Theory of periodically driven,current-carrying,superconducting filaments. I. Spatially homogeneous states

Starting from the nonequilibrium theory of dirty superconductors in the Ginzburg-Landau regime, spatially homogeneous states with an applied currentI=I ₀+I ₁ cos (t) are considered. Expressions for the linear response (I₁ small) valid up to high frequencies (k _BT_c) are derived and evaluated analytically for the experimentally important case of smallI ₀ and ₀(T). Then the nonlinear response is treated for frequencies with _E1. Interesting new behavior is found for frequencies ₀ 1, where ₀ is essentially the GL relaxation time.     

Dielectric properties of thin solid films formed on silicon

We report on the measurement of the frequency-dependent complex permittivity, ()=()-i(), over the frequency range, 30 MHz to 6 GHz, of silicon wafers and of thin dielectric films formed on silicon. Measurements, as a function of temperature and time treatments, were obtained by means of an HP Network Analyzer and dielectric probe and the resulting ()and()plots for the silicon wafers are shown to have a Debye-type [1] profile, thereby indicating that the associated polarization mechanism is of the orientational variety.     

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.     

Thermodynamic properties of the superconductorsBaPb 0.7 Bi 0.3 O 3 andBa 0.7 K 0.3 BiO 3 using Eliashberg theory

We present results of a thermodynamic analysis for the superconductors compounds BaPb_0.7Bi_0.3O₃ and Ba_0.7K_0.3BiO₃. The physical quantities are calculated making use of the Eliashberg theory and the electron-phonon spectra ²()F() as calculated by Shirai et al. For the superconductor BaPb_0.7Bi_0.3O₃, several models of the ²()F() were studied looking for a better agreement with experimental data. The best fit is achieved with a simple constant scaling (C = 1.25) of the Shirai's spectra. The functional derivative of the deviation function D(t) with respect to changes in ²()F() is also calculated.     

Normal-State Optical Response Functions of MgB2 Superconductor

The reflectivity of superconducting MgB₂ (T _c = 39 K) has been measured on a randomly oriented thin film at room temperature over a wide-range of frequencies, 20 < 100000 cm^–1. The conductivity shows highly metallic behavior but cannot be explained with a simple Drude model alone. The electronic contribution is analyzed by a generalized Drude model. The scattering rate 1/() and the mass renormalization ratio m*()/m = 1 + () exhibit clear frequency dependence. The electron–phonon coupling strength is estimated to be 1.5 ± 0.5 while the plasma frequency _p is 2.4 eV.     

Theory of neutron scattering from the two-roton,two-maxon and maxon-roton states in superfluid4He

In 1970, Ruvalds and Zawadowski (RZ) outlined a microscopic theory of the two-roton pair excitation spectrum in superfluid⁴He. They pointed out that because of a Base condensate-induced coupling into the density fluctuation spectrum, these pair excitations show up in inelastic neutron data for S(Q, ) as high energy multiparticle scattering above the maxon-roton quasiparticle peak. Stimulated by recent high-resolution neutron data from ILL, we have carried out an extensive study of the single-particle ₁(Q, ) and the two-particle ₂(Q, ) spectral densities within the RZ scenario, over a wide range of wavevectors (1 Q 3 Å^–1), frequencies and temperatures. We extend the original RZ analysis (which concentrated on the two-roton spectrum) to include the multiparticle structure associated with the maxonroton and maxon-maxon spectra and present numerical results for both attractive and repulsive quasiparticle interactions. We also point out that the microscopic theory of S(Q, ) in a Bose-condensed fluid shows that it involves a weighted sum of both ₁(Q, )and ₂(Q, ). As a result, multiparticle structure exhibited by S(Q, ) is not easily related to theoretical results for ₁(Q, ) and ₂(Q, ). Previous attempts in the literature to fit neutron data for S(Q, ) to either ₁(Q, ) or ₂(Q, ) would not appear to have much quantitative basis, especially in the two-roton frequency region 2_R.     

