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.     

On the equivalence of boundary conditions

We show that ifb andb are two boundary conditions (b.c.) for general spin systems on ^d such that the difference in the energies of a spin configuration in ^d is uniformly bounded, |H _,b ()–H _,b()|C < , then any infinite-volume Gibbs states and obtained with these b.c. have the same measure-zero sets. This implies that the decompositions of and into extremal Gibbs states are equivalent (mutually absolutely continuous). In particular, if is extremal,=. Application of this observation yields in an easy way (among other things) (a) the uniqueness of the Gibbs states for one-dimensional systems with forces that are not too long-range; (b) the fact that various b.c. that are natural candidates for producing non-translation-invariant Gibbs states cannot lead to such an extremal Gibbs state in two dimensions.Supported in part by NSF Grant PHY 78–15920 and by the Swiss National Foundation For Scientific Research.     

Generalized Stefan-Boltzmann law

Thermodynamics arguments have been employed to derive how the energy density depends on the temperatureT for a fluid whose pressurep obeys the equation of statep = ( –1), where is a constant. Three different methods, among them the one considered by Boltzmann (Carnot cycle), lead to the expression = T/( –1), where is a constant. This result also appears naturally in the framework of general relativity for spacetimes with constant spatial curvature. Some particular cases are vacuum (p = –), cosmic strings (p= –1/3), radiation (p = 1/3), and stiff matter (p = ). It is also shown that such results can be adapted for blackbody radiation inN spatial dimensions.     

Relative change of the electron density at the Cu nucleus in Cu-Ag alloys

The decay constant of⁶⁴Cu in Cu–Ag solid solutions has been measured at various Cu concentrations. Deduced values of the relative changes of electron densities (0)/(0) at the Cu nucleus are given. The observed concentration dependence of (0)/(0) is discussed in terms of a volume effect and charge transfer from Cu to Ag.     

Growth of correlation in the Hopfield model

Introducing a finite correlation ₀ between any two learned patterns (others remaining uncorrelated), we observe in a numerical simulation that the Hopfield model stores these two patterns with correlation _f such that _f0 for any loading capacity. The patterns are memorized perfectly (with _f= ₀) up to -0.05 for finite correlations ₀ not exceeding a value _c(), where _c() decreases continuously to zero at -0.05.     

The role of the distribution of nucleons in finite nuclei

The total energy of many-nucleon system is expressed as a functional E[ _p(r), _n(r)] of the proton and neutron densities _p(r) and _n(r), respectively. The distribution(r) of nucleons in the nucleus, which is essential to determine the energy functional, is chosen. The energy density formalism is applied to finite nuclei, and then the binding energies per nucleon together with the mean square radii, for some medium and heavy nuclei, are obtained. Finally the achieved results are compared with the corresponding experimental values.     

The hydrodynamic limit of a one-dimensional nearest neighbor gradient system

We study the hydrodynamic behavior of a one-dimensional nearest neighbor gradient system with respect to a positive convex potential . In the hydrodynamic limit the density distribution is shown to evolve according to the nonlinear diffusion equation ,(q)/t= (²/dq²){F([1/₁(q)]), with F= –.     

Determination of the electron density at the Cu nucleus in Cu-Au alloys

The half-life of⁶⁴Cu in Cu–Au solid solutions has been measured as a function of the Cu concentration. Relative changes of electron densities (0)/(0) at the Cu nucleus are deduced. The observed nonlinear concentration dependence of (0)/(0) is discussed in terms of volume and charge transfer effects.     

Electrical and optical properties and stabilization of the Fermi level in GaP crystals irradiated by electrons and H+ ions

Electrical and optical properties and Fermi level stabilization are studied in GaP crystals irradiated by electrons (E2.2 MeV, D1·10¹⁹ cm^–2) and H⁺ ions (E5 MeV, D1.7·10¹⁶ cm^–2). It is shown that the limiting position of the Fermi level (F_limE_G/2±0.2 eV) is independent of the initial GaP parameters and the type of bombarding particle, but is determined by the condition of local neutrality of the defective GaP. Resistivity values for the irradiated specimens of _max(D)1·10¹³ ·cm were obtained at 300 K. At maximum integral particle fluxes a decrease in crystal resistivity to (3–6)·10⁹ ·cm was observed. The readjustment of GaP absorption spectra in the region hvE_G upon irradiation is related to recharging of gap states by radiation defects upon motion of the Fermi level toward F_lim.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 37–42, December, 1994.     

