Density of states of substoichiometric TiN1−x

The electronic states of substoichiometric TiN_1–x are studied by the CPA method and both the partial and total densities of states (DOS) are calculated. The results reveal that with increasing vacancy concentrationx the Fermi levelE _F moves to higher energies and the DOS atE _F,g(E _F), increases linearly. The calculated L_{II, III} X-ray spectra of Ti compare well with experiment.Work supported by the Research Institute for Powder Metallurgy, Sumperk, Czechoslovakia.The author is indebted to Dr. B. Velický, CSc for suggestion of the method to solve the Soven's equation. The financial assistance of the Research Institute for Powder Metallurgy, umperk, Czechoslovakia is gratefully acknowledged.     

Densité des vecteurs propres généralisés d'une classe d'opérateurs compacts non auto-adjoints et applications

We consider a closed densely defined linear operatorT in a Hilbert spaceE, and assume the existence of ₀ (T) such thatK = (T - ₀ I)^-1 is compact and the existence ofp>0 such thats _n (K)=o((n ^–1/p)), whereS _n (K) denotes the sequence of non-zero eigenvalues of the compact hermitian operator . In this work, sufficient conditions (announced in [1]) are introduced to assure that the closed subspace ofE spanned by the generalized eigenvectors ofT coincides withE. These conditions are in particular verified by a family of non-self-adjoint operators arising in reggeon's field theory.     

Internal Lifschitz singularities of disordered finite-difference Schrödinger operators

The integrated density of states has C-like singularities, ln|k(E)–k(E _c )|=–|E–E _c |^–v/2 _c (E), with _c >0, a milder function at the edges of the spectral gaps which appear when the distribution function of the potentiald has a sufficiently large gap. The behaviour of _c nearE _c is determined by the local continuity properties ofd near the relevant edge: _c (E)=O(1) ifd has an atom and =O(ln|E–E _c |) if is (absolutely) continuous and power bounded.     

Gauge invariance of the Euler-Lagrange expressions

We prove, for a Lagrangian density L(g_ij;A _i ⁱ ;A _i ^j ), that the gauge invariance of the Euler-Lagrange expressionsE ⁱ (L) implies the existence of a gauge-invariant scalar densityL ₁, such thatE ⁱ (L) =E ⁱ (L₁). We then prove the uniqueness of the Yang-Mills field equations.     

On Strong Superadditivity of the Entanglement of Formation

We employ a basic formalism from convex analysis to show a simple relation between the entanglement of formation E_F and the conjugate function E^* of the entanglement function E()=S(Tr_A). We then consider the conjectured strong superadditivity of the entanglement of formation E_F()E_F(_I)+E_F(_II), where _I and _II are the reductions of to the different Hilbert space copies, and prove that it is equivalent with subadditivity of E^*. Furthermore, we show that strong superadditivity would follow from multiplicativity of the maximal channel output purity for quantum filtering operations, when purity is measured by Schatten p-norms for p tending to 1.     

Anisotropic low-temperature heat transport in YBa2Cu3O6.9 single crystal

We report measurements of the low-temperature thermal conductivity of YBa₂Cu₃O_7– (0.1) single crystals (T _c =84 K) both parallel ( ^{a, b} ) and perpendicular ( ^c ) to the CuO₂ planes. Whereas ^c (T) is found to be identical, within experimental resolution, with the phonon contribution _ph (T), ^{a, b} (T) contains an additional term linear in temperature,AT. We ascribeAT to the contribution of unpaired electronic carriers residing in the chain layers. Measurements performed in external magnetic fieldsB8 T support this interpretation. Our observations can be explained by an internal multilayer (IML) model in which it is assumed that strong superconductivity is generated within the CuO₂ layers and weak superconductivity is induced in the chain layers by the proximity effect. The fit of the experimental results to the IML model reveals that approximately 15% of the electronic carriers remain unpaired in YBa₂Cu₃O₇ belowT=1 K.     

Anisotropic fiber with cylindrical polar axes

The newly proposed anisotropic fiber structures with cylindrical polar principal axes appear to be an interesting novel class of special lightguides. In this paper, some interesting results relating to such fibers are derived which, to the knowledge of this author, have not yet been reported in the literature. It is found that, ifn _c0 ( )^1/2>n _zc0( _r )^1/2, TE₀₁ will be the fundament mode with a range of single-mode operation given by 2.61n _zc0 (2 _r )^1/2 /a<2.61n _c0(2 )^1/2. On the other hand, ifn _zc0 ( _r )^1/2>n _c0( )^1/2, then TM₀₁ becomes the fundamental mode whose single-mode operation range is 2.61n _c0 (2 )^1/2 /a<2.61n _zc0(2 _r )^1/2.     

