Frequency and temperature dependencies of a.c. conductivity of polyvinyl alcohol (PVA)-CoCl2 composites

The a.c. conductivity for polyvinyl alcohol (PVA)-CoCl₂ composites prepared by a casting method has been measured at different frequencies (0.1–10 kHz) in the temperature range 300–450 K. At constant temperature, the frequency dependence of a.c. conductivity, (), was found to fit the established equation () = A ^s quite well. On the other hand, the temperature dependence of a.c. conductivity suggested an electronic hopping conduction mechanism in a thermally assisted electric field. Various theoretical mechanisms have been discussed to clarify the conduction processes in these samples. The correlated barrier hopping (CBH) mechanism, proposed by Elliott, was found to be the most appropriate one.     

Longitudinal dielectric function and collective surface oscillations in superconductors

The electrodynamic approach to the problem of collective oscillations in superconductors is considered. The kinetic equation for quasiparticles is used to find the longitudinal dielectric function ₁ (, k) of a pure superconductor at ( is the collision frequency). With the help of the evaluated ₁ (, k) the existence of collective oscillations localized near the boundary of the superconductor is investigated.     

Electron-phonon coupling as a mechanism for high-temperature superconductivity

We have solved the Eliashberg gap equations which are valid for arbitrary phonon frequency, (_ph), electron-phonon coupling constant, (), and screened Coulomb interaction, ( ^*). We have used values of (_ph),, and ( ^*) appropriate to the cuprate superconductors, and calculated the density of states, the pair potential., and the value of the gap at T=0 K. Using the linearized Eliashberg equations in the matrix representation, we have calculatedT _c and 2/k T _c . We have found that we can account for the highT _c 's in the cuprates with reasonable values for, ^*, and _ph.     

NMR Studies on 3He-3He and 3He-4He tunneling motions in solid 3He-4He mixtures

Helium-3 nuclear spin relaxation times T ₁, T ₂, and T ₁have been measured for ³He-⁴He solid mixtures at the exchange plateau region (~0.5K). The ³He concentrations X ₃of the samples were 7.2, 2.9, 1.8, 1.4, 0.67, 0.65, and 0.22%, and their molar volumes varied between 19.9 and 20.9cm³/mole in hcp phase. The spectral density function J() for dipolar field fluctuations was determined in the low-frequency branch from T ₁measurements and in the high-frequency branch from conventional T ₁measurements. It was found that J() is given by J() = cJ()|_3–4 + (1–c)J()|_3–3, where J()|_3–4 is the spectral density function due to the ³He-⁴He tunneling motions, and J()|_3–3 is that due to the ³He-³He tunneling motions. Using the Torrey theory, the correlation frequency of the ³He-⁴He tunneling motions was evaluated from T ₁data, and was found to be in good agreement with Landesman 's theory.Supported in part by the Japan Society for the Promotion of Science through a grant to Y.H.     

The specific heat and critical magnetic field of superconducting PdH(D)

From the solution of the Eliashberg equations on the imaginary axis, the thermodynamic properties, specific heat, and critical magnetic field of PdH(D) have been calculated. The Eliashberg kernels ²()F() were constructed using a published value of ²(), and F() was obtained from inelastic neutron scattering data. The results for the specific heat are in good agreement with published experimental data. The critical magnetic field shows a nearly parabolic behavior as a function of temperature, in disagreement with the linear experimental behavior. The deviation function D(t) and the ratios C(T _c)/T _c and [T _c/H _c(0)]² indicate that the PdH(D) system is BCS-like. The functional derivative of T _c with respect to changes in the kernel is also calculated.On sabbatical leave from the Instituto de Investigaciones en Materiales, UNAM, Mexico.     

Thermodynamic properties of superconducting niobium

The thermodynamic properties of superconducting Nb are calculated numerically from the solution of the Eliashberg equations on the imaginary axis for several possible electron-phonon spectral densities ²()F(). Comparison with experiment is made in order to see which spectrum gives the best agreement, and functional derivatives with respect to ²()F() are used to estimate how this agreement might be improved by small changes in ²()F(). Possible gap anisotropy effects are also considered with the help of a simple model anisotropy for the interaction.Research supported by Natural Science and Engineering Research Council of Canada.     

Axi-symmetric natural frequencies and response of a spinning liquid column under strong surface tension

Summary The response of a solidly rotating anchored finite liquid column consisting of frictionless liquid is subjected to axial harmonic excitation. The response of the free liquid surface elevation and velocity distribution has been determined analytically in the elliptic (>2 ₀) and hyperbolic frequency range (>2 ₀). For the liquid surface displacement the response has been evaluated numerically as a function of the forcing frequency/2 ₀. In addition the first natural stuck-edge frequency has been determined and compared with the slipping case.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - Weber number - z₀ axial excitation amplitude - elliptic case (>2 ₀) - hyperbolic case (>2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _0n natural frequency of harmonic axial response     

Frequency dependence of the spin-fluctuation spectrum in Pd: Calculations within the finite bandwidth model

The frequency dependence of the electron-paramagnon spectrumP() in Pd is calculated within the finite bandwidth model. It is found that for an almost full band, the magnitude, the range, and the position of the peak frequency inP() are dramatically reduced compared to their values in the usual paramagnon theory. Also, we find that the frequency dependence of the spin-fluctuation contribution to the electron self-energy is strongly affected by a close proximity of the Fermi level to the top of the band. We speculate that an unusually large value of the Coulomb pseudopotential is probably partially responsible for the absence of superconductivity in Pd.     

Neutron scattering as a probe of particle-like excitations in superfluid4He: A model calculation

In the microscopic theory of Bose-condensed liquids, the condensate wave function leads to a coupling of the density fluctuations and the single-particle excitations. A simple parametrized model of this based on coupling weakly damped zero-sound modes with strongly damped free-particle-like excitations Q ²/2m* explains why the phonon-roton resonance inS(Q, ) for superfluid⁴He exists above and belowT but only plays the role of an elementary excitation belowT . It is pointed out that this model also predicts thatS(Q, ) should exhibit a weak, low-frequency peak centered atQ ²/2m*, with weight roughly proportional to the condensate fractionn ₀. As a stimulus to further experimental searches for this branch, some model calculations are given forS(Q, ) forQ1 Å^–1.     

Viscous response of an anchored spinning liquid column to various axial excitations

Summary For a solidly rotating viscous cylindrical liquid column of finite length the response to axial synchronous, counter- and one-sided excitation is determined for anchored contact lines at the disc-rim. For a rotating column additional responses of inertial waves (hyperbolic range) appear for < 2 ₀, while in the elliptic range < 2 ₀ the sloshing response occurs. The various responses for the free surface displacement have been numerically evaluated. Only in the one-sided exitation case all resonance peaks appear, while for synchronous excitation only the odd resonances and for counter-excitation only the even resonance peaks occur.Notation a radius of column - h length of liquid bridge - I _n modified Bessel function - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution - Weber number - z ₀ excitation amplitude - liquid density - surface tension - surface tension parameter - Ohnesorge number - liquid surface displacement - kinematic viscosity - ₀ rotational speed - dimensionless rotational speed - forcing frequency - dimensionless forcing frequency - dimensionless forcing frequency for non-viscous liquid - a= root of bi-cubic Eq.(33) - root of bi-cubic Eq.(33)     

Impulse approximation in solid helium

The incoherent dynamic form factorS _i(Q, ) is evaluated in solid helium for comparison with the impulse approximation (IA). The purpose is to determine theQ values for which the IA is valid for systems such as helium where the atoms interact via a potential having a steeply repulsive but not infinite hard core. For³He,S _i(Q, ) is evaluated from first principles, beginning with the pair potential. The density of statesg() is evaluated using the self-consistent phonon theory andS _i(Q, ) is expressed in terms ofg(). For solid⁴He reasonable models ofg() using observed input parameters are used to evaluateS _i(Q, ). In both casesS _i(Q, ) is found to approach the impulse approximationS _IA(Q, ) closely for wave vector transfersQ20 Å^–1. The difference betweenS _i andS _IA, which is due to final state interactions of the scattering atom with the remainder of the atoms in the solid, is also predominantly antisymmetric in (–_R), where _R is the recoil frequency. This suggests that the symmetrization procedure proposed by Sears to eliminate final state contributions should work well in solid helium.     

