The Heisenberg ferromagnet as a quantum field theory

We consider a lattice of spin 1/2 ions, described by the discrete form of the current commutation relationsJ _i J _(i) =1/2, [J _i ,J _i ]=i _ij J _i where =1, 2, 3 andi label the lattice sites. The algebra is realized as the Clifford algebra over a Hilbert space. The equations of motion are specified by a formal Hamiltonian of the Heisenberg form: , wheref _ij 0 and only a finite numberQ of ions are linked to any given lattice site. We prove that the Hamiltonian is non-negative in a representation of , and has a ground state exhibiting ferromagnetism. The time displacement group acts continuously on , inducing automorphisms. is asymptotically abelian with respect to the space translations of the lattice.The model is an example of an algebraic quantum field theory and possesses a broken symmetry, the rotation group 0(3). The consequent Goldstone theorem is proved, namely, there is no energy gap in the spectrum ofH.     

ZZ production in e+ e- int eractions at $\sqrt{s} =$ 183-209 G eV

Measurements of on-shell ZZ production are described, using data from the DELPHI experiment at LEP in e ⁺ e ^- collisions at centre-of-mass energies between 183 and 209 GeV, corresponding to an integrated luminosity of about 665 pb^-1. Results obtained in each of the final states , , , , , l ⁺ l ^- l ⁺ l ^-, and (with ) are presented. The measured production cross-sections are consistent with the Standard Model expectations. These results update and supersede those already published at 183 and 189 GeV.Received: 3 March 2002, Revised: 28 May 2003, Published online: 19 September 2003     

Covariant (hh′)-Deformed Bosonic and Fermionic Algebras as Contraction Limits of q-Deformed Ones

GL_h(n) ×GL_h(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras are built in terms of thecorresponding R_h and -matrices by contracting theGL_q(n) × -covariant q-bosonic (or q-fermionic) algebras , = 1, 2.When using a basis of wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra U_q(gl(n)) , a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingU_h(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some U_h(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of (2, 1).     

Minimal supersymmetric standard model with the gauge mediated supersymmetry breaking and the neutrinoless double-beta decay

Neutrinoless double-beta decay within Minimal Supersymmetric Standard Model with gauge mediated supersymmetry breaking is considered. Limits on R-parity breaking constant coming from non-observability of 0 in ⁷⁶Ge are found. The dependence of on different parameters at the messenger scale M are shown, with special attention paid to nuclear part of calculations. We have found that strongly depends on the effective supersymmetry breaking scale only and deduced limits imposed on this non-standard parameter by the germanium experiment.     

Scaling characteristics of ac conductivity and dielectric function in fractal regime of the metal-insulator transition

An analysis of the ac conductivity _ac(), and the ac dielectric constant, (), of the metal-insulator percolation systems is presented in the critical regime near the transition threshold. It is argued that the polarization and relaxation of the finite fractal metallic clusters play dominant roles in controlling the dynamic response of the system on both sides of the threshold. The relaxation time constant of a fractal cluster is shown to scale with its size as withd _t = 4 – 2d +d _c + /, whered is tge Euclidean dimension, andd _c , , and are the scaling indices for the charging, the dc conductivity, and the correlation length respectively. The average time dependent response of the system is shown to scale with a new time scale , where is the correlation length and ₀ is a microscopic time constant. It is shown that at frequencies and with /d_t 1, in close agreement with experiments. The effects of the anomalous transport along the infinite cluster and the medium polarizability are also discussed.     

Eigenvalue Asymptotics for the Schrödinger Operator with a δ-Interaction on a Punctured Surface

Given n2, we put r=min . Let be a compact, C ^r -smooth surface in ⁿ which contains the origin. Let further be a family of measurable subsets of such that as . We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator in L ²( ⁿ ), where is a positive constant, as . An analogous result is given also for geometrically induced bound states due to a interaction supported by an infinite planar curve.     

