CP-violating effects inZ decays to τ leptons

We calculate CP-odd correlations inZ decays to leptons, . These correlations are sensitive to the weak dipole moment of the . With 10⁷ producedZ particles and with observation of the decay channels and v we estimate that can be determined with an accuracy of about (1 s.d.).     

Scaling characteristics of ac conductivity and dielectric function in fractal regime of the metal-insulator transition

An analysis of the ac conductivity _ac(), and the ac dielectric constant, (), of the metal-insulator percolation systems is presented in the critical regime near the transition threshold. It is argued that the polarization and relaxation of the finite fractal metallic clusters play dominant roles in controlling the dynamic response of the system on both sides of the threshold. The relaxation time constant of a fractal cluster is shown to scale with its size as withd _t = 4 – 2d +d _c + /, whered is tge Euclidean dimension, andd _c , , and are the scaling indices for the charging, the dc conductivity, and the correlation length respectively. The average time dependent response of the system is shown to scale with a new time scale , where is the correlation length and ₀ is a microscopic time constant. It is shown that at frequencies and with /d_t 1, in close agreement with experiments. The effects of the anomalous transport along the infinite cluster and the medium polarizability are also discussed.     

Large Deviations for Quantum Spin Systems

We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages , where the X _i 's are copies of a self-adjoint element X (level one large deviations). From the analyticity of the generating function, we obtain the central limit theorem. We generalize to a level two large deviation principle for the distribution of      

Spin relaxation in the amorphous spin glass Al2Mn3Si3O12

Neutron scattering measurements on the amorphous spin glass Al₂Mn₃Si₃O₁₂ have been made using the time-of-flight method. The scattering lawS(Q, ) reveals a quasielastic line with temperature andQ-dependent linewidth and an elastic line with constant intensity between 15 and 294K. The linewidth of the quasielastic scattering diminishes with decreasing temperature following an Arrhenius law at least down to 15K. Deviations from this exponential form are strictly correlated with an increase of the elastic intensity below 15K. We favour the opinion that this effect is caused by the instrumental resolution rather than by the onset of spin glass freezing.     

Intersections in Genus 3 and the Boussinesq Hierarchy

In this Letter we prove that the enlarged Witten conjecture is true in the case of the Boussinesq hierarchy for correlators .     

Dynamics of vector spin glasses with random anisotropy

The dynamics of vector spin glasses with additional random anisotropy is investigated in the mean field approximation. We find a cross-over of the upper critical line from a behaviour of Heisenberg spins with a field-temperature dependence , for large fieldsH, to Ising like behaviourT _f –TT ^2/3 , for small fields and fixed anisotropy, in agreement with results of Kotliar and Sompolinsky. Here, andT _f are characteristic spin glass temperatures. In addition, one has a second line with reversed behaviour which presumably represents a cross-over line from weak to strong non-ergodicity. The local transverse susceptibility _T () varies for large fields and 0 along the upper critical line as ^vT , with a critical exponentV _T = 1/2 – 11D/60 J, whereD andJ are the anisotropy and exchange coupling constants, respectively. On the Ising-like part of the upper critical line one has isotropic spin glass parameters,q _L =q _T , and susceptibilities, and a critical exponent, which is similar to that of Ising spins along the de Almeida-Thouless line.Dedicated to B. Mühlschlegel on the occasion of his 60th birthdaySFB Aachen-Jülich-Köln     

NMR enhancement factor inCuMn(Fe) spin glasses

The spin glass magnetic enhancement factor has been measured at T=1.3 K with^63/65Cu NMR spin echo technique. Alloying iron to CuMn, (H_o) shows a large range of constancy against an external field H_o, applied in and opposite to the direction of the freezing field H_c. It is supposed that the stiffness of the frozen spin glass is stabilized in this range by a subsystem of ferromagnetic iron clusters. Bound by its own crystalline anisotropy energy, the subsystem has its own stiffness. It probably behaves as a powder system consisting of ferromagnetic single domain particle spheres, having also an isotropic distribution of domain magnetization directions and giving rise to a mean ferromagnetic NMR enhancement factor.     

How universal are the low temperature acoustic properties of glasses?

We evaluated already published data on ultrasound absorption and velocity changes below 1 K for a set of 18 different glasses. By uniformly analysing these data according to the tunnelling model we have calculated the standard spectral density of two-level-systems (TLS) and their coupling energy ₁ and ₁ to longitudinal and transversal phonons. Contrary to literature, we have not observed any correlation between and the glass transition temperatureT _g for our set of 18 glasses. As far asT _g is concerned we only found a relation _min ^0.1K withn2.5 and where _min is the shortest TLS-phonon relaxation time at 0.1 K. Since the values for and _1,t scatter within half an order of magnitude, we conclude that the TLS parameters of a certain glass are only weakly dependent on bulk properties. We find that the ratio _t ² /C ₄₄ (whereC ₄₄ is the shear elastic constant) is a more sensitive parameter for tests on the variation of the TLS spectral density of glasses.     