Spectral shape dependence in the very strong coupling regime of Eliashberg theory

The effect of ² F() shape dependence on several physical properties of superconductors is studied at various values of the strong coupling indexT _c/ _ln . Our results indicate that the degree of shape dependence of each property is sensitive to the value ofT _c/ _ln . Generally, for the region we examine, 0.25T _c/ _ln 1.3, the dependence on shape is found to be higher than in the conventional strong coupling regimeT _c/ _ln 0.2. However, with the exception of the mass enhancement parameter , the amount of shape dependence does not increase steadily withT _c/ _ln and there appears to be regions of maximum shape sensitivity.     

Breakup of an anomolously viscous liquid film in a centrifugal force field

An equation is obtained for the breakup radius with consideration of tipping moments and Laplacian pressure forces acting on the liquid ridge at the critical point.Notation K, n rhenological constants - density - surface tension - r current cup radius - R maximum cup radius - r_c critical radius for film breakup - ¯r=¯r=r/R dimensionless current radius - ¯r_c=r_c/R dimensionless critical radius - ₀, _c actual and critical film thicknesses - current thickness - R_r ridge radius - h₀ ridge height - h current ridge height - ₀ limiting wetting angle - current angle of tangent to ridge surface - angle between axis of rotation and tangent to cup surface - angular velocity of rotation - q volume liquid flow rate - v₁ and v meridional and tangential velocities - =4vv _lm/r,=4v_m/r dimensionless velocities - M moments of surface and centrifugal forces - M_v moment from velocity head - p_r pressure within ridge - P_vm pressure from velocity head - p_m, p_pm pressures from centrifugal force components tangent and normal to cup surface - deviation range of breakup radius from calculated value - ¯r_max, ¯r_min limiting deviations of breakup radius - _c angle of tangent to curve _c/°₀=f(¯r) at critical point - t random oscillation of ratio _c/_c Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 51–56, July, 1980.     

Signal and noise theory for a dc SQUID amplifier

A theory is presented for the gain and noise in an amplifier based on a dc SQUID. In the lumped circuit approximation, the total inductance of the input circuitL _T is coupled to the SQUID inductanceL via a mutual inductanceM _ii = _e (LL _T )^1/2 and is in series with a voltage source with a resistanceR _i and a capacitanceC _i . The results are expressed in terms of parameters for a SQUID with reduced inductance (1– _e ² )L. The voltage gain of the amplifier at frequency /2 isM _i V ^r /Z _T ^* (), while the total voltage noise at the output of the SQUID isV _N ^r ()+M _i ² V ^r J _N ^r () (R _i + 1/jC _i )/L _TZ _T ^* (). Here,Z _T ^* ()=Z _T ()–J ^r M _i ² (R _i + 1/jC _i )/L _i , whereZ _T () is the total impedance of the unloaded input circuit,V ^r andJ ^r are the flux-to-voltage and flux-to-circulating current transfer functions of the reduced SQUID, andV _N ^r () andJ _N ^r () are the noise voltage and noise current of the reduced SQUID.     

Functional derivative ofT c with α2(ω)F(ω) for weak coupling anisotropic superconductors

Approximate analytic calculations of the functional derivative ofT _c with respect to ²()F() for anisotropic superconductors are presented, with the primary purpose of identifying the determining material parameters. The square-well model for the phonon-mediated electron-electron interaction, the weak coupling limit ( _c /2T _c 1), and separable anisotropy are used. The general behavior of T _c /²()F() is the same as that found in numerical calculations for the case of small anisotropy, a ²/(–*)1; the regime of * is also discussed.     

The athermal α → ω transformation in Zr-2 at% Nb alloy

The athermal transformation in Zr-2 at.% Nb alloy has been investigated by transmission electron microscopy. Analysis of the selected-area diffraction pattern has shown that the orientation relationships between the omega and the parent-phase in quenched Zr-2 at.% Nb alloy are the same as have been previously observed for the reaction in pure zirconium. Thus it was deduced that the direct transition has taken place in the alloy during cooling. The-originated -particles were visualized using the dark-field technique. The formation of the athermal omega in the-region of-stabilized Zr-Nb alloy is discussed in terms of the relative positions of the free energy equilibrium curvesT ₀ ,T ₀ ,T ₀ and the correspondingM _s ,M _s andT _s start curves. It is concluded that the omega phase can occur over a much wider range of alloy compositions than is usually recognized on the basis of transformation data.     

Deformation Phenomena on the Charged Helium Film in Presence of Cyclotron Pumping

The possibilities are discussed for the investigation of 2D quasienergetic electron states on liquid helium surface in presence of the normal magnetic field and a.c. electric field E with the frequency _c, where _c is the cyclotron frequency.     

Solutions to the dispersion equation for transverse sound in a Fermi liquid with nonzero LandauF 2

The Boltzmann equation for the Fermi-liquid quasiparticle distribution on the Fermi surface is expanded in spherical harmonics of symmetry appropriate to transverse sound, of which all higher terms relax together with relaxation time . Assuming a solution exp[i(kz – t)], one obtains a dispersion equation for complex /k. In the zero-sound limit,T 0 and , real solutions exist for /k v _F when the LandauF ₁>6 as quoted experimentally andF ₂<0, supporting a previous theory of thermal conduction, where a fit to experiment also gaveF ₂<0. Undamped modes can also exist forF ₁<6,F ₂/s>0, which were not found by Abrikosov and Khalatnikov and Lea and co-authors, who neglectedF ₂. In the hydrodynamic limit, isO(k ²) and imaginary, indicating relaxational behavior for transverse first sound in agreement with earlier treatments. Existence of highly damped modes atT=0 is examined, and it is found most can be ruled out by the principle that LandauF _n parameters decrease in magnitude withn.     

Eliashberg analysis of the specific heat of Nb0.75Zr0.25

The specific heat of Nb_0.75Zr_0.25 is measured from 1.2 to 50 K in zero magnetic field. A phonon density of statesF() and a spectral electron-phonon coupling function ²()F() are fitted to the data in the normal state and in the superconducting state. The results are compared with a previous similar analysis of the specific heat of pure Nb and with published tunneling data. It is found that in Nb_0.75Zr_0.25, –*=1.13, _log=109 K, and N(0)=0.85 eV^–1 at^–1 spin^–1, compared with the figures 0.84, 146 K, and 0.85 eV^–1 at^–1 spin^–1, respectively, in pure Nb. These data confirm that the increase ofT _c upon the alloying of Nb with Zr is due to phonon softening. They further show that the electronic density of states at the Fermi level is identical in Nb and Nb_0.75Zr_0.25. Dimensionless thermodynamic ratios predicted from tunneling data are entirely confirmed, thus confirming the internal consistency of the Eliashberg theory for superconductivity.     

Absence of Phase-Fluctuation Contribution to the Low-Frequency Optical Conductivity in d-Wave Superconductors at Zero Temperature

The behavior of the low-frequency optical conductivity _reg() in superconducting cuprates is, at the present, an open and interesting issue. In particular, since the zero-temperature and zero-frequency limit of _reg() attains a value much larger than the universal value expected within a self-consistent T-matrix calculation, an intriguing possibility is that the collective mode can also contribute to _reg(). By taking into account the effect of dissipation on the collective mode in a d-wave superconductor, we evaluate the phase-fluctuation contribution to _reg(0) within the formalism of the phase-only action. We show that even though the collective mode contributes to _reg() at finite frequencies, approaching the zero-temperature and zero-frequency regime the corrections at _reg() due to phase fluctuations vanish.     

Phase transformations in Ti-Nb-Ta and Ti-Nb-Ta-Zr alloys

Phase transformations in solution treated and quenched Ti-(13-26) Nb-(22-38) Ta (wt.%) and Ti-(13-35.5) Nb-(5-22) Ta-(4-7.2) Zr alloys have been studied. It has been observed that phase transformations in these alloys are sensitive to both composition and cooling rate. In ternary alloys, water and oil quenching resulted in the formation of orthorhombic martensite () in a retained + _athermal matrix, whereas slower cooling showed evidence of fine and _isothermal formation within the matrix. Increase of Nb + Ta content decreases the volume percentage of martensite. Moreover, addition of Zr stabilized the phase, lowered the martensite start temperature and suppressed formation. Finally, dynamic moduli of air cooled quaternary alloys showed that the modulus was sensitive to the composition, a minima at Nb/Ta ratio of 12.0 and 5 at% Zr being observed, this minimum in dynamic modulus being consistent with phase suppression.     

