent π⁰ photo- and electroproduction on ⁴He and ¹²C nuclei is investigated in the framework of a distorted wave impulse approximation in momentum space. The elementary process is described by the recently developed unitary isobar model. Medium effects are considered by introducing a phenomenological Δ self-energy. Recent experimental data for ⁴He and ¹²C can be well described over a wide range of energies and emission angles by the assumption that the Δ–nuclear interaction saturates.     

High density quark matter and the renormalization group in QCD with two and three flavors

We consider the most general four fermion operators in QCD for two and three massless flavors and study their renormalization in the vicinity of the Fermi surface. We show that, asymptotically, the largest coupling corresponds to scalar diquark condensation. Asymptotically the direct and iterated (molecular) instanton interactions become equal. We provide simple arguments for the form of the operators that diagonalize the evolution equations. Some solutions of the flow equations exhibit instabilities arising out of purely repulsive interactions.