Bounds on the density of states in disordered systems

In magnetic systems the radio frequency fieldH ₁ seen by the nuclei is often enhanced by a factor . If the atomic spins are distributed in multi directions, as in Bloch walls or spin glasses, one has to consider a spatial distribution (r) of enhancement factors. The usual way to define a mean enhancement factor is shown to lead to inconsistent results giving rise to errors up to more than 100%. One has to distinguish between two mean factors, and , depending on measuring conditions. Their deviations from the true value are discussed.     

Paramagnetic resonance of the (Cr5+O4)H2 Halperin-Varma center in NH4H2AsO4 and KH2AsO4

The electron paramagnetic resonance (EPR) spectrum of Cr⁵⁺(3d ¹,S=1/2) in undeuterated and 58%-deuterated NH₄H₂AsO₄ was investigated. The EPRg-value tensors in the paraelectric and antiferroelectric phases are almost the same as those observed at high and low temperatures in KH₂PO₄ and KH₂AsO₄. This shows that the (Cr⁵⁺O₄)H₂ complex is the same in all crystals, i.e., a wave function ofd _x ²–y ² character coupled to two lateral protons which reorient among the four possible Slater configurations in the paraelectric phase. The remarkable isotope shift of the local dynamic reorientational slowing-down observed in KH₂PO₄ and KH₂AsO₄ in approximate proportion to the shift of the bulk ferroelectric transition temperaturesT _c ^F , and the antiferroelectricT _c ^AF of NH₄H₂AsO₄, is analyzed qualitatively. It is shown to result mainly from the isotope effect of the short-range interactionJ _sr via protons and deuterons for the impurity and for the bulk. Q-band data of the (Cr⁵⁺O₄)H₂ center in 75%-deuterated KH₂AsO₄ are also reported. An averaged high- and nonaveraged low-temperature EPR spectrum is observed in a temperature range of 250 to 290 K. The intensity ratio of the two follows an exp 2(T—T)/ law over four orders of magnitude atT=266 to 273 K and=5.3 to 6.1 K depending on the orientation of the external magnetic field. This novel result in motional narrowing is analyzed analytically to be compatible with a distributionP _A of ₀(T, T, ) of half width, in reorientation times withE=0.23 ±0.02 eV, , probably resulting from the statistical occupation of deuterium atoms among the O—–H–O bridges. Comparison with a theory of Binder definitely proves the extrinsic slowing-down and thus Halperin-Varma type character. In the range of temperatures investigated no local freeze-out has been detected.     

Spectral distribution and kinetics of the high-voltage photoelectromotive force of PbS layers

The spectral dependences of the short-circuit current Iph and the photoconductivity _ph of photovoltaic PbS layers are similar in shape and in the position of the long-wavelength threshold. As the temperature is reduced, the spectral curves shift toward longer wavelengths. Several samples show a photoemf of different sign in different parts of the spectrum. The relaxation of the photoemf V_ph, the current I_ph, and the photoconductivity _ph is characterized by times , respectively, where > \tau \sigma > > \tau I$$ " align="middle" border="0"> . The temperature dependences of these times and of the layer resistance have been studied. The results are interpreted on the basis of a barrier model for the high-voltage photoemf in PbS layers.     

Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy , we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) . We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in . We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's , which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.     

Relaxation effects in the Mössbauer spectra of iron complexes with fatty acids

Six new oxo trinuclear iron(III) complexes of the type [Fe₃O(R–COO)₆(H₂O)₃] X, where X= or Cl^– and R=C₅, C₇, C₈, C₉ were synthesized and investigated by Infra Red, Mössbauer Spectroscopy and magnetic measurements. The data pointed to a high spin state (S=5/2) for iron and for antiferromagnetic interactions. The asymmetrical shape of the Mössbauer doublet and its temperature dependence was treated using the Blume relaxation model. The relaxation process is influenced by both X and R components.     

Fast relaxation of polycrystalline Fe(III) complexes studied by Mössbauer spectroscopy

Mössbauer spectra of polycrystalline samples of Fe(Ox)₃, Fe(BPHA)₃ and K₃[Fe(malonate)₃] · 3H₂O exhibit fast relaxation patterns in the temperature range 4.2–300 K. The magnetic hyperfine splitting has nearly completely collapsed due to rapid electronic spin-spin relaxation of the Fe ions. We use a static Hamiltonian and describe the spin-spin interaction by an effective field Hamiltonian . From this the relaxation supermatrix and the Mössbauer spectra are calculated. The random texture of the samples is taken into account by averaging the radiation dipole operators over the whole sphere. Least-squares fits of the spectra for longitudinal, isotropic and transverse spin relaxation are presented. From the fits the temperature dependence of the relaxation is obtained. We conclude that in these materials the iron is present as high-spin Fe(III) and that the crystal field splitting constantD is greater than zero. The sign ofV _zz is found to be positive.     

