Deviation from Matthiessen's rule of dilute al-alloys, 3 group model

The deviation from Matthiessen's rule has been investigated. The calculations were based upon three group model, in which the Fermi surface is split up into three regions. The mean free paths over the three major regions are denoted byL ₁,L ₂ andL ₃. Besides the Fermi surface anisotropy, the anisotropy of electron scattering with phonons and impurities have also been employed in the calculations. Simple formulae for the residual resistivity, the resistivity associated with phonon scattering and the deviation from Matthiessen's rule Δ(C, T), in terms of the anisotropic parameters, were derived. The formulae were used to throw light on the deviation from Matthiessen's rule.     

Extension of the 3D-scaling rule for resistivity as a function of magnetic field and its orientation for anisotropic high-temperature superconductors

The measurement of the c-axis resistivity of single crystalline La_1.86Sr_0.14CuO₄ is performed at different constant temperatures as a function of magnetic field H and angle θ between H and the ab-plane. It is shown that the 2D- or 3D-scaling rule proposed for high-T _c superconductors does not work well for the present system. Taking into account unusual vortex dynamics in the high-T _c systems, an extension is made to the 3D-scaling rule developed on the basis of the effective-mass model. Based on this extended rule, it is shown that at each given temperature the observed resistivity as a function of H and θ could be consistently scaled onto the corresponding Lorentz-force-free magnetoresistivity curves directly measured in H‖I‖c.     

Relativistic γ-scaling and the Coulomb sum rule in nuclei

In this paper dividing factors G_L and G_T are constructed for the longitudinal and transverse responses of the relativistic Fermi gas in such a way that the reduced responses so obtained scale. These factors parallel another dividing factor studied previously, H_L, that yields a (different) reduced response which fulfills the Coulomb sum rule. G_L, G_T and H_L are all found to be only very weakly model-dependent, thus providing essentially universal dividing factors. To explore the residual degree of dependence which remains, the scaling and sum rule properties of several specific models have been considered. It is seen that the relativistic Fermi gas (by construction) and also typical shell-model reduced responses successfully scale and satisfy the Coulomb sum rule, as do experimental results at medium to high momentum transfers. On the other hand, it is observed that the quantum hadrodynamic model does so only if interaction effects become weaker with increasing momentum transfer, as predicted in the most recent versions of that model.     

Geometrical Dissipation for Dynamical Systems

On a Riemannian manifold (M, g) we consider the k?+?1 functions F ₁, . . . , F _k , G and construct the vector fields that conserve F ₁, . . . , F _k and dissipate G with a prescribed rate. We study the geometry of these vector fields and prove that they are of gradient type on regular leaves corresponding to F ₁, . . . , F _k . By using these constructions we show that the cubic Morrison dissipation and the Landau-Lifschitz equation can be formulated in a unitary form.     

Nambu sum rule in the NJL Models: from superfluidity to top quark condensation

It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. We point out the possibility that the Higgs bosons appear in models of top-quark condensation, where the masses of the bosonic excitations are related to the top quark mass by the sum rule similar to the Nambu sum rule of the NJL models [1]. This rule was originally considered by Nambu for superfluid ³He-B and for the BCS model of superconductivity. It relates the two masses of bosonic excitations existing in each channel of Cooper pairing to the fermion mass. An example of the Nambu partners is provided by the amplitude and the phase modes in the BCS model describing Cooper pairing in the s-wave channel. This sum rule suggests the existence of the Nambu partners for the 125 GeV Higgs boson. Their masses can be predicted by the Nambu sum rule under certain circumstances. For example, if there are only two states in the given channel, the mass of the Nambu partner is ～ 325 GeV. They together satisfy the Nambu sum rule M ₁ ² + M ₂ ² = 4M _t ² , where M _t ～ 174 GeV is the mass of the top quark. If there are two doubly degenerated states, then the second mass is ～210 GeV. In this case the Nambu sum rule is 2M ₁ ² + 2M ₂ ² = 4M _t ² . In addition, the properties of the Higgs modes in superfluid ³He-A, where the symmetry breaking is similar to that of the Standard Model of particle physics, suggest the existence of two electrically charged Higgs particles with masses around 245 GeV, which together also obey the Nambu sum rule M ₊ ² + M _? ² = 4M _t ² .     

Reduction of the wave function: an operational approach

Possible experimental demonstration of the reduction hypothesis is discussed. It is argued that the two-time distribution function w(t₁, t₂), measurable in the time-of-flight experiments, can not be calculated without the reduction postulate. The calculation of w(t₁, t₂), using the Wigner rule and a model of the particle's detection process, is presented.     