Gelfand Pairs with Coherent States

The notion of solvable Gelfand pairs (K,N) (K is a compact Lie group acting on N, a solvable connected and simply connected Lie group) is due to Benson, Jenkins and Ratcliff. Thanks to the localization lemma, they came back to the case where K is a connected subgroup of U(n) acting on N = Hn, the 2n + 1-dimensional Heisenberg group. They gave a geometrical condition for such a pair: (K,Hn) is a Gelfand pair if and only if the intersection of each coadjoint orbit of G = K Hn with (Lie K) contains at most one integral K-orbit. Using coherent states, we define here a generating function of multiplicity m for each in K^. m is holomorphic on D(0,1), m (r) = n = 0 an rn, an and limr 1 m (r) = mtp (, W) (W is the generic representation of Hn naturally extended to K). (K,Hn) is thus a Gelfand pair if and only if limr 1 m 1. We prove here that if m is a non homogeneous function, then there is at least two K-orbits in the intersection of the generic coadjoint orbit associated to with (Lie K).     

Theory of percolation in fluids of long molecules

We use the reference interaction site model (RISM) integral equation theory to study the percolation behavior of fluids composed of long molecules. We examine the roles of hard core size and of length-to-width ratio on the percolation threshold. The critical density _c is a nonmonotonic function of these parameters exhibiting competition of different effects. Comparisons with Monte Carlo calculations of others are reasonably good. For critical exponents, the theory yields =2=2 for molecules of any noninfinite lengthL. WhenL is very large, the theory yields _cL ^–2. These predictions compare favorably with observations of the conductivity for random assemblies of conductive fibers. The threshold region where asymptotic scaling holds requires the correlation length (/ _c ) ^–v to be much larger thanL. Evidently, the range of densities in this region diminishes asL increases, requiring that density deviations from _c be no larger thanL ^–2. Otherwise, crossover behavior will be observed.     

Ferromagnetism in the single-band Hubbard model: An exact high-temperature expansion

The first ten terms of the high-temperature expansion of the susceptibility of the single-band Hubbard model in the strong correlation limit are obtained for arbitrary electron density. The series is analyzed by ratio methods and Padé approximants. A critical temperature is found for 0.2 0.8; for > 1 further terms in the series are required.Supported in part by the National Research Council of Canada.     

Polymer models and generalized Potts-Kasteleyn models

The well-established relation between Potts models withv spin values and random-cluster models (with intracluster bonding favored over intercluster bonding by a factorv) is explored, but with the random-cluster model replaced by a much generalized polymer model, implying a corresponding generalization of the Potts model. The analysis is carried out in terms a given defined functionR(), an entropy/free-energy density for the polymer model in the casev=1, expressed as a function of the density of units. The aim of the analysis is to determine the analogR _v () ofR() for general nonnegativev in terms ofR(), and thence to determine the critical value of density _vg at which gelation occurs. This critical value is independent ofv up to a valuev _P, the Potts-critical value. What is principally required ofR() is that it should show a certain given concave/convex behavior, although differentiability and another regularizing condition are required for complete conclusions. Under these conditions the unique evaluation ofR _v () in terms ofR() is given in a form known to hold for integralv but not previously extended. The analysis is carried out in terms of the Legendre transforms of these functions, in terms of which the phenomena of criticality (gelation) and Potts criticality appear very transparently andv _P is easily determined. The value ofv _P is 2 under mild conditions onR. Special interest attaches to the functionR ₀(), which is shown to be the greatest concave minorant ofR(). The naturalness of the approach is demonstrated by explicit treatment of the first-shell model.     

Electron-electron interaction and magnon scattering in the d-electron dominated resistivity of Ni80−xFe x Si8B12 glasses

Our investigation of the electrical resistivity (T) betweenT=0.1 K and 295 K revealed for all Fe-concentrations, 2.4x16, a minimum of betweenT _min=7 K and 15 K. Above the minimum, scattering from structural disorder prevails in the paramagnetic alloy (x=2.4), while in the ferromagnetic glasses (x5.6) coherent magnon scattering appears to dominate. With one exception, (TT _min) increases as down to the lowest temperatures for all investigated Fe-contents (x10.4) in zero magnetic field as well as in applied 6 T. The value of the slopes, 6.3(6) ( cm)^–1 K^–1/2, agrees with the universal scaling behaviour reported recently by Cochrane and Strom-Olsen for systems with strong electron-electron interaction. A large, linear rise of (T<T _min,B=0) observed in the most diluted sample (x=2.4) is tentatively attributed to quantum localization in the non-reentrant spin glass phase. The magnitude of the temperature effects on (T) above as well as belowT _min indicates significantd-band contributions to the conductivity.     

