Peierls transitions in semimetallic one dimensional charge transfer salts

Peierls transitions in one dimensional charge transfer salts in which both donor and acceptor molecules have even valency such as TTF-TCNQ have been studied. Transitions involving macroscopic occupation of phonon states of wavevector $\text{k}{}_{\mathrm{<mtext>F</mtext>}}\text{(TTF)}\text{+ k}{}_{\mathrm{<mtext>F</mtext>}}\text{(TCNQ)}\text{=}\text{1}\text{2}\text{G}$ and |k_F(TTF) ? k_F (TCNQ)| can occur as well as transitions of wavevector 2k_F(TTF) [and 2k_F(TCNQ)].     

The renormalization of the string operator in QCD

We shall observe that the renormalization of the string operator U(x₁, x₂; C) = Pexp{ig∫_x1^x2dx_μA^μ(x)} with an open path C (smooth and non-intersecting) is path-independently performed in any order of perturbation. To demonstrate this, the renormalization constants will be calculated up to order g⁴. Next the renormalization effect on the algebraic identity $\text{U(x}{}_1\text{, x}{}_2\text{;}\text{C}\text{)U(x}{}_2\text{, x}{}_3\text{;}\text{C}\text{) = U(x}{}_1\text{, x}{}_3\text{;}\text{C}\text{∪}\text{C}\text{)}$ will be discussed and it will be proved that the renormalization preserves the algebraic identity in any order of perturbation if the paths C and $\text{C}$ are smoothly connected at x₂. Finally, the string operator renormalization is extended to the case when the path C is smoothly closed (the Wilson loop operator). It is then shown that the renormalization factor which multiplicatively renormalizes the string operator in the case of the open path, is cancelled in any order of perturbation by the divergence appearing in the coincidence of the end points. As a results, the Wilson loop operator can be renormalized by the coupling constant renormalization alone.     

Conductivite ionique des systemes Kx(Znx/2Ge1-x/2)O2 et Kx(GaxGe1-x)O2 de structure cristobalite

The crystal chemistry of the K_x(Zn_x/2Ge_{1-$\text{x}\text{2}$})O₂ and K_x(Ga_xGe_1-x)O₂ systems has been investigated. In each of them a solid solution with a cristobalite-type structure has been obtained with a 0.90?×?1 range. The K⁺ conductivity increases strongly with vacancy content, while the activation energy remains nearly constant.Influence of various crystal chemical parameters on the conductivity (lattice covalency, size of the bottlenecks, etc...) is discussed.     

Perturbation theory for the effective interaction in nuclei

Starting from a decomposition of the Hamiltonian H(x) of the nuclear many-body problem in the form H(x) = H₀ + xV, where H₀ is a shell-model Hamiltonian, V the residual interaction, and x a strength parameter, we introduce a general effective interaction W(x) describing the interaction of nucleons within a shell, and the associated effective operators $\text{A}\text{?}\text{(x)}$. We display some properties of these operators. From a particular choice of W(x) we obtain the expressions introduced earlier by several authors. The convergence of the expansions for W(x) and $\text{A}\text{?}\text{(x)}$ in powers of x is investigated. It is shown that W(x) and $\text{A}\text{?}\text{(x)}$ are holomorphic in a domain of the complex x-plane including the point x = 0. With the help of a generalization of the von Neumann-Wigner noncrossing rule, we exhibit the nature of the common singularity of W(x) and $\text{A}\text{?}\text{(x)}$ which is closest to the origin and thus defines the radius r₀ of convergence of the expansions of W and $\text{A}\text{?}$. It is shown that r₀ is unaffected by the cancellation of unlinked diagrams. A criterion of consistency is established, which shows that most of the practical calculations of W lead to results which are inconsistent with the definition of W.     