Spontaneous breaking of global baryon number symmetry

We study the possibility that theU(1) _B global symmetry associated with baryon number is spontaneously broken. We present realistic examples implemented in the context of a suitably extended standardSU(2) _L×U(1)×SU(3)_c model and of a composite model of quarks and leptons. The globalU(1) _B symmetry in both cases is spontaneously broken at a relatively low mass scale without any conflict with observations. The dominant baryon number nonconserving process in these models obeys the ΔB=2 selection rule.     

Temperature dependence of the electrical resistivity of the nickel-platinum alloy system

The temperature dependence of the electrical resistivity of Ni_1?xPt_x (x = 1, 2, 3, 4, 5, 8, 10, 15, 20, 25 and 30 at.%) between 77 and 700 K has been investigated. The experimental results are interpreted according to the theoretical model developed by Mott. It is shown that for this system Matthiessen's rule is not obeyed.     

Symplectic large-N theory of topological heavy-fermion semiconductors

The electronic properties of three different oxides (ZnO, SnO₂ and SiO₂) are investigated within many-body perturbation theory in the G ⁰ W ⁰ approximation. The frequency dependence of the dielectric function is either approximated using two different well-established plasmon-pole models (one of which enforces the fulfillment of the f-sum rule) or treated explicitly by means of the contour-deformation approach. Comparing these results, it is found that the plasmon-pole model enforcing the f-sum rule gives less accurate results for all three oxides. The calculated electronic properties are also compared with the available experimental data and previous ab initio results, focusing on the d state binding energies. The G ⁰ W ⁰ approach leads to significantly improved band gaps with respect to calculations based on the density functional theory in the local density approximation.     

Optical sum rule in metals with a strong interaction

The restricted optical sum rule and its dependence on the temperature, a superconducting gap and the cutoff energy have been investigated. As known this sum rule depends on the cutoff energy and the relaxation rate Γ(T) even for a homogeneous electron gas interacting with impurities or phonons. It is shown here that additional dependence of the spectral weight on a superconducting gap is very small in this model and this effect disappears totally when Γ=0. The model metal with a single band is considered in details. It is well known that for this model there is the dependence of the sum rule on the temperature and the energy gap even in the case when Γ=0. This dependence exists due to the smearing of the electron distribution function and it is expressed in the terms of Sommerfeld expansion. Here it is shown that these effects are considerably smaller than that of related with the relaxation rate if the band width is larger than the average phonon frequency. It is shown also that the experimental data about the temperature dependence of the spectral weight for the high-T_c materials can be successfully explained in the framework approach based on the temperature dependence of the relaxation rate.     

QCD analysis of the Bjorken sum rule revisited

We present extended analysis of the polarized Bjorken sum rule using the four-loop expression for the coefficient function C _Bj(α_s) available now and the recent low Q ²-data from the Jefferson Lab and COMPASS experiments. We demonstrate that the perturbative series for the function C _Bj gives a hint to its asymptotic nature manifesting itself in the region Q ² ? 1 GeV². It is confirmed by the considered integral model for the perturbative QCD correction. We analyze values of higher-twist terms extracted from the mentioned data and discuss the interplay between higher orders perturbative and higher-twist contributions. We extend our consideration to the Gross-Llewellyn Smith sum rule and investigate the relation between higher twist coefficients in these two sum rules.     

On the relation between XPS and AES relaxation energies in metals

XPS (R₁) and AES cross-relaxation (R_c) energies are calculated by means of a Pseudopotential linear-response electron-gas method using norm-conserving Pseudopotentials, including intraatomic non-linearity contributions. The results are compared with excited atom model calculations and with self-consistent local density results from the literature. It is pointed out that deviations from the linear response rule R_c = 2R₁ are largely due to a shrinking of the core in the presence of the spectator hole. The remainder is due to non-linear response of the electron-gas.     

Urbach tails and the structure of chalcogenide glasses

A novel analysis of optical absorption tails of inorganic network glasses is shown to provide important information on the structure of the glass. The anomalous composition and temperature dependence of absorption tails in Ge_xSe_1?x and As_xSe_1?x systems indicate that these glasses retain locally layered structures at particular stoichiometries corresponding to GeSe₂ and As₂Se₃, and a reversible structural change is taking place well below the glass transition temperature. A phenomenological model for the absorption tail slope of glasses is proposed, analogous to the Urbach rule for crystalline materials.     