A refinement of Simon's correlation inequality

A general formulation is given of Simon's Ising model inequality: whereB is any set of spins separating from . We show that _b can be replaced by _{b A} whereA is the spin system insideB containing . An advantage of this is that a finite algorithm can be given to compute the transition temperature to any desired accuracy. The analogous inequality for plane rotors is shown to hold if a certain conjecture can be proved. This conjecture is indeed verified in the simplest case, and leads to an upper bound on the critical temperature. (The conjecture has been proved in general by Rivasseau. See notes added in proof.)Work partially supported by U.S. National Science Foundation grant PHY-7825390 A01     

On Multifractality and Fractional Derivatives

It is shown phenomenologically that the fractional derivative = D u of order of a multifractal function has a power-law tail in its cumulative probability, for a suitable range of 's. The exponent is determined by the condition , where _p is the exponent of the structure function of order p. A detailed study is made for the case of random multiplicative processes (Benzi et al., Physica D 65:352 (1993)) which are amenable to both theory and numerical simulations. Large deviations theory provides a concrete criterion, which involves the departure from straightness of the _p graph, for the presence of power-law tails when there is only a limited range over which the data possess scaling properties (e.g., because of the presence of a viscous cutoff). The method is also applied to wind tunnel data and financial data.     

Central decomposition of invariant states applications to the groups of time translations and of euclidean transformations in algebraic field theory

With aC*-algebra with unit andgG _g a homomorphic map of a groupG into the automorphism group ofG, the central measure of a state of is invariant under the action ofG (in the state space of ) iff is -invariant. Furthermore if the pair { ,G} is asymptotically abelian, is ergodic iff is ergodic. Transitive ergodic states (corresponding to transitive central measures) are centrally decomposed into primary states whose isotropy groups form a conjugacy class of subgroups. IfG is locally compact and acts continuously on , the associated covariant representations of { , } are those induced by such subgroups. Transitive states under time-translations must be primary if required to be stable. The last section offers a complete classification of the isotropy groups of the primary states occurring in the central decomposition of euclidean transitive ergodic invariant states.     

Probing signals of the littlest Higgs model via the WW fusion processes at the high energy e + e- collider

In the framework of the littlest Higgs (LH) model, we consider the processes and , and we calculate the contributions of new particles to the cross sections of these processes in the future high energy e ⁺ e^- collider (ILC) with TeV. We find that, with reasonable values of the free parameters, the deviations of the cross sections for the processes from their SM values might be comparable to the future ILC measurement precision. The contributions of the light Higgs boson H⁰ to the process are significantly large in all of the parameter space preferred by the electroweak precision data, which might be detected in the future ILC experiments. However, the contributions of the new gauge bosons B_H and Z_H to this process are very small.Received: 22 February 2005, Revised: 27 April 2005, Published online: 6 July 2005PACS: 12.60.Cn, 14.70.Pw, 14.80.Cp     

Impact of four-quark shape functions on inclusive B decay spectra

It has recently been pointed out that a new class of subleading shape functions involving B-meson matrix elements of non-local four-quark operators contributes at order to decay distributions in the endpoint region. The corresponding functions and are estimated using the vacuum-insertion approximation. A numerical analysis of various decay spectra suggests that these power corrections are very small, below present theoretical uncertainties due to other subleading shape-function contributions. Received: 29 June 2005, Published online: 13 September 2005     

Zero Modes’ Fusion Ring and Braid Group Representations for the Extended Chiral <Emphasis Type="Italic">su</Emphasis>(2) WZNW Model

A zero modes’ Fock space is constructed for the extended chiral WZNW model. It gives room to a realization of the fusion ring of representations of the restricted quantum universal enveloping algebra at an even root of unity, and of its infinite dimensional extension by the Lusztig operators We provide a streamlined derivation of the characteristic equation for the Casimir invariant from the defining relations of A central result is the characterization of the Grothendieck ring of both and in Theorem 3.1. The properties of the fusion ring in are related to the braiding properties of correlation functions of primary fields of the conformal current algebra model.      

Phase separation of symmetrical polymer mixtures in thin-film geometry

Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two neutral repulsive walls are presented for chain lengthN _A=N _B=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesT _c (D) of unmixing are located by finite-size scaling methods, and it is shown that , wherev ₃0.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensional exponents, e.g., the coexistence curve (difference in volume fraction of A-rich and A-poor phases) scales as , where ₂ is the critical exponent of the two-dimensional Ising universality class ( ₂=1/8). Since for largeD this asymptotic critical behavior is confined to an extremely narrow vicinity ofT _c (D), one observes in practice effective exponents which gradually cross over from ₂ to ₃ with increasing film thickness. This anomalous flattening of the coexistence curve should be observable experimentally.     

Vacuum Einstein spaces with axial symmetry

Four classes of solutions are found to the equations R=–2_{; ;} and g _;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations R_ij=0 in a vacuum for the metric . The metric ds² assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.     