The Role of the Hall Field in the Transverse Magnetotransport

The direct measurements show that the Hall field makes no contribution to the electric-field electron heating. The volt-ampere characteristics of n-InSb are measured at T = 4.2 K and the quantizing magnetic field up to 7.4 T for E _y = 0 and E _y 0. A significant effect of the Hall-contact shorting on the magnetoresistance oscillation curve is revealed.     

Hyperbolic initial-boundary-value problem for magnetic flux compression by plane liners

Based on the (relativistic) Maxwell equations with displacement current E/t, the initial-boundary-value problem for the compression of an initially homogeneous magnetic fieldB={0,B(x,t),0} between a fixed liner atx=0 and a detonation-driven liner atx=s(t) is solved analytically. By homogenizing the boundary conditions at the moving boundary, the transient electromagnetic fields are shown to be a superposition of quasistatic elliptic (E/t=0) and hyperbolic (E/t0) wave solutions. The wave equation is solved by a Fourier expansion in time-dependent eigenfunctionsf _n =f _n [nx/s(t)] for the variable region 0xs(t), where the Fourier amplitudes _n (t) are determined by coupled differential equations of second order. It is concluded that the conventional elliptic flux compression theories (E/t=0) hold approximately for nonrelativistic liner speeds , whereas the hyperbolic theory (E/t0) is valid for arbitrary liner speeds .     

Analyticity properties and power law estimates of functions in percolation theory

We consider percolation on the sites of a graphG, e.g., a regulard-dimensional lattice. All sites ofG are occupied (vacant) with probabilityp (respectively,q=1–p), independently of each other.W denotes the cluster of occupied sites containing a fixed site (which will usually be taken to be the origin) andW the cardinality ofW. The percolation probability is the probability that #W=, i.e.,(p)=P _p{# W=}. Some critical values ofp,p _H andp _T, are defined, respectively, as the smallest value ofp for which(p)> 0, and for which the expectation of #W is infinite. Formally,p _H=inf {p(p)>0} andp _T=inf{p E _p{#W}=}. We show for fairly general graphsGthat ifp _T, thenP _P{#W n} decreases exponentially inn. For the special casesG =G ₀= the simple quadratic lattice andG ₁= the graph which corresponds to bond-percolation on ², we obtain upper and lower bounds for(p) of the formC¦p¦-P _H¦, and bounds forEp{#W} of the formC¦p–p _H¦^–. We also investigate smoothness properties of (p)=E _p{number of clusters per site} =E _p {(#W)^–1; (#W) 1}. This function was introduced by Sykes and Essam, who assumed that (·) has exactly one singularity, namely, atp=p _H. For the graphsG ₀ andG ₁, (i.e., site or bond percolation on ²) we show that (p) is analytic atp p _H and has two continuous derivatives atp=p _H. The emphasis is on rigorous proofs.Research supported by the NSF through a grant to Cornell University.     

Parametric relaxation of spectra

We study the change of an quasienergy spectrum upon variation of the weight of a perturbation in the Floquet operatorF=F ₀e^–iV . Employing ideas from level dynamics and random matrix-theory we show that the distribution of nearest-neighbor spacings can display effectively irreversible behavior. Small deviations from equilibrium relax in a certain collision time which scales with the numberN of levels as _collN ^–3/2.     

Annealing behavior ot trap-centers in silicon containing A-swirl defects

The annealing behavior of trap-centers was studied in float-zone silicon wafers containing A-swirl defects. Samples from areas of high and low A-swirl density were annealed in nitrogen ambient between 100° and 900 °C, and analysed using the Deep Level Transient Spectroscopy. The results indicate, that two levels atE _c }-0.07 eV, _n=4.6×10^–16 cm², andE _c–0.49eV, _n=6.6×10^–16cm² are caused by one defect, for which the silicon di-selfinterstitial is a likely interpretation. A level atE _c }-0.11 eV was assigned to interstitial carbon. Both defects annealed out at about 170 °C. After 600 °C annealing an additional level atE _c–0.2 eV was detected, which was attributed to an interstitial silicon carbon complex. Heat treatment at 800 °C generated a new level atE _c–0.49 eV, _n=2.9×10^–16cm² only in the area of high A-swirl defect density. This level was also observed after oxidation and subsequent annealing of silicon.     

Finitely Generated Free Orthomodular Lattices. III

The finitely generated free algebras F _V(Lk)(n) (k 2, n 3) in the varieties V(L _k )of orthomodular lattices generated by the ortholattices L _k which are horizontalsums of one block 2³ and k – 1 blocks 2² are described as abstract algebras. Thisis a continuation of earlier work and indicates the complexity one must expectwhen describing the finitely generated free algebras in finitely generated varietiesof orthomodular lattices generated by ortholattices containing Boolean blockslarger than 2².     