Ni-Zr amorphous alloys: Low temperature specific heat and superconductivity

The specific heat (C_p) of the amorphous alloys Ni_100-xZr_x for x = 75, 65, 55 and 35 was measured from 0.8K to 40K and the composition trends of the transition temperature T_c, the enhanced density of states at the Fermi level N_γ(_F) and the Debye temperatures θ_D(0), θ_D(T) established. For the three superconducting compositions (x=75, 65, 55) N_γ(E_F increases rapidly with increasing [Zr] in agreement with the trend in amorphous Cu-Zr alloys. However, for the Zr-Ni alloys the bare density of states $\text{N}{}_0\text{(E}{}_{\mathrm{F}}\text{) =}\text{N}{}_{\mathrm{\gamma }}\text{(E}{}_{\mathrm{F}}\text{)}\text{(1 + λ}{}_{\mathrm{p}}\text{)}$ increases strongly with [Zr] in contrast to the Zr-Cu alloys where it is reported to be almost constant. We conclude that for the Ni-Zr alloys the electron-ion matrix element <I²> decreases with increasing [Zr]. Other results are related to recent photoemission studies of these alloys.     

Recoil implantation from a thin source: I. Underlying theory and numerical results

Recoil implantation from a monolayer source, for example an adsorbed layer or a layer of altered stoichiometry, is considered. We introduce the incident ion current I, the fractional surface coverage characterizing the recoil source θ, the differential scattering cross-section dσ, and the integral distribution function F(x, ψ) for recoil-source atoms entering the target at angle ψ and stopping beyond x. The number of atoms implanted beyond x follows as $\text{H(x) = IθλN? σ F(x,ψ)}$. The receding of the target surface at velocity υ due to sputtering can be allowed for by integrating over $\text{x: H(x, t) = (}\text{1}\text{υ}\text{) ∫ H(x′)dx′}$. For very high doses the result is a steady-state situation in which the number of implanted atoms is given by H(x, ∞). Numerical results of four kinds are presented: H(x, H(x, ∞), the half-time for the build-up of the steady-state situation, and the half-depth of the implanted atoms, in all cases for oxygen on the surface of Be, Al, Mo and W.     

Evolution of the density for a chaotic map

For the discrete-time map x_t+11 = 4x_t(1?x_t) an exact, explicit expression is given for the time-dependent density r_t (x) evolving from a uniform initial density on (0,1). As t → ∞, r_t(x) approaches the known invariant density $\text{r(x) = 1/[π}\text{x(1?x)}\text{]}$.     

SU(6) symmetry breaking effects in deep inelastic scattering

The fact that the N and Δ states of the $\text{56}$ baryons are not degenerate in mass is shown to imply that the deep inelastic scattering ratio F_2n(x)/F_2p(x) should approach $\text{1}\text{4}$ as x → 1. The rate of approach is predicted to be approximatel linear in x. The possibility of observing analogous effects in other large momentum transfer processes is also discussed.     

Angular distributions and structure functions from two-jet events at the CERN SPS pp collider

The two-jet cross section measured in the UA1 apparatus at the CERN $\text{p}\text{p}$ Collider has been analysed in terms of the centre-of-mass scattering angle θ and the scaled longitudinal parton momenta x₁ and x₂. The angular distribution dσ/d cos σ rises rapidly as cos → 1, independent of x₂ and x₂, as expected in vector gluon theories (QCD). The differential cross section in x₁ and x₂ is consistent with factorization and provides a measurement of the proton structure function $\text{F(x) = G(x) +}\text{4}\text{9}\text{[Q(x) +}\text{Q}\text{(x)]}$ at values of the four-momentum transfer squared, -t? ≈ 2000 GeV². Over the range x = 0.10?0.80 the structure function shows an exponential x dependence and may be parametrized by the form F(x) = 6.2 exp (?9.5x).     