Quantum Derivation of Ginzburg-Landau Equation. New Formula for Penetration Depth

The Cooper pair (pairon) field operator ψ(r,t) changes in time, following Heisenberg’ s equation of motion. If the system Hamiltonian $\mathcal{H}The Cooper pair (pairon) field operator ?(r,t) changes in time, following Heisenberg's equationof motion. If the system Hamiltonian contains the pairon kineticenergies h ₀, the condensation energy per pairon(< 0) and the repulsive point-like potential(r ₁ –r ₂), > 0, the evolution equation for ?is non-linear, from which we obtain the Ginzburg-Landau equation: for the complex order parameter $$ " align="middle" border="0"> , where denotes thestate of the condensed pairons, and n the pairon densityoperator. The total kinetic energy h ₀ forelectron (1) and hole(2) pairons is where are Fermi velocities, and A thevector potential. A new expression for the penetration depth isobtained: where p and n ₀ are respectively themomentum and density of condensed pairons.     

Kondo effect,spin dynamics and magnetism in anomalous rare earth and actinide compounds

The influence of spin dynamics on the Kondo effect manifestations in the Kondo lattices is investigated within perturbation theory with respect to thes-f interaction. It may give rise to Kondo-like divergencies in the electron self-energy already in the second order, resulting in an appreciable effective mass enhancement. As for usual Kondo contributions to thermodynamic and transport properties, the effect of spin dynamics reduces roughly to the replacement ln , with the characteristic spin-fluctuation energy. The thermoelectric power of dense Kondo systems is discussed. Singular contributions to the electron self-energies in the ferro-and antiferromagnetic state are considered. Kondo-like corrections to the intersite exchange interactions, saturation magnetic moment and total energy in a magnetically ordered state are calculated. The strong-coupling regionT<T _K is investigated within the Anderson lattice model. A decrease ofT _K due to spin fluctuations is demonstrated.     

Hyperfine interaction of166Er impurities implanted in iron and nickel

Sources of¹⁶⁶Ho implanted in iron and nickel foils have been studied by means of Mössbauer spectroscopy on the 80.6 KeV transition in¹⁶⁶Er. The spectra could be fitted with a unique hyperfine interaction in the temperature range studied (4.2–78 K). At 4.2 K the hfi parameters wereB _hf=7.68(13) MG and 1/4e ² qQ=+0.288(9) cm/s=+187(6) MHz. The temperature dependence of the hyperfine interaction could be described reasonably with a localized moment model with an exchange field of 3.7 MG acting on the Er electron spin. The spectra could be decomposed into 2 components of about equal intensity, component 1 withB _hf=7.01 (14) MG, 1/4e ² qQ=+0.20(3) cm/s =+130(20) MHz and component 2 withB _hf=4.76(9) MG and 1/4e ² qQ=+0.114(11) cm/s=+74(7) MHz. From a measurement on an annealed source it is concluded that component 2 is associated with ions in substitutional sites, whereas the ions contributing to component 1 probably are associated with vacancies. Internal oxidation of the rare earth impurities, which was suggested as the origin of the non-substitutional fraction in these systems, is completely absent in our samples.     

Limiting behavior of asymptotically flat gravitational fields

Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that , (d/dr) and (/x ^A ) , wherex ^A (A = 2, 3) are angular coordinates, they show that , where ₁ 2 and ₁<₀; , where ₂ 1 and ₁< ₁; and ₄ and ₃ peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption , (d/dr) , and (/x ^A ) does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.In part based on a dissertation by Stephanie Novak and submitted to Syracuse University in partial fulfillment of the requirement for the Ph.D. degree.     

Phonon-Exchange Attraction. Optical Phonons and Type II Superconductivity, and d-Wave Cooper Pairs

The electron-pair density matrix (k ₁, k ₂; k ₃, k ₄, t) =: (1, 2; 3, 4, t) changes in time, following a quantum Liouville equation \rho (5,6;3,4,t) - < 5,6|v_c |3,4 >\rho (1,2,5,6,t)} \right]} } $$ " align="middle" border="0"> with : = 4\pi e^2 k_0 (\Omega q^2 )^{ - 1} \delta _{k_1 + k_2 ,k_3 + k_4 } \delta _{k_s - k_1 ,q} $$ " align="middle" border="0"> in the presence of a Coulomb interaction _c, where is the volume. If the virtual phonon exchange is in action, the density matrix is shown to change similarly with an effective interaction _e, \hfill \\ = |V_q |^2 \bar h\omega _q |(\varepsilon _3 - \varepsilon _1 )^2 - \bar h^2 \omega _q^2 |^{ - 1} \delta _{k_1 + k_2 ,k_3 + k_4 } \delta _{k_3 - k_1 ,q} \hfill \\ \end{gathered} $$ " align="middle" border="0"> , by using a time-dependent perturbation theory and a Markoffian approximation. The dominant longitudinal-acoustic-(optical)-phonon-exchange attraction at 0K is shown to be q-independent (-dependent). The results are used to discuss the Cooper pair size, the origin of type II superconductivity and the formation of d-wave Cooper pairs in the cuprates.