Direction-direction correlations of oriented polymers

We calculate the direction-direction correlations between the tangent vectors of an oriented self-avoiding walk (SAW). LetJ (x) andJ ^v (0) be components of unit-length tangent vectors of an oriented SAW, at the spatial pointsx and 0, respectively. Then for distances |x| much less than the average distance between the endpoints of the walk, the correlation function ofJ (x) withJ ^v (0) has, ind dimensions, the form . The dimensionless amplitudek(d) is universal, and can be calculated exactly in two dimensions by using Coulomb gas techniques, where it is found to bek(2)=12/25 ². In three dimensions, the -expansion to second order in together with the exact value ofk(2)in two dimensions allows the estimatek(3)=0.0178±0.0005. In dimensionsd4, the universal amplitudek(d) of the direction-direction correlation functions of an oriented SAW is the same as the universal amplitude of the direction-direction correlation functions of an oriented random walk, and is given byk(d)= ²(d/2)/(d–2) ^d .     

Study of Z pair production and anomalous couplingsin e + e- collisions at $\sqrt{s}$ between 190 GeV and 209 GeV

A study of Z-boson pair production in e ⁺ e^- annihilation at center-of-mass energies between 190 GeV and 209 GeV is reported. Final states containing only leptons, ( and ), quark and lepton pairs, ( , ) and only hadrons ( ) are considered. In all states with at least one Z boson decaying hadronically, lifetime, lepton and event-shape tags are used to separate pairs from final states. Limits on anomalous ZZ and ZZZ couplings are derived from the measured cross sections and from event kinematics using an optimal observable method. Limits on low scale gravity with large extra dimensions are derived from the cross sections and their dependence on polar angle.Received: 14 July 2003, Published online: 18 December 2003     

Singular Spectrum Near a Singular Point of Friedrichs Model Operators of Absolute Type

In we consider a family of selfadjoint operators of the Friedrichs model: . Here is the operator of multiplication by the corresponding function of the independent variable , and (perturbation) is a trace-class integral operator with a continuous Hermitian kernel satisfying some smoothness condition. These absolute type operators have one singular point of order . Conditions on the kernel are found guaranteeing the absence of the point spectrum and the singular continuous one of such operators near the origin. These conditions are actually necessary and sufficient. They depend on the finiteness of the rank of a perturbation operator and on the order of singularity . The sharpness of these conditions is confirmed by counterexamples.     

Quantum Derivation of Ginzburg-Landau Equation. New Formula for Penetration Depth

The Cooper pair (pairon) field operator ψ(r,t) changes in time, following Heisenberg’ s equation of motion. If the system Hamiltonian $\mathcal{H}The Cooper pair (pairon) field operator ?(r,t) changes in time, following Heisenberg's equationof motion. If the system Hamiltonian contains the pairon kineticenergies h ₀, the condensation energy per pairon(< 0) and the repulsive point-like potential(r ₁ –r ₂), > 0, the evolution equation for ?is non-linear, from which we obtain the Ginzburg-Landau equation: for the complex order parameter $$ " align="middle" border="0"> , where denotes thestate of the condensed pairons, and n the pairon densityoperator. The total kinetic energy h ₀ forelectron (1) and hole(2) pairons is where are Fermi velocities, and A thevector potential. A new expression for the penetration depth isobtained: where p and n ₀ are respectively themomentum and density of condensed pairons.     

Layering transition in SOS model with external magnetic field

For the SOS model defined by the Hamiltonian , where _x , _x ,{1,2,...},h>0,x ^d ,d2 it is shown that in the low-temperature region an infinite sequence of first-order phase transitions takes place whenh»0 and the temperature is fixed.     

Gelation and Cluster Growth with Cluster-Wall Interactions

Metallic cluster growth within a reactive polymer matrix is modeled by augmenting coagulation equations to include the influence of side reactions of metal atoms with the polymer matrix: where > 0 and where c _k denotes the concentration of the kth cluster and p denotes the concentration of reactive sites available within the polymer matrix for reaction with metallic atoms. The initial conditions are required to be non-negative and satisfy and p(0) = p ₀. We assume that for 01, which encompasses both bond linking kernels (R _jk = j k ) and surface reaction kernels (R _jk = j + k ). Our analytical and numerical results indicate that the side reactions delay gelation in some cases and inhibit gelation in others. We provide numerical evidence that gelation occurs for the classical coagulation equations ( = 0) with the bond linking kernel (d ) for 1/2<1. We examine the relative fraction of metal atoms, which coagulate compared to those which interact with the polymer matrix, and demonstrate in particular a linear dependence on ^–1 in the limiting case R _{= jk} , p ₀=1.