ESR of Ni doped amorphous chalcogenide semiconductors

ESR signals with g = 2.08 and 2.13 due to Ni were observed for evaporated (Ge_0.32Se_0.32Te_0.32As_0.4) 100_-xNi_x and $\text{(Ge}{}_{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{Se}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{100}{}_{\mathrm{-x}}\text{Ni}{}_{\mathrm{x}}$ films respectively. The large increase of the electrical conductivity by the addition of Ni is discussed in connection with the ESR signal. Bulk glasses prepared by melt-quenching are also investigated for comparison.     

Positive cones in enveloping algebras

The concept of strong ordering on enveloping algebras of finite-dimensional Lie algebras is introduced and studied as a generalization of the corresponding notion for the commutative polynomial algebra. A linear functional f on an enveloping algebra $\text{E}$ (G) is called strongly positive if f(x) ? 0 for all x ? $\text{E}$(G) which are mapped on positive operators for all G-integrable irreducible representations of $\text{E}$(G). We prove that for each real connected Lie group G ≠ R₁ there are positive, not strongly positive, linear functionals on $\text{E}$(G). A non-commutative problem of moments is defined. It has a solution iff the corresponding linear functional is strongly positive.     

Coupled mode behavior of the soft E(TO) phonon of Pb(Ti1-x,Zrx)O3 and (Pb1-3x2, Lax)TiO3

We report the temperature dependence of the low frequency part (ω < 100 cm^?1) of the Raman spectra of the Pb(Ti_1-x, Zr_x)O₃ and $\text{(}\text{Pb}{}_{\mathrm{<mtext>1-</mtext><mtext>3x</mtext><mtext>2</mtext>}}$, La_x)TiO₃ systems. The spectra indicate a coupled mode behavior between the soft E(TO) phonon and a mode which produces an additional band in the spectra. We discuss the possibility that the additional band might be due to zone boundary tranverse acoustical phonons which couple to the q ～ 0 soft E(TO) mode because of the disorder existing in the systems.     

Band filling and disorder in molecular conductors

We have systematically probed the roles of band filling and disorder in molecular conductors utilizing the (NMP)_x(Phen)_1-x(TCNQ)(0.5 < × ≤ 1.0) system. Conductivity results show a semiconducting behavior with charge carriers activated to extended states with a large strongly temperature dependent mobility. The energy gap is found to decrease with decreasing band filling, varying as x². The inconsistency of these results with various disorder model is indicated.     

Calculation of the magnetic susceptibility of a praseodymium Kondo system in the Anderson model

We have calculated the magnetic susceptibility of a praseodymium Kondo system in the Anderson model.This calculation explains correctly the negative conduction electron polarization found in the Kondo system La_1?xPr_xSn₃ and gives an evaluation of the parameter $\text{Гn(E}{}_{\mathrm{F}}\text{)}$ in satisfactory agreement with other determinations.     

Gauge invariance and renormalization

The renormalization of Abelian and non-Abelian local gauge theories is discussed. It is recalled that whereas Abelian gauge theories are invariant to local c-number gauge transformations δA_μ(x) = ?_μ,…, with □Λ = 0, and to the operator gauge transformation δA_μ(x) = ?_μφ(x), …, δφ(x) = α^?1?·A(x), with □φ = 0, non-Abelian gauge theories are invariant only to the operator gauge transformations $\text{δA}{}_{\mathrm{\mu }}\text{(x) ～}\textcolor{red}{}{}_{\mathrm{\mu }}\text{C(x)}$, …, introduced by Becchi, Rouet and Stora, where

