The zone boundary mode in periodic nonlinear electrical lattices

We study the existence and linear stability of the zone boundary mode in a nonlinear electrical lattice consisting of N inductors and N voltage-dependent capacitors with periodic boundary conditions. The inductances are allowed to alternate, while the capacitors are identical and each have a quadratic dependence on voltage. By block-diagonalizing a 2N×2N Floquet problem, we reduce the question of the stability of the mode to a single Hill’s equation that is analyzed using methods of perturbation theory and averaging. We show that periodicity of the lattice inductances degrades stability, and also show that the instability threshold is proportional to N⁻². Numerical computations validate the perturbative results.     

The off-shell infrared problem in N = 1 supersymmetric yang-mills theories (II). General massless models

We prove that in a general massless N = I SYM theory off-shell Green functions exist such that Green functions of gauge invariant operators are supersymmetrically covariant. The off-shell infrared problem present in the superfield treatment of these theories is thus shown to remain a gauge artefact. The N = 2, 4 pure SYM theories are covered by this result and thus exist as N = 1 SYM theories.     

Renormalization and phase transition in the quantum ofCPN−1 model (D=2,3)

We prove in the framework of the 1/N expansion the ultraviolet renormalizibility of the ofCP^N?1 model when D = 2, 3. It is shown that when D = 2 the model gains infrared divergences in higher orders of 1/N. When D = 3, the phase transition of second order occurs: above the critical points there exist N massive scalar charged particles and one particle corresponding to the massless isoscalar vector field, but below it there exist only N ? 1 massless particles.     

Scalar quantum chromodynamics in two dimensions and the parton model

We study SU(N) scalar quantum chromodynamics in two space-time dimensions in the large-N limit. This is the model of color gauge fields interacting with scalar quarks. We find that the consensual properties of four-dimensional QCD, i.e. infrared slavery, quark confinement, the charmonium picture, etc. are all realized. Moreover, the current in this model mimics nicely the behavior of the current in four-dimensional QCD, in contrast to the original model of 't Hooft.     

The weak-coupling phase of lattice spin and gauge models

We analyze the lattice weak-coupling (w.c.) expansion of O(N), CP^N?1 and chiral spin models, and of large-N reduced chiral and gauge models.We find that the w.c. expansion always agrees with mean field results, whenever comparable, for arbitrary space-time dimensions, and that the expansion of the reduced models agrees with that of the original ones. However, w.c. results disagree with one-dimensional large-N and (old and new) exact results. We explain this phenomenon as a failure of the analytic continuation from higher dimensions that defines lattice w.c. perturbation theory for massless models (even if infrared singularities always cancel).We use an improved version of the mean field (m.f.) technique suitable for reduced models. We compute the m.f. approximation of chiral models and use this result to determine the large-d (m.f.) behaviour of reduced gauge models, finding agreement with standard Wilson theory results.We give a new characterization of large-N chiral models in terms of the single-link integral for the adjoint representation of SU(N).     

SiCN thin film prepared at room temperature by r.f. reactive sputtering

Silicon–carbon nitride (SiCN) thin films were deposited on Si substrate at room temperature by r.f. reactive sputtering. Fourier transform infrared spectroscopy (FTIR), optical absorption spectra (α(λ)) and electrical conductivity (σ) were studied for the thin films. The effect of the annealing on IR and σ was investigated at different temperatures. IR analysis indicates that Si–H, C–N, Si–C, Si–N, C–N and CN bonds are present in a-SiCN:H films. A shift of the stretching mode for Si–H bond to the high-wavenumber side is observed with increasing the nitrogen flow ratio γ_N2(=N₂/(Ar+H₂+N₂+CH₄)). The shift is from 2000 to 2190 cm⁻¹ when γ_N2=13.7%. The study shows that the film structure and optical and electrical properties are obviously modified readily by controlling the process parameters of deposition. The improvement in the film properties, e.g., good thermal stability, is explained mainly in terms of the cross-linked structure between the Si, C and N atoms.     

On the infrared scaling solution of SU(N) Yang–Mills theories in the maximally Abelian gauge

An improved method for extracting infrared exponents from functional equations is presented. The generalizations introduced allow for an analysis of quite complicated systems such as Yang–Mills theory in the maximally Abelian gauge. Assuming the absence of cancellations in the appropriately renormalized integrals the only consistent scaling solution yields an infrared enhanced diagonal gluon propagator in support of the Abelian dominance hypothesis. This is explicitly shown for SU(2) and subsequently verified for SU(N), where additional interactions exist. We also derive the most infrared divergent scaling solution possible for vertex functions in terms of the propagators’ infrared exponents. We provide general conditions for the existence of a scaling solution for a given system and comment on the cases of linear covariant gauges and ghost–anti-ghost symmetric gauges.     

Renormalizability and asymptotic freedom in quantum gravity

We discuss a previously proposed renormalizable theory of gravity involving R²_μν, and N massless fermion (vector boson) fields in which the unitarity problem is resolved within a $\text{1}\text{N}$ expansion. The infrared limit is precisely Einstein's theory, but the high-energy behavior is determined by the dimensionless, asymptotically free coupling of the R²_μν. Various attractive possible consequences of the theory are pointed out.     

Quantum theory of compact and non-compact σ models

We discuss quantization of SO(N + 1) σ models and CP^N models, and of certain non-compact counterparts, SO(N, 1) and QP^N respectively, of these, both in canonical operator formalism and the covariant path integral formulation, showing the equivalence of the two approaches. We discuss also a class of supersymmetric σ models formulated in d ? 3 dimensions and apply the results to the SO(N + 1) and SO(N, 1) cases. This allows us to calculate the Witten index in each case. For SO(2l + 1,1) we thereby find supersymmetry breaking. However, for SO(2l, 1), we find supersymmetry is unbroken. Moreover, there is no unique ground state, invariant under SO(2l, 1), rather an infinite multiple of zero energy states, carrying a unitary irreducible representation of the non-compact SO(2l, 1) group. We discuss also field theoretic aspects of the models in d ? 2 dimensions, stressing differences of the non-compact to the compact cases. These include infrared instead of ultraviolet asymptotic freedom, lack of an energy gap, failure (in the QP^N case) of the auxiliary vector field to become dynamical. A further conclusion that is argued concerns the absence of a consistent particle interpretation for the QP^N model in exactly two dimensions. For d > 2 the non-compact symmetry of QP^N is broken down to the compact subgroup.     

Magnets with random uniaxial anisotropy: Large-N effective potential and infrared properties

We study the magnetic properties of systems with random uniaxial anisotropy using a large-N effective potential approach for d = 4, 3.It is found that the random interactions induce a strong infrared behavior that prevents the existence of a ferromagnetic phase and massless transverse modes.The transverse susceptibility is finite for all values of the temperature and at d = 4 it has an esential singularity in the couplings. We argue that this is indicative of a mechanism of dynamical mass generation due to the infrared instabilities of the theory.For both d = 4, 3 there is a spin-glass low-temperature phase and a paramagnetic high-temperature phase, the susceptibility having a cusp across the transition.We prove that these phases are stable and that the transverse and longitudinal susceptibilities are equal.     

More about the S-matrix of the chiral SU(N) Thirring model

We fix the bound state poles of the S-matrix of the chiral SU(N) Thirring model by general arguments. Avoiding an infrared problem by using a modified $\text{1}\text{N}$ expansion, the result is confirmed in leading order.     

The role of instantons in scale-invariant gauge theories

Instanton calculations in scale-invariant gauge theories, such as QCD, have long been plaqued by divergences at large distances where strong coupling effects are important. Furthermore, Witten has argued that quantum effects may cause the instanton gas to disappear and has displayed this phenomenon in the CP^(N?1) model at large N. It is argued here that instantons can play a role in calculations involving an inherent infrared cut-off, and this is demonstrated in the CP^(N?1) model for large N at a finite temperature. Some results on finite-temperature QED are also obtained in passing.     

Isomerization and channels of the loss of stability in chains of C20 fullerenes

The stability of quasi-one-dimensional chains consisting of C₂₀ fullerenes is investigated theoretically. The heights U of the potential barriers separating different metastable configurations (C₂₀) _N and the potential barriers preventing the decay of C₂₀ fullerences in the chains and their coalescence are determined. The results obtained indicate that chains with N ? 1 are characterized by a high stability and have a large number of isomers separated by low barriers.     

Systematic study of decay properties of heaviest elements

Decay properties and stability of heaviest nuclei with Z ?? 132 are studied within the macro-microscopical approach for nuclear ground-state masses. We use phenomenological relations for the half-lives with respect to ??-decay, ??-decay and spontaneous fission. Our calculations demonstrate that the ??-stable isotopes ²⁹¹Cn and ²⁹³Cn with a half-life of about 100 years are the longest-living superheavy nuclei located on the first island of stability. We found the second island of stability of superheavy nuclei in the region of Z ?? 124 and N ?? 198. It is separated from the ??continent?? by the ??gulf?? of short-living nuclei with half-lives shorted than 1 ??s.     

N = 3 and N = 1 supersymmetry in a new class of solutions for d = 11 supergravity

We present a new class of compactifying solutions for d = 11 supergravity. The internal 7-spaces are described by coset manifolds N^pqr of the form SU(3) × U(1)/U(1) × U(1). The three integers p, q, r characterize the embedding of the stability subgroup U(1) × U(1) in SU(3) × U(1).Their supersymmetry content is quite remarkable. For a particular choice of p, q, r the isometry of N^pqr is SU(3) × SU(2): in this case we find that N = 3 supersymmetry survives. For all the other values of p, q, r, supersymmetry is broken to N = 1, and the isometry group is SU(3) × U(1).We also find a class of solutions with internal photon curl F_αβγδ ≠ 0, breaking all supersymmetries.     

On the avalanche-finiteness of Abelian Sandpiles

We prove a necessary and sufficient condition for an Abelian Sandpile Model (ASM) to be avalanche-finite, namely: all unstable states of the system can be brought back to stability in finite number of topplings. The method is also computationally feasible since it involves no greater than O(N³) arithmetic computations where N is the total number of sites of the system.     

Self-consistent study of triaxial deformations: Application to the isotopes of Kr,Sr, Zr and Mo

Self-consistent mean-field calculations of deformation energy surfaces have been performed for more than 30 exotic isotopes of the Kr, Sr, Zr and Mo elements. Our calculations extend to the proton drip line. We investigate the triaxial stability of the deformed ground states in the deformation regions N ≈ 38 and N ≈ 60. The results are in good agreement with the observed trends.     

Single bremsstrahlung processes in gauge theories

We find that, for QED and for SU(N) gauge theories, single hard bremsstrahlung cross sections are remarkably simple in the ultrarelativistic limit. They can be written as a product of two factors: one factor is connected with the lowest order, elastic process, and the second one is related to the infrared factor which describes soft quantum emission. We present explicit formulae for various processes.     

The Vlasov equation and the Hamiltonian mean-field model

We show that the quasi-stationary states of homogeneous (zero magnetization) states observed in the N-particle dynamics of the Hamiltonian mean-field (HMF) model are nothing but Vlasov stable homogeneous states. There is an infinity of Vlasov stable homogeneous states corresponding to different initial momentum distributions. Tsallis q-exponentials in momentum, homogeneous in angle, distribution functions are possible, however, they are not special in any respect, among an infinity of others. All Vlasov stable homogeneous states lose their stability because of finite N effects and, after a relaxation time diverging with a power-law of the number of particles, the system converges to the Boltzmann–Gibbs equilibrium.