Neutral currents in thermal np capture

We present a calculation of the circular polarization P_γ and asymmetry A_γ of gamma radiation in thermal neutron-proton capture with a tested numerical accuracy of 1%. The effect of neutral currents is discussed on the example of the Weinberg-Salam model of weak interaction. It is also shown that a one percent contribution of the ³S₁ scattering state to the regular np capture cross section destroys the favourable isospin selection rule in the polarization.     

Gottfried and Bjorken sum rules: The role of vector diquarks

A quark-diquark model of the nucleon is considered and the value of the Gottfried sum ruleS _G , recently measured by the NMC group and found to differ considerably from the quark parton model expectation,S _G =1/3, is computed allowing for both elastic and inelastic contributions from the diquarks. This approach fails to reproduce the data, unless vector diquark contributions persist at very largeQ ² values, contrary to the usual assumptions. The Bjorken sum rule andSU(6) violations due to the quark-diquark structure of the nucleon are also briefly discussed.     

Line mixing in the QQ sub branches of the ν1 band of methyl chloride

Line-mixing effects have been studied in the ν₁ ^QQ_K (K from 0 to 10) sub branches of methyl chloride (CH₃Cl) perturbed by nitrogen (N₂). Laboratory Fourier transform spectra have been recorded at room temperature for various pressures of atmospheric interest. In order to accurately model these spectra, a theoretical approach accounting for line-mixing effects is necessary and proposed in this study. The common model used in this work is based on the state-to-state rotational cross-sections calculated by a statistical modified exponential-gap fitting law depending on few empirical parameters. These parameters have been deduced by least-squares fitting a sum rule to the N₂-broadening coefficients modeled previously. Comparisons between experimental and calculated spectra for various ^QQ sub branches at various pressures of N₂ demonstrate the adequacy of the model as compared to the use of the Voigt profile.     

Correlation function for topological charge densities within the instanton model in QCD

The QCD sum rule for the correlation of topological charge densities χ(Q ²) and for the longitudinal part of the correlation function for singlet axial currents (the latter is related to the former) is considered within the instanton model. The constant f _η′ of η′-meson coupling to the singlet axial current is determined. Its value appears to be in good agreement with that determined recently from the relation between the proton-spin fraction Σ carried by u, d, and s quarks and the derivative of the QCD topological susceptibility χ′(0). On the basis of the same sum rule, the η-η′ mixing angle θ₈ is found within the model employing two mixing angles. The value of θ₈ coincides with that in effective chiral theory. The correlation function for topological charge densities χ(Q ²) at large Q ² is calculated. It is shown that the Q ² dependence at high Q ² matches well with that at low Q ², the latter being determined by the known values χ′(0) and by the contributions of the π and η mesons.     

Hierarchy of interactions and mass relations in asymptotically free E6 model of unified interactions

The hierarchy of gauge interactions within the E₆ model is proved, and the vector and spinor field masses are obtained. The mass spectrum of the charged W-bosons is found, and the mass scale is fixed so that the mass of the lightest of them is about 70 GeV. The lepton spectroscopy is studied and a new charged lepton, with mass of order 4–8 GeV is predicted. For the low-energy phenomenology, the model may be considered as a theory of 6 flavoured quarks and 4 charged leptons, each with its neutrino. Being 4-component the neutrinos are massive except for the ν_e (m_νe = 0, exactly) and ν_μ (m_νμ ≈ 0, approximately) particles. The problem of the “superfluous” particles which as a rule accompanies the asymptotic freedom in such theories is also briefly discussed.     

Deviations of Matthiessen's rule in some PdAu alloys

The low temperature electrical resistivity of Pd_1?cAu_c alloys (c = 0.1, 0.22, 0.38, 0.69, 0.82 and 1.1 at.%) have been studied in detail between 1.5 and 300 K. Deviations from Matthiessen's rule (DMR) have been analysed on the basis of a two-band model, and the agreement is found to be reasonably good. The parameter λ was found to decrease monotonically with temperature, and no anomalous maximum was observed as with earlier studies of $\text{Pd}$Ti. The variation of β shows a weak temperature dependence. The limitations of the model are also discussed.     

The use of finite energy sum rules for the description of the hadronic properties of QCD

We use finite energy sum rules, taking into account nonperturbative corrections, for the calculation of hadron masses within QCD. As a rule, we obtain reasonable agreement with experimental data. We also estimate the proton lifetime in theSU(5) model to beτ _p =10²⁸ (M _x /10¹⁴GeV)⁴ years.