Models of superfrustration

Earlier studies of the triangular lattice antiferromagnet and the fully frustrated model on the square lattice proved that in these models the pair correlation S ₀ S _r decreases asymptotically asr ^–1/2 at zero temperature. In the present paper the existence of two and higher dimensional models is shown in which the frustration is so strong that it destroys the phase transition even atT=0: the correlation length remains finite. The influence of this superfrustration on the free energy and on the ground state properties is also discussed.     

Superconducting and electronic properties of the metallic glass system La75Si25−x M x (M=Cr,Mn, Fe,Co, Ni,Cu, B,Al, Ga,In)

A new ternary metallic glass system, La₇₅Si_25–x M _x (where M is a 3d or a IIIA element) has been prepared by melt spinning. The superconducting transition temperature,T _c , is depressed by the magnetic 3d elements. For low Fe concentrations (less than 5 at.%) the depression is about 0.3 K/at.%. Part of the depression may be explained by a decreased density of states atE _F as determined by UPS measurements. The strongest depression is associated with the magnetic pair breaking due to spin scattering. In the IIIA additions we correlateT _c with the atomic radius of the additive.     

Final-state interactions and repulsive Coulomb effects ind+3He→3H+p+p reaction

Differential cross sections of the reactiond+³He³H+p+p have been measured atE _d =23.083 MeV in two different kinematical configurations. A gas target was used in order to obtain absolute differential cross sections and two E–E telescopes allowed a very good identification of the various particles coming from thed+³He reaction. The role of the finalstate interactions and repulsive Coulomb effects appears rather distinctly.     

Semiempirical QSAR study and ligand receptor interaction of estrogens

Softness values E_n of estrogen derivatives and softness values E_m of receptor lysine, histidine, tyrosine and cysteine have been evaluated by Klopman equation. The required parameters for the solution of Klopman equation have been calculated with the help of PM3 method. The difference E_nm between E_n and E_m has been derived for QSAR study. The estrogen derivatives have been divided into four different sets on the basis of their structural similarities, and their biological activity taken from literature in terms of relative binding affinity (RBA). The QSAR study shows that, E_nm values provide good relationship with biological activity.     

Acoustic properties of amorphous SiO2 and PdSiCu,and of crystalline Ag,NbTi and Ta at very low temperatures

With the vibrating reed and vibrating wire techniques we have investigated the acoustic properties of vitreous silica (SiO₂, Suprasil I) and of amorphous PdSiCu as well as of polycrystalline Ag, NbTi and Ta at frequencies of 100 Hz/2<6 kHz and at temperatures of 0.1 mKT1 K. The relative change of sound velocity v/v of SiO₂ shows saturation effects, strain amplitude dependence, as well as an unexpected temperature dependence below its maximum atT<50 mK. For PdSiCu we observe that below a certain temperature, which depends on the applied strain, the temperature dependence of the sound velocityv deviates from the logarithmic behavior observed at higher temperatures and reaches an almost constant value atT<1 mK. In the same temperature rangeQ ^–1 does not remain constant but steadily decreases. The acoustic properties of the two amorphous materials at finite strain show substantial deviations from the standard tunneling model. Some of the observed anomalies can be explained taking into account the change of population of the tunneling systems energy states and a nonlinear relaxation absorption. For polycrystalline Ag we find v/v lnT andQ ^–1T ^1/3 over three decades inT atT<100 mK; it shows low-temperature acoustic properties which are strikingly similar to those of amorphous materials. The temperature and strain dependencies of the acoustic properties of polycrystalline superconducting NbTi and Ta resemble those obtained for SiO₂. These results indicate that there are basically no differences in the low-temperature acoustic properties of polycrystals and amorphous materials.     

Superconducting pairing in the singlet band of the Emery model

The pairing due to electron-phonon and exchange interaction in the two-band Emery model is considered. The Emery model is reduced to an effective singlet-triplet problem. The Eliashberg-equations are formulated in terms of Hubbard operators for the singlet band. The dependence of the critical temperatureT _c on the number of holesn in the doped CuO₂ plane has been calculated. The electron-phonon coupling gives rise to s-wave pairing with a maximum inT _c atn1.2. It corresponds to a maximum in the density of states for a doping value ofn=1.24. The anisotropic electron-electron coupling due to the exchange interaction produces extended s-wave pairing with a maximum atn1.05 and d-wave pairing with a maximum atn1.2.     

One-dimensional site percolation on a finite lattice

The behaviour of the numbers n _s of clusters withs sites each in the case of a chain ofN sites is studied for free and cyclic boundary conditions. Explicit expressions for the n _s, which differ from (1–p)² p ^s=q ² p ^s for the infinite lattice, are given. Also the total numberG(p) of clusters and the mean cluster sizeS(p) are calculated. In the thermodynamic limit the correction terms are found to be of order 1/N. An investigation of the scaling behaviour shows that the scaling of n _s is described by two independent variables in contrast toG(p) andS(p) which require only one variable.