Tunneling spectrum analysis regarding phonon contribution to highT c cooper pairing

Improved tunneling spectroscopy with point contact junction of [BSCCO (2212) / SiO_x] / Au-tip provided us information of the quasi-particle that mediates the high T_c Cooper pairing. Fine structure in the tunneling conductance derivative spectrum d²I/dV² — V reflects the quasi particle coupling spectrum function ²()F(gw), and really significant peaks have been observed ranging to 0.2eV. Their peak energy level eV_i could be systematically assigned by eV_i – = n₀ + h_i(ph) with n=0, 1, 2, Here h_i, means each phonon mode energy, and the characteristic energy ₀ = 72 meV was found to correspond to the breathing mode which is essentially Cu-O bond stretching mode. This means that these characteristic phonons play a significant role on the high T_c superconductivity. Similar peak series had been also observed in the infra-red (IR) optical reflection spectrum, R() by Capizzi et al. The Cooper pairing characteristics are discussed from the comparison between both spectra of the tunneling and the IR.     

Surface waves in a rotating fluid due to sources and internal boundaries

Summary The problem of surface waves generated by an oscillatory point source oscillating with frequency in a fluid rotating with constant angular velocity has been investigated. The Green's function solution is obtained for an unbounded region and a region bounded internally by a circular cylinder using an appropiate Fourier transform. It is seen that in the case when >2, the surface waves are similar to the ones existing in a potential flow but when <2, the surface waves correspond to the inertial waves which are generated entirely due to rotation and have no counterpart in a non-rotating fluid motion.

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Oberflächenwellen in einer rotierenden Flüssigkeit als Folge von Quellen und Randbedingungen

Zusammenfassung Es wird das Problem der Erzeugung von Oberflächenwellen durch eine oszillierende Punktquelle (Frequenz ) in einer rotierenden Strömung (Winkelgeschwindigkeit ) untersucht. Die Greensche Funktion wird für einen unbegrenzten Bereich sowie für das Äußere eines Kreiszylinders durch eine geeignete Fouriertransformation hergeleitet. Für >2 sind die Oberflächenwellen ähnlich denen einer Potentialströmung, für <2 ergeben sich Wellen, die vollständig durch die Drehbewegung bedingt sind und die kein Gegenstück im nichtrotierenden Fall besitzen.

     

Transverse acoustic impedance of normal liquid3He

Both the real and imaginary parts of the transverse acoustic impedance of normal liquid³He have been measured at excitation frequencies of 10 and 30 MHz, fluid pressures from 0.7 to 27 bar, and temperatures from 3 mK to 1 K. The impedance is obtained from the changes in resonance frequency and Q of a quartz crystal, which is electrically driven to oscillate in a thickness shear mode while immersed in liquid³He. These results are compared with the predictions of Fermi liquid theory, which takes into account two contributions to the impedance: (1) incoherent single-quasiparticle excitations, and (2) the excitation of the collective transverse sound mode. At 0.7 bar, our measurements of the impedance are in agreement with the predictions of Fermi liquid theory and imply that the symmetric Fermi liquid parameterF ₂=1.25±0.4 ifF ₁=6.3. At higher pressures, we also observe agreement in the region <0.3, where is the excitation frequency and is the quasiparticle scattering time. However, above 8 bar in the zero-sound regime (1), the impedance is observed to be frequency dependent, at constant . This frequency dependence cannot be explained within the present framework of Fermi liquid theory.This work was supported by the National Science Foundation under Grants DMR 76-02043 and DMR 78-08650.     

On the motion of a heavy rigid body about a fixed point

Summary The paper considers the classical problem of the motion of a heavy rigid body about a fixed point. The Euler-Poisson equations are used for the presentation of that motion. Three first integrals of these equations are well known. To solve this problem completely one further first integral has to be found. The main purpose of the paper is to obtain a necessary and sufficient condition for some functionF(₁,₂,₃, ₁, ₂, ₃) to be a new first integral of Euler-Poisson equations.