Resonance structure of the beta-strength function

The beta-decay strength function S _β(E) is described within two approaches: numerical solution of equation of the theory of finite Fermi systems for the effective nuclear field and solution of these equations using the quasi-classical approximation. Calculations were carried out for the isotopes ⁷¹Ge and ¹²⁷Xe. A comparison with experimental data showed their good accuracy. The resonance structure of the function S _β(E) and the quenching-effect resulting from the effective charge of quasiparticles in the nucleus are discussed.     

Moduli Space of BPS Walls in Supersymmetric Gauge Theories

Existence and uniqueness of the solution are proved for the ‘master equation’ derived from the BPS equation for the vector multiplet scalar in the U(1) gauge theory with N _F charged matter hypermultiplets with eight supercharges. This proof establishes that the solutions of the BPS equations are completely characterized by the moduli matrices divided by the V-equivalence relation for the gauge theory at finite gauge couplings. Therefore the moduli space at finite gauge couplings is topologically the same manifold as that at infinite gauge coupling, where the gauged linear sigma model reduces to a nonlinear sigma model. The proof is extended to the U(N _C) gauge theory with N _F hypermultiplets in the fundamental representation, provided the moduli matrix of the domain wall solution is U(1)-factorizable. Thus the dimension of the moduli space of U(N _C) gauge theory is bounded from below by the dimension of the U(1)-factorizable part of the moduli space. We also obtain sharp estimates of the asymptotic exponential decay which depend on both the gauge coupling and the hypermultiplet mass differences.     

Hypothesis of the fundamental length and quantum electrodynamics

Under the hypothesis of a fundamental lengthl ₀, the Bopp equation is considered as a basic equation of motion instead of the Klein-Gordon equation. Assuming that the mass is a function of₀, we derive a mass relationm(/2l ₀ c). The propagators obtained in the framework of the present theory have the same types as those with a simple cutoff. However, because of the mass relation, the tildon field with indefinite metric is always confined in the virtual state and never appears in real processes as a physical entity. Thus, our new version leads to a finite theory of quantum electrodynamics.     

Weak Power-Counting Theorem for the Renormalization of the Nonlinear Sigma Model in Four Dimensions

The formulation of the non linear σ-model in terms of flat connection allows the construction of a perturbative solution of a local functional equation by means of cohomological techniques which are implemented in gauge theories. In this paper we discuss some properties of the solution at the one-loop level in D = 4. We prove the validity of a weak power-counting theorem in the following form: although the number of divergent amplitudes is infinite only a finite number of counterterms parameters have to be introduced in the effective action in order to make the theory finite at one loop, while respecting the functional equation (fully symmetric subtraction in the cohomological sense). The proof uses the linearized functional equation of which we provide the general solution in terms of local functionals. The counterterms are expressed in terms of linear combinations of these invariants and the coefficients are fixed by a finite number of divergent amplitudes. These latter amplitudes contain only insertions of the composite operators φ₀ (the constraint of the non linear σ-model) and F _μ (the flat connection). The structure of the functional equation suggests a hierarchy of the Green functions. In particular once the amplitudes for the composite operators φ₀ and F _μ are given all the others can be derived by functional derivatives. In this paper we show that at one loop the renormalization of the theory is achieved by the subtraction of divergences of the amplitudes at the top of the hierarchy. As an example we derive the counterterms for the four-point amplitudes. PACS numbers: 11.10.Gh, 11.30.Rd     

Gravity on Finite Groups

Gravity theories are constructed on finite groups G. A self-consistent review of the differential calculi on finite G is given, with some new developments. The example of a bicovariant differential calculus on the nonabelian finite group S ₃ is treated in detail, and used to build a gravity-like field theory on S ₃. Received: 11 November 1999 / Accepted: 11 December 2000     

The inverse conjecture for the revised Enskog equation

It is shown that the pair correlation function (which is by definition the high-density factor in the revised Enskog theory) is not always a well-defined functional of the local density. Moreover, for a finite system with periodic boundary conditions and in the space homogeneous case, this function, computed at the contact value, is bounded at the maximum allowed density (i.e., a densityn _max such that, in one dimension, 1/a–1/Ln _max<1/a; equality sign, which corresponds to the usual close-packing density for whichL/a is an integer, being included as a particular case). At least for the one-dimensional gas model this finite value is shown to approach infinity in the thermodynamic and in the hydrodynamic limits. A new form for the revised Enskog equation, which does not depend on the inverse conjecture, is finally given.     