_μ is the covariant derivative matrix and C is the vector of ghost fields. The renormalization of these gauge transformation is discussed in a formal way, assuming that a gauge-invariant regularization is present. The naive renormalized local non-Abelian c-number gauge transformation $\text{δA}{}_{\mathrm{\mu }}\text{(x) = (Z}{}_1\text{/Z}{}_3\text{)gA}{}_{\mathrm{\mu }}\text{(x) ×}\text{Λ}\text{(x)+?}{}_{\mathrm{\mu }}\text{Λ}\text{(x)}$, …, is never a symmetry transformation and is never finite in perturbation theory. Only for $\text{Λ}\text{(x) = (Z}{}_3\text{/Z}{}_1\text{)L}$ with L finite constants or for $\text{Λ}\text{(x) = Ω}\text{z}\text{?}{}_3\text{C(x)}$ with Ω a finite constant does it become a finite symmetry transformation, where $\text{z}\text{?}{}_3$ is the ghost field renormalization constant. The renormalized non-Abelian Ward-Takahashi (Slavnov-Taylor) identities are consequences of the invariance of the renormalized gauge theory to this formation. It is also shown how the symmetry generators are renormalized, how photons appear as Goldstone bosons, how the (non-multiplicatively renormalizable) composite operator A_μ × C is renormalized, and how an Abelian c-number gauge symmetry may be reinstated in the exact solution of many asymptotically fr ee non-Abelian gauge theories.     

The strong topology on the algebra of polynomials

It is shown that under a quite general condition on the operator T (unbounded, symmetric) and on the domain $\text{D}$ for the representation x → T of the algebra $\text{P}$(x) on $\text{D}$ in $\text{P}$(T) the strongest locally convex topology τ_∞ coincides with the strong topology σ^$\text{D}$.     

Transport phenomena in low and high magnetic field (Shubnikov-de haas effect) in n-type Ga1−xAlxSb alloys

Galvanomagnetic measurements have been performed on n-type Ga_1?xAl_xSb with $\text{x ? 0.3}$. For the first time the Shubnikov-de Haas oscillations have been observed. The Г band contribution to the conductivity for x < 0.15 was clearly pointed out from the measurements of the periods of oscillations and Hall effect. The conduction effective mass at the Fermi level was deduced for several samples.     

Preliminary evidence for UA(1) breaking in QCD from lattice calculations

We suggest a simple definition of the topological charge density Q(x) in the lattice Yang-Mills theory and evaluate A≡∝d⁴x〈Q(x)Q(0)〉 in SU(2) by Monte Carlo simulation. The “data” interpolate well between the strong and weak coupling expansions, which we compute to order g^?12 and g⁶, respectively. After subtraction of the perturbative tail, our points exhibit the expected asymptotic freedom behaviour giving $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{≌(0.11±0.02)K}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, K being the SU(2) quarkless string tension. Although a larger value for $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{K}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ would be preferable, we are led to conclude (at least tentatively) that the U_A(1) problem of QCD is indeed solved perturbatively in the quark loop expansion.     

Inclusive pion distributions in e+e− annihilation from sum rules and duality

The threshold behaviour of pion production presented in our earlier work is successfully compared with the new SPEAR data. By using duality and sum rules we derive F_T^(π+)(x) ≈ F_L^(π+)(x) ≈ F_T^(π0)(x) ? F_L^(π0)(x) for x near 1. An accompanying results is $\text{σ}{}_{\mathrm{<mtext>\pi </mtext><mtext>A</mtext>}}{}_2\text{(s) ≈ 2σ}{}_{\mathrm{\pi \omega }}\text{(s) ≈ 4σ}{}_{\mathrm{\pi \pi }}\text{(s) ≈ 9(m}{}_{\mathrm{?}}{}^2\text{/s)}{}^3\text{σ}{}_{\mathrm{<mtext>\mu </mtext><mtext>\mu </mtext>}}$ for large s.     

Bosonic construction of the Lie algebras of some non-compact groups appearing in supergravity theories and their oscillator-like unitary representations

We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups $\text{SP}\text{(2n,}\text{R}$ and $\text{SO}\text{(2n)}{}^1$ from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n?4 and stops at n = 8 leading to the Lei algebras of SU(4) × SU(1, 1), SU(1, 1), SU(5, 1), SO(12)¹ and E₇(7). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for E₇₍₇₎ and SO(12)¹ obtained from the extended construction). We illustrate our construction with the examples of SU(5, 1) and SO(12)¹.