Spatial structure in diffusion-limited two-particle reactions

We analyze the limiting behavior of the densities _A(t) and _B(t), and the random spatial structure(r) = ( _A(t)., _B(t)), for the diffusion-controlled chemical reaction A+Binert. For equal initial densities _B(0) = _b(0) there is a change in behavior fromd 4, where _A(t) = _B(t) C/t^d/4, tod 4, where _A(t) = _b(t) C/t ast ; the termC depends on the initial densities and changes withd. There is a corresponding change in the spatial structure. Ind < 4, the particle types separate with only one type present locally, and , after suitable rescaling, tends to a random Gaussian process. Ind >4, both particle types are, after large times, present locally in concentrations not depending on type or location. Ind=4, both particle types are present locally, but with random concentrations, and the process tends to a limit.     

Hydrogenated and irradiatedA15 Nb3Sn layers — Preparation,Rutherford scattering analysis,resistivity and superconductivity

Niobium films on sapphire were reacted in tin-vapour to Nb₃Sn with resistance ratiosR(297 K)/R(18.3 K) up to 6 and resistively measured superconducting transition temperaturesT _c up to 17.93 K. The composition Nb_3+z Sn_1–z H _x of electrolytically hydrogenated samples was determined depth dependent by Rutherford backscattering of 30 MeV³²S and simultaneous detection of recoiled protons. Considerable concentration gradients in the thin layers (0.27 m) were detected. The increase of resistivity with hydrogen content and the change in the temperature dependence of is analyzed. A correlation betweenT _c and ₀= is found: An increase of T _c =0.2 K at ₀25cm andx0.03 is followed by a drastic decrease toT _c <1.1 K at ₀80cm andx1. TheT _c vs. ₀ andT _c vs. (T) characteristic correlations are different from universal irradiation or preparation induced correlations. The discrepancies can be interpreted by a stiffening of phonon modes and a band-shifting caused by the hydrogen.     

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.     

Spin manifolds,killing spinors and universality of the Hijazi inequality

In terms of the Dirac operator P, we introduce on any field a first-order operator D and show that the operator (–) on the spinors (=(n/4(n–1))R; dim W=n) is positive. By means of a universal formula, we show that, on a compact spin manifold of dimension 3, the Hijazi inequality [8] holds for every spinor field such that (P, P) = ²(, ) (=const.). In the limiting case, the manifold admits a Killing spinor which can be evaluated in terms of . Different properties of spin manifolds admitting Killing spinors are proved. D is nothing but the twistor operator.     

Hall effect in heterogeneous Fe-Ni vacuum condensates

The temperature dependence of the electric conductivity and the Hall and Nernst-Ettinghausen effects of amorphous and microcrystalline Fe-Ni films obtained by ion-plasma sputtering, with a content of technological impurities of about 3 at. %, was studied for the first time. The relationship R_a(T) a²(T), was found between the anomalous Hall constant R_a and . R_a was found to be more sensitive to peculiarities of the complex transformation amorphous, microheterogeneous-crystalline state.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 29–33, September, 1990.     

Analysis of the dc-resistivity of YBa2Cu3Ox: Deduction of the intragrain resistivity

The resistivity (100 K) scatters very much for YBa₂Cu₃O_x prepared as single crystals, epitaxial films or bulk samples which consist of grains of 1 to 10 m diameter. An analysis of (T) for granular bulk samples is presented indicating the existence of a low intrinsic resistivity ⁱ (T)= _0L ⁱ + ⁱ T with _0L ⁱ 0 and ⁱ 0.5µcm/K. The large grain boundary resistivity _b between the grains (>1 m) yield a macroscopic percolative conduction path lengtheningL/L ₀>1 with a reduced effective cross sectionC<C ₀ and thus, (T)= _b +(LC ₀/L ₀ C)· ⁱ (T). Evidence is presented for weak links inside single crystals and grains.