Orientational dynamics of superfluid He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

On the theory of temporal aberrations for cathode lenses

A new approach to the theory of temporal aberration for cathode lenses is given in the present paper. A definition of temporal aberration is given in which a certain initial energy of electron emission along the axial direction ε_z1 (0ε_z1ε_0max) is considered. A new method to calculate the temporal aberration coefficients of cathode lenses named “direct integral method” is also presented. The “direct integral method” gives new expressions of the temporal aberration coefficients which are expressed in integral forms. The difference between “direct integral method” and “τ-variation method” is that the “τ-variation method” needs to solve the differential equations for the three of temporal geometrical aberration coefficients of second order, while the “direct integral method” only needs to carry out the integral calculation for all of these temporal aberration coefficients of second order.All of the formulae of the temporal aberration coefficients deduced from “direct integral method” and “τ-variation method” have been verified by an electrostatic concentric spherical system model, and contrasted with the analytical solutions. Results show that these two methods have got identical solutions and the solutions of temporal aberration coefficients of the first and second order are the same as with the analytical solutions. Although some forms of the results seem different, but they can be transformed into the same form. Thus, it can be concluded these two methods given by us are equivalent and correct, but the “direct integral method” is related to solve integral equations, which is more convenient for computation and could be suggested for use in practical design.     

Internal dynamics of hydroxymethyl rotation from CH2 cross-correlated dipolar relaxation in methyