Exact solutions of the SO(3)-invariant nonlinear O-model in the special theory of relativity

Exact solutions for the four-dimensional SO(3)-invariant-model are obtained using the relation between groups of isometric motions in the space-time V₄ and chiral space U_N. A means for separating corresponding solutions in the two-dimensional-model is found. It is shown that the classical instanton and meron solutions correspond to consistent rotation of V₄ and U₂, and a general solution for this case is obtained. Four-dimensional analogs of free fields for two-dimensional-models are considered using a local approach. A non-trivial general solution which diverges logarithmically is given for the SO(N)-invariant-model.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 22–26, October, 1985.In conclusion I would like to thank G. G. Ivanov for his statement of the problem and useful discussions and D. Maison from Munich for delivering study [10].     

Non-local matrix generalizations ofW-algebras

There is a standard way to define two symplectic (hamiltonian) structures, the first and second Gelfand-Dikii brackets, on the space of ordinarym ^th-order linear differential opeatorsL=–d ^m +U ₁ d ^m–1+U ₂ d ^m–2+...+U _m . In this paper, I consider in detail the case where theU _k aren×n-matrix-valued functions, with particular emphasis on the (more interesting) second Gelfand-Dikii bracket. Of particular interest is the reduction to the symplectic submanifoldU ₁=0. This reduction gives rise to matrix generalizations of (the classical version of) thenon-linear W _m -algebras, calledV _{n, m} -algebras. The non-commutativity of the matrices leads tonon-local terms in theseV _{n, m} -algebra.s I show that these algebras contain a conformal Virasoro subalgebra and that combinationsW _k of theU _k can be formed that aren×n-matrices of conformally primary fields of spink, in analogy with the scalar casen=1. In general however, theV _{m, n} -algebras have a much richer structure than theW _m -algebras as can be seen on the examples of thenon-linear andnon-local Poisson brackets {(U _2)ab(), (U _2)cd()}, {(U _2)ab(), (W _3)cd()} and {(W _3)ab(), (W _3)cd()} which I work out explicitly for allm andn. A matrix Miura transformations is derived, mapping these complicated (second Gelfand-Dikii) brackets of theU _k to a set of much simpler Poisson brackets, providing the analogoue of the free-field representation of theW _m -algebras.     

Survey of the pre-factor of the power-law frequency dependence in the silver conducting chalcogenide glasses

The variation of parameter A in the power-law conductivity dependence on the frequency,() = A ^s, for chalcogenide glasses (Ag₂S)_x(GeS₂)_1-x, where 0相似文献   

On the variation of hopping transport in amorphous silicon with preparation conditions

Thedc conductivity of amorphous silicon prepared by two successive ion bombardments at different temperatures has been measured as a function of temperature. The results may be expressed in terms of a generalized hopping formula =₀ exp [–(T ₀/T) ⁿ where the parameter set {n,T ₀, ₀} varies with the irradiation conditions. In particular, the hopping exponent has been found to assume the limiting values ofn1/4 at irradiation temperatures ofT _i100 K and ofn1/2 atT _i500 K, whereas intermediate values ofn have been observed for temperatures inbetween. It is concluded that thermally activated redistribution processes of radiation defects control the final state of disorder in the irradiated samples, which in turn determines the particular hopping characteristics. Within the framework of existing theories the two limiting cases can be explained to be due to a disordered solid of homogeneous and granular structure, respectively.     

The metal-semiconductor transition in amorphous Si1−x Cr x films:T 0.19-contribution to the metallic conductivity

A detailed phenomenological re-analysis of previously published conductivity data, (T, x), is presented. It is based on the investigation of differences, (T, x ₁)–(T, x ₂). In this way, the cusp-like low-temperature term is amplified against the other temperature dependent contributions. This term can be described by wherep=0.19±0.03. It is present, if (4.2 K,x) exceeds 260 ^–1 cm^–1, at least up to (4.2 K,x)1350 ^–1 cm^–1 and forT60 K. But it is absent, if (4.2 K,x)180 ^–1 cm^–1. The disappearance of this contribution should be related to the metal-semiconductor transition, taking place atx _c 0.14. On the other hand, the presence of a term proportional toT ^1/2, as predicted by Altshuler and Aronov, seems unlikely.It is argued that the term should be related to the interplay of electron-electron interaction and disorder. The comparison with data from the literature shows that this contribution might also be present in heavily doped crystalline semiconductors.     

Convexity and concavity of eigenvalue sums

It is well known that(H), the sum of the negative eigenvalues of a Hermitian matrixH, is a concave and increasing function ofH. In contrast to this, we prove that forA nonsingular Hermitian andP positive definite, the functionP(AP)=(P ^1/2 AP ^1/2) is convex and decreasing. Several other results of this nature are also proved.     

Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model

We find the asymptotic decrease of correlations < _{A +y} , _B >,yZ ^v +1, |y|, in the Ising model at high temperatures. For the case when monomials _A and _B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials _A , _B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory.     

Averaged electron Green function and CDW pinning in one-dimensional random potential

The averaged retarded electron Green functionG ⁺(,k) in 1d disordered metal is calculated using the Berezinsky diagram technique. Using the Gorkov's theory it is shown, that the substitution of inG ⁺ (,k) by the square of the external frequency atk=0 gives the dependence of Fröhlich conductivity _F(). This dependence describes the impurity pinning of CDW in 1d disordered metals. The good agreement of this dependence with experimental data Zeller et al. about _F() in quasi-1d conductor KCP is found     

Linear radiation transport in randomly distributed binary mixtures: A one-dimensional and exact treatment for the scattering case

Scattering effects are considered for radiative transfer within randomly distributed and binary mixtures in one dimension. The most general formalism is developed within the framework of the invariant imbedding method. The lengthL of the random sample thus appears as a new variable. One transmission coefficientT(L) suffices to specify locally the intensities. By analogy with the homogeneous situation, one introduces an effective opacity with T=(1+_eff L)^–1 fulfilling _eff<=p ₀₀+p ₁₁(0 and 1 refer, respectively, to the components involved in the mixture). Equality is reached whenL0, . Otherwise, _eff displays a deep transmission window. It is numerically expressed for three combinations of opacities (₀,₁) and average grain sizes (₀, ₁). These results are of crucial concern in optimizing an ICF compression for a pellet nonuniformly illuminated by intense laser or ion beams.     

Hydromagnetic laminar flow of a conducting fluid in an annulus in presence of a radial magnetic field

The object of the present paper is to study the MHD effects on the laminar flow of a viscous, incompressible and conducting fluid in an annulus with arbitrary time-varying pressure gradient and arbitrary initial velocity in presence of a radial magnetic field. Using finite Hankel transform, solutions for both the unsteady and steady flows under different prescribed pressure gradients have been found out.Notation H a constant characterising the intensity of the magnetic field - p hydrostatic pressure - _e magnetic permeability - coefficient of viscosity - kinematic coefficient of voscosity - conductivity of the medium - density - a radius of the inner cylinder - b radius of the outer cylinder - parameter - s positive root - J (sr) Bessel's function of first kind of ordergl - Y (sr) Bessel's function of second kind of order     

Interfaces in the Potts model II: Antonov's rule and rigidity of the order disorder interface

Within the ferromagneticq-state Potts model we discuss the wetting of the interface between two ordered phasesa andb by the disordered phasef at the transition temperature. In two or more dimensions and forq large we establish the validity of the Antonov's rule, _ab = _af + _fb , where denotes the surface tension between the considered phases. We also prove that at this temperature, in three or more dimensions the interface between any ordered phase and the disordered one is rigid.Laboratoire Propre du CNRS: LP 7061     

Mixing properties,differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature

For the Ising model with nearest neighbour interaction it is shown that the spin correlations _{A B} - _{A B} decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT _c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).     

On the relative entropy

ForA any subset of () (the bounded operators on a Hilbert space) containing the unit, and and restrictions of states on () toA, ent _A (|)—the entropy of relative to given the information inA—is defined and given an axiomatic characterisation. It is compared with ent _A ^A (|)—the relative entropy introduced by Umegaki and generalised by various authors—which is defined only forA an algebra. It is proved that ent and ent ^S agree on pairs of normal states on an injective von Neumann algebra. It is also proved that ent always has all the most important properties known for ent ^S : monotonicity, concavity,w* upper semicontinuity, etc.     

Reduction of two-dimensional G-invariant σ-models

The Euclidean two-dimensional SO(n)-invariant -model is reduced to the system of equations for the Toda lattice. The similar reduction is studied for the SU(n)-invariant -model.     

Interpretation of the stress dependence of the steady state creep rate of Zirkaloy 4 at 873 K in terms of the knitting model

The creep rate of Zircaloy 4 has been determined as a function of strain at constant stress in the range 50 </MPa < 124. The steady state dislocation structure is a subgrain structure. The average subgrain size varies with stress as9·9G b/ (G: shear modulus,b: Burgers vector). Stress reduction tests have been performed during steady state creep to determine the static elastic modulus, the anelastic back flow and the transient creep curve caused by the stress reductions. The results are analysed in terms of the knitting model of creep. It is shown that the stress dependence of the steady state creep rate can be described by the model provided that a particle hardening term is taken into account.We thank KWU, Erlangen for providing the specimens.     

On galvanomagnetic size effects in metals

The importance of open electron trajectories formed by specular reflections of charge carriers by the sample boundary to the metal electric conductivities in the strong magnetic fieldH is analyzed. It is shown that the electric conductivity of the near-surface layer _skin is rather sensitive to the state of the conductor surface. The electron-hole Umklapp processes during the surface scattering of charge carriers do not change the dependence _skin(H), while skipping from the closed Fermi surface section to the open one is able to affect _skin essentially only in bulk samples. The method is proposed to restore the indicatrix of conduction electron scattering by the sample boundary through an experimental investigation of the Sondheimer effect and the static skin effect.     

Mates toE=mc 2 and to the Heisenberg uncertainty relations

E=mc ² is found to be a special case ofE= ^±1cⁿ, where is any one of four susceptibilities, namely electric, magnetic, gravitational, and elastic. Letl be length,t time,t time dilation, andl a measure of Fitzgerald-Lorentz contraction. A particle is stated to be the manifestation of a collection of susceptibilities which arise when(l)/1=(t)/t. Then(E)/E=5 (t)/2t=±()/. Corresponding to susceptibility, special energy particles are postulated which exhibitSU(3) symmetry, Related to the susceptibilities are five new Heisenberg uncertainty relations. Three new conservation laws for particles are proposed.     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Elastic and inelastic scattering of electrons by aligned light nuclei

The contribution to the elastic and inelastic scattering cross sections, , due to alignment of nuclei having axial symmetry was calculated for scattering of unpolarized, ultra-relativistic electrons by⁷Li atoms. This contribution turned out to be on the order of magnitude of the cross section ₀ previously calculated in the absence of nuclear alignment. For various nuclear orientations, the ratios /_o were calculated as a function of the momentum transfer q, which may be useful, for example, in increasing the reliability of identification of quantum numbers of nuclear states and multipole transitions.In contrast with the expression for _o, the expression for contains cross products of reduced matrix elements (RME), along with the squares of their moduli. This permits one, having previously experimentally found ₀ and under various kinematical conditions but for fixed q (the RME depend only on q), to obtain a system of equations for the RME and the statistical tensor g₂, which characterizes the degree of alignment of the nuclear target, along with the separation of the parallel and perpendicular cross sections as in the case of unaligned nuclei. Having solved the system of equations, one finds g₂ both in terms of the moduli of the RME of each multipole transition individually, and also in terms of their relative phases. The additional information thus obtained for each nuclear transition may serve as a more strict criterion for checking models of nuclei used in calculations than measurement of ₀ alone.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 94–98, January, 1990.     

An algebraic approach to quantum field theory and commutation relations for energy momentum in the framework of general relativity

We present a consistent set of commutation relations (C.R.) for a quantum system immersed in a classical gravitational field. The gravity field is described by metric tensorg _ik (x) andg ₀₀(x) with coordinate gaugeg _i0=0. The Hamiltonian of the system is found to be a linear function of [–g ₀₀(x)]^1/2. Its properties we define by C.R. avoiding explicit expression in terms of fields, as well as its splitting into free and interaction parts. In this way a consistent set of C.R., which are equally simple for a flat and curvilinear space, can be established. To stress the main idea of our approach, we consider the simple but still nontrivial example of a scalar electrodynamics immersed in a gravity field. The electromagnetic current operator we define by its C.R. and not explicitly. An interesting feature of this approach is that the Poisson equation follows from the consistency of the C.R. The C.R. for the energy and momentum operators of the system in a gravity field are established which generalize the usual Poincare group generators C.R. For example, we find (i/hc ²)[H _(x) ,H _(x) ]=P _– , whereH _(x) is the Hamiltonian of the system, which is a linear functional of (x)[–g ₀₀(x)]^1/2 andP _s(x) represents the momentum-density operator [averaged with the classical functions(x)].