Hot electrons in metals at low temperatures

Hot electrons in metals at helium temperatures under steady conditions can be produced by passing an electric current of moderate density ( 10⁶ A/cm²) through thin, narrow (~1 m wide) metallic films in good thermal contact with bulk single-crystal dielectric substrates. This paper is concerned with the theory of hot electrons in normal metals at low temperatures (when _D, where is the average electron energy and _D is the Debye temperature). The theory is formulated in terms of realistic electron and phonon dispersion laws, taking into account the experimental possibility of heat removal from the sample. In the case in which the temperature approximation of Kagnov, Lifshitz, and Tanatarov is not satisfied when elastic scattering of electrons is dominant in a steady state electric field, the kinetic equation is derived for the energy-dependent, hot electron distribution function, which determines the associated nonlinear responses. The solution of this equation is discussed for a simple model. It is shown that the experimental information on the electron-phonon interaction in a metal can be obtained in terms of the well-known spectral functions S() ² F() and g() _tr ² F(). This is illustrated by experiments determining the nonlinear field dependence of the resistance, by tunnel experiments, and by critical current hysteresis measurements (for superconducting metals). Theoretical estimates which support the observability of the effects under discussion are presented.     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

Critical field and specific heat of superconducting Tl-Pb-Bi alloys

The Eliashberg kernels ² ()F() obtained from tunneling experiments for a series of weak to strong coupling Tl-Pb-Bi alloys are used to calculate numerically on the imaginary axis the thermodynamic properties of these alloys in the superconducting state. The functional derivatives ofT _c andH _c with respect to changes in the kernel are also calculated.Research supported by the National Research Council of Canada.Partially supported by Conacyt, Mexico.     

4He very nearT λ heated from above

We discuss the feasibility and likely results of measurements of the thermal conductivity (Q,t) of⁴He very nearT T (Q = 0) as a function of the heat currentQ and the reduced temperature t [T —T]/T by heating a sample from above and cooling it from below. Although the expansion coefficient is negative, the experiment should be possible without inducing convection in the HeI layer provided the sample length does not significantly exceed one cm. Fort 10^–7(Q 0.2 erg/s cm²), a state of self-organized criticality can be attained. For these conditions, the thermal gradient cancels the gradient inT induced by gravity, thus permitting measurements extremely close to the transition even in an Earthbound laboratory. However, the data will be only for a unique path in the Q—t plane. For 0.2 Q 0.5 erg/s cm² (10^–7t 10^–8) they will be in the range of linear response and give (0,t); for Q between about 0.5 and 10 erg/s cm² and over a temperature range of about 20 nK, the experimental path samples the regime where the conductivity is expected to be influenced by nonlinear finite-current effects. The small currents and narrow temperature range of the experiment imply that ultra-high resolution thermometry as well as very careful control of stray heat currents will be required. ForQ 10 erg/s cm² and up to very largeQ, the method can be used to determine the onset temperatureT _c (Q) of thermal resistance.     

A.c. conductivity for amorphous TeO2-P2O5 glass system

The a.c. conductivity for the TeO₂-P₂O₅ glassy system was measured in the temperature range 300–573 K and in the frequency range 100 Hz to 10 kHz. The a.c. conductivity () increased with frequency according to the relation ()^s. The frequency exponent s was found to decrease with increasing temperature. The composition dependence of the conductivity was also investigated. The density of states was also calculated using the Elliott model. The a.c. conductivity increased over the studied temperature range. The obtained experimental data have been analysed with reference to various theoretical models. The analysis shows that the correlated barrier hopping (CBH) model is the most appropriate mechanism for conduction in the TeO₂-P₂O₅ glass system.     

A new formalism for time-dependent electromagnetic scattering from a bounded obstacle

In this paper a time-dependent three-dimensional electromagnetic scattering problem is considered. Let R ³ be the three-dimensional real Euclidean space filled with a medium of electric permittivity , magnetic permeability and zero electric conductivity. The quantities , are positive constants and there are no free charges in the space and the free current is taken to be zero. Let R ³ be a bounded simply connected obstacle with a locally Lipschitz boundary , that is assumed to have a nonnegative constant boundary electromagnetic impedance. The limit cases of perfectly conducting and perfectly insulating obstacles are studied. An incoming electromagnetic wave packet that hits is considered, and a method that solves the Maxwell equations to compute the corresponding electromagnetic field scattered by as a superposition of time harmonic electromagnetic waves is proposed. These time-harmonic electromagnetic waves are the solutions of exterior boundary-value problems for the vector Helmholtz equation with the divergence-free condition and they are computed with an `operator expansion' method that generalizes the method presented by L. Fatone et al.[J. Math. Phys. 40 (1999) 4859–4887]. The method proposed here is computationally very efficient. In fact, it is highly parallelizable with respect to time and space variables. Several numerical experiments obtained with a parallel implementation of the method are shown. The numerical results obtained are discussed from a numerical and a physical point of view. The quantitative character of the numerical experiments shown is established. The website: http://www.econ.unian.it/recchioni/w4/ contains some animations relative to the numerical experiments.     