Link invariants of finite type and perturbation theory

The Vassiliev-Gusarov link invariants of finite type are known to be closely related to perturbation theory for Chern-Simons theory. In order to clarify the perturbative nature of such link invariants, we introduce an algebra V _x containing elements g _i satisfying the usual braid group relations and elements a _i satisfying g _i–g _infi ^sup-1 =a _i, where is a formal variable that may be regarded as measuring the failure of g _infi ^sup2 to equal 1. Topologically, the elements a _i signify intersections. We show that a large class of link invariants of finite type are in one-to-one correspondence with homogeneous Markov traces on V _x. We sketch a possible application of link invariants of finite type to a manifestly diffeomorphisminvariant perturbation theory for quantum gravity in the loop representation.     

Theory of high-temperature superconductivity in cuprates

A microscopic theory of electronic spectrum and superconducting pairing in the high-temperature cuprate superconductors is presented. The theory is based on consideration of strong electron correlations within the Bogolyubov polar model. The Dyson equation is derived by using the equation of motion method for the thermodynamic Green functions in terms of the Hubbard operators. The self-energy is evaluated in the noncrossing approximation for electron scattering on spin and charge fluctuations induced by kinematic interaction. The theory demonstrates that a strong Coulomb repulsion results in the anomalous electronic spectrum and unconventional (d-wave) superconducting pairing with high T _c mediated by the antiferromagnetic exchange and spin fluctuations.     

Fast and Slow Convergence to Equilibrium for Maxwellian Molecules via Wild Sums

We consider the spatially homogeneous Boltzmann equation for Maxwellian molecules and general finite energy initial data: positive Borel measures with finite moments up to order 2. We show that the coefficients in the Wild sum converge strongly to the equilibrium, and quantitatively estimate the rate. We show that this depends on the initial data F essentially only through on the behavior near r=0 of the function J _F (r)=_|v|>1/r |v|² dF(v). These estimates on the terms in the Wild sum yield a quantitative estimate, in the strongest physical norm, on the rate at which the solution converges to equilibrium, as well as a global stability estimate. We show that our upper bounds are qualitatively sharp by producing examples of solutions for which the convergence is as slow as permitted by our bounds. These are the first examples of solutions of the Boltzmann equation that converge to equilibrium more slowly than exponentially.     

Experimental Consequences of the Asymptotically Free SU(5)-Model

The experimental consequences of the asymptotically free SU(5)-theory are presented which make it possible to judge about its reliability. The phenomenology of the τ-lepton is analysed with special attention paid to the so-called exotic processes which must solve whether “light” or “heavy” the ν_τ-neutrino should be. These exotic processes are completely forbidden within standard SU(5) schemes. The problem of the finite mass of the e, μ-neutrino which is a four-component Dirac spinor interacting via the Zel'dovitch-Mahmound-Konopinski scheme is discussed. The finiteness of such neutrino mass is a peculiarity of the SU(5) theory under discussion, although its value is not fixed here in a unique way. The version of the theory wherein m_ν ≦ 10⁻³ eV is of especial interest since in this case the proton instability and the finite e, μ-neutrino mass are found to be explained in a common way as manifestations of the existence of superheavy leptoquark bosons in the theory. The possibility is pointed out to explain within the SU(5) theory under consideration the existing experimental situations concerning the search for parity violating effects in atoms. It is shown that the present SU(5) theory encounters no difficulty in this respect and can recommend itself to any experimental set of data, whereas the standard schemes of SU(5) unification cannot. Cosmological consequences of the asymptotically free SU(5) theory are briefly discussed and the latter is found to rather reasonably explain a number of facts about the very early evolution of the Universe.     

α-Ti2Zr高压物性的第一性原理计算研究

基于密度泛函理论的第一性原理计算获得了α-Ti₂Zr的晶体结构、弹性常数、德拜温度和电子分布情况, 研究了它们与压力的关系. 计算得到的晶体结构参数与实验值一致. 运用有限应变方法计算得到了α-Ti₂Zr的体积模量B、剪切模量G、杨氏模量E和泊松比σ. B和E的零压值分别为101.2和35.6 GPa. G/B的值较小, 并且随着压力的增加而减小, 表明α-Ti₂Zr具有优异的延展性. 基于弹性常数得到平均声速, 从而获得了德拜温度Θ=321.7 K. 通过解Christoffel方程获得的压缩波和剪切波数据揭示α-Ti₂Zr具有较强的各向异性. 此外, 压力诱导电子从s轨道到d轨道的转移说明在一定压力下α-Ti₂Zr将转变为β相. 关键词： 第一性原理 α-Ti₂Zr')" href="#">α-Ti₂Zr 物性 高压     

Liquids in equilibrium: Beyond the hypernetted chain

Density functional techniques are used to derive a charging expression for the non-uniform density of a molecular liquid. In the atomic limit the equation reduces to an exact form due to Fixman. The theory is simplified greatly via a physical approximation that accounts for three-body correlations beyond those included in the hypernetted chain (HNC) closure of the Ornstein-Zernike (OZ) equation. The radial distribution function is obtained as a special case. The theory is tested by examining the phase behavior of two fundamental complex fluids: the homopolymer blend and diblock copolymer melts. For the former it is found, contrary to HNC theory and its molecular generalizations, that a critical temperature T_c is predicted from the structure route. This T_c scales linearly with degree of polymerization N in agreement with Flory theory. The simplest form of the theory can be considered as a way to incorporate attractive interactions within a formalism that is very similar to that of the OZ or reference interaction site model (RISM). The relevance of the theory to charged liquids is also discussed.     

Properties of the t-J model in the dynamical mean field theory: One-particle properties in the antiferromagnetic phase

We study the one-particle properties of the t-J model within the framework of Vollhardt's dynamical mean field theory. By introducing an AB-sublattice structure we explicitly allow for a broken symmetry for the spin degrees of freedom and are thus able to calculate the one-particle spectral function in the antiferromagnetic phase. We observe surprisingly rich structures in the one-particle density of states for T < T _N at finite doping up to 15%. These structures can be related to the well known results for one single hole in the Néel background. We are thus able to establish the relevance of this at a first sight academic limit to physical properties of the t-J model with a finite density of holes in the thermodynamical limit.     

Phase transitions of a spin-one alternating magnetic superlattice

We examine the critical behavior of a magnetic superlattice which made up of two magnetic materials, A and B. Using the effective field theory with a probability distribution technique that accounts for the single-site spin correlation, we derive the analytical equation for the Curie temperature of the superlattice which alternates as ABAB...AB. The dependence of the Curie temperature on the interface coupling strength J_ab and the layer number of the finite superlattice was calculated. The effects of the surface modification are also studied. Received 2 March 2001     

Vibration-rotation wavefunctions and energies for any molecule obtained by a variational method

This paper presents an alternative method to the usual approach via perturbation theory for the determination of vibrational-rotational energy levels of a molecule in a given electronic state. It is assumed that the electronic Born-Oppenheimer equation has been solved, by an ab initio method, to give a potential function which is used in the nuclear Born-Oppenheimer equation. But the method can also be used with any potential obtained by any method. An approximate solution to the nuclear equation is derived in the form of a linear combination of expansion functions, the coefficients being determined by the standard linear variational method. Angular momentum theory is used to show that the nuclear wavefunction for m = 0 can be represented by a linear combination of functions of the form

where qi are variables which are closely related to the vibrational normal coordinates, and β, γ are two of the Euler angles. m is the eigenvalue of the Z-component of angular momentum operator in space-fixed axes OXYZ. The H_vi (qi) denote Hermite polynomials while Y^J8 (β, γ) are spherical harmonics. It is explicitly shown how all the matrix elements can be evaluated using a (3N–6) dimensional numerical integration technique. The theory in its present form is not suitable for molecules which are linear in the equilibrium configuration. In the following paper the method is used in a calculation on the water molecule.     

The Bethe-Salpeter equation with fermions

The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a fermion theory: two fermion fields (constituents) with mass m interacting via an exchange of a scalar field with mass μ. The BS equation can be written in the form of an integral equation in the configuration Euclidean x-space with the symmetric kernel K for which Tr K ² = ∞ due to the singular character of the fermion propagator. This kernel is represented in the form K = K ₀ + K _I . The operator K ₀ with Tr K ₀ ² = ∞ is of the “fall at the center” potential type and describes a continuous spectrum only. Besides the presence of this operator leads to a restriction on the value of the coupling constant. The kernel K _I with Tr K _I ² < ∞ is responsible for bound fermion-fermion states. Our approach is that the eigenvalue problem of the equation $\Lambda\Psi = g^2(K_0 + K_I)\Psi \qquad {\rm with}\qquad \Lambda = 1The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a fermion theory: two fermion fields (constituents) with mass m interacting via an exchange of a scalar field with mass μ. The BS equation can be written in the form of an integral equation in the configuration Euclidean x-space with the symmetric kernel K for which Tr K ² = ∞ due to the singular character of the fermion propagator. This kernel is represented in the form K = K ₀ + K _I . The operator K ₀ with Tr K ₀ ² = ∞ is of the “fall at the center” potential type and describes a continuous spectrum only. Besides the presence of this operator leads to a restriction on the value of the coupling constant. The kernel K _I with Tr K _I ² < ∞ is responsible for bound fermion-fermion states. Our approach is that the eigenvalue problem of the equation can be rewritten in the form The kernel of the last equation is finite for g ² < g _c ² and the variational procedure of calculations of eigenvalues and eigenfunctions can be applied. The quantum pseudoscalar and scalar mesodynamics is considered. The binding energy of the state 1⁺ (deuteron) as a function of the coupling constant is calculated in the framework of the procedure formulated above. It is shown that this bound state is absent in the pseudoscalar mesodynamics and does exist in the scalar mesodynamics. A comparison with the non-relativistic Schr?dinger picture is made. Correspondence: G. V. Efimov, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia     

Giant Gamow-Teller resonance: 40 Years after the prediction

A brief survey of the physics of the giant Gamow-Teller resonance, from the history of its prediction and the first attempts at theoretically describing it to the present-day state of this realmof nuclear physics, is given. The structure of Gamow-Teller resonances is analyzed within the theory of finite Fermi systems. Simple expressions for the energy of the Gamow-Teller resonance and for the matrix elements of its excitation are derived via approximately solving the equations of this theory by the semiclassicalmethod. The calculated values of the energy difference between the Gamow-Teller resonance and the analogous resonance are found to be in good agreement with their experimental counterparts. Strength functions for the beta decay of neutron-rich nuclei, S _β (E), are analyzed, and the calculated values of S _β (E) are contrasted against relevant experimental data.     

Rigorous Analysis of the Disk-Loaded Waveguide Slow-Wave Structures

Recently disk-loaded waveguide has been widely used in high-power traveling wave tubes (HPTWT). Although TM ₀₁ mode is it's main mode, the asymmetry mode may be excited by slight asymmetry of the structure, misalignment of the beam, or the asymmetry associated with the input or output structure. So research about asymmetry mode of disk-loaded waveguide is necessary. The general dispersion equation and interaction impedance expression of disk-loaded waveguide is obtained with accurate field theory for the first time. Based on these results, a broadband and a narrowband disk-loaded waveguides are designed which can be used in the Ka band HPTWT. Moreover, the theoretical calculated results are compared with the simulated results from the HFSS (High Frequency Structure Simulator) code using finite element method. It is found that frequency domain overlapped by these two modes of the narrowband structure is very narrow, so the HEM ₁₁ mode may be ignored when calculating Beam-wave interaction. In the other hand, the interaction impedance of HEM ₁₁ mode is very low generally.     

Zur unitarisierten Gravitationstheorie mit lang- und kurzrechweitigen Termen (mit ruhmasselosen und schweren Gravitonen)

In our papers, TREDER [1, 2] we have formulated a unified electrodynamics of the fourth order with bi-wave equations for the vector potential A. In this electrodynamics EINSTEIN ian photon and heavy W-mesons are the field quanta. In correspondence to this field theory we are able to formulate a unified theory of gravitation, too. The field equations for the gravitational metrics grr in this theory are corresponding with the EINSTEIN equations of General Relativity in the same way like the electromagnetic bi-wave equations are corresponding with the MAXWELL equations. The metric g_μν is a linear functional of an EINSTEIN ian long-range potential g_μν and of a subatomic short-range potential definierte Materie-Tensor die gemeinsame Quelle für alle drei Felder ist. Dann ist g1_μν, g2_μν und g_μν und es gelten die Funktional-Bedingungen wobei hier g2_μν Feldgleichungen vom “kosmologischen Typ” befriedigt. By these conditions, the short-range interaction becomes a repulsive force and the action of the NEWTON -EINSTEIN ian attraction and of the subatomic repulsion makes the matter point-like (as in the E.-I.-H.-method) but self-consistent. The gravitational metrics g2_μν become regulary. P. e., in the EINSTEIN approximation the field of a point-like mass M is given by a SCHWARZSCHILD     

Long-Time Asymptotics for Strong Solutions¶of the Thin Film Equation

In this paper we investigate the large-time behavior of strong solutions to the one-dimensional fourth order degenerate parabolic equation u _t =−(u u _xxx ) _x , modeling the evolution of the interface of a spreading droplet. For nonnegative initial values u ₀(x)∈H ¹(ℝ), both compactly supported or of finite second moment, we prove explicit and universal algebraic decay in the L ¹-norm of the strong solution u(x,t) towards the unique (among source type solutions) strong source type solution of the equation with the same mass. The method we use is based on the study of the time decay of the entropy introduced in [13] for the porous medium equation, and uses analogies between the thin film equation and the porous medium equation. Received: 2 February 2001 / Accepted: 7 October 2001