Natural frequencies and response of spinning liquid column with apparently sliding contact line

Summary The contact line of a liquid with a solid does in many cases—depending on the smoothness of the solid, the viscosity, the surface tension and the excitation force—apparently flow along the solid during oscillations. The influence of this effect upon the natural frequencies, the stability and the response of the system has been investigated at an oscillating and spinning cylindrical liquid column.List of symbols a radius of liquid bridge - h length of liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - p liquid pressure - r, ,z cylindrical polar coordinates - t time - u, v, w velocity distribution in rotating liquid - Weber number - axial excitation amplitude - elliptic case ( > 2 ₀) - hyperbolic case ( > 2 ₀) - liquid density - surface tension - liquid surface displacement - acceleration potential - ₀ rotational speed - axial forcing frequency - natural frequency of rotating system - _on natural frequency of harmonic axial response     

Effect of phase transitions in copper-germanium thin film alloys on their electrical resistivity

An investigation was carried out to study the phase transitions in Cu-Ge thin films (80–200 nm in thickness) containing 0, 5, 15, 20, 25, 30, 35, 40, 45 and 50 at% Ge, and the corresponding effects on electrical resistivity. For these films, the phase transitions were found to follow the sequence: -phase (disordered face centred cubic, fcc, solid solution); 5 at% Ge -phase (disordered hexagonal close packed, hcp); 15 at% Ge -phase + ₁-phase (ordered orthorhombic, Cu₃Ge); 20 at% Ge ₁-phase; 25 at% Ge (₁-phase + progressively increasing proportions of a disordered Ge-rich solid solution); 30–50 at% Ge. Germanium was found to have no marked effect on grain size of all films studied excluding grain boundaries as electron scattering centres. Transition of the -phase into the -phase was found to occur in a highly coherent manner, which could be related to the reduced stacking fault energy of Cu by the addition of Ge. Most evidence pointed out that the initial increase in resistivity within the -phase range was related to hcp scattering centres, which could be associated with a localized high concentration of Ge. At 15 at% Ge, the resistivity reached a maximum value of about 50 cm associated with the complete transformation of -phase into the -phase. With continued increase in Ge concentration, the resistivity was found to gradually decrease reaching a minimum value of about 10 at 25 at% Ge, which was correlated with complete transition of the -phase into the ordered ₁-phase (Cu₃Ge). It was shown that the superlattice of Cu₃Ge could directly be derived from the disordered -phase by minor atom rearrangement on the [0 0 0 1]_hcp plane. Even though, minor proportions of a Ge-rich solid solution containing a small concentration of Cu were formed at Ge concentrations above 25 at%, the minimum resistivity of 10 cm was maintained as the Ge concentration was increased to 35 at%. Subsequently, the resistivity was increased reaching about 46 cm at 50 at% Ge.     

Stability of the nonequilibrium state of a superconductor irradiated by an electromagnetic field

Irradiation of a superconductor by an electromagnetic field with a frequency ₀ larger than twice the energy gap (order parameter) decreases the order parameter . We obtain the quasiparticle distribution function n and the dependence of the order parameter on the power of the electromagnetic field P by solving numerically the kinetic equations for n and in the steady state. We take ₀/₀ = 2.1, 8, and 20, where ₀ is the equilibrium value of the order parameter at T = 0 K. In the examples considered the dependence of on the pumping power P becomes double-valued above a critical power. We allow phonons also to be out of thermal equilibrium. To discuss the stability of the steady state thus obtained, we derive kinetic equations for small deviations of the quasiparticle distribution function and the order parameter from the steady state n and by means of the nonequilibrium Green's function theory. Assuming n, exp(i kr – t), (k) is computed using n _s/, where n _sis the steadystate quasiparticle distribution function for arbitrary . It is concluded in general that the steady state on the upper branch ( > _{c 2}) is stable with respect to both spatially homogeneous and inhomogeneous fluctuations, and the lower branch ( > _{c 2}) is unstable; _{c 2}is the value where the upper and lower branches of (P) coalesce.This work is partly supported by a Grant-in-Aid for Special Project Research from the Ministry of Education, Science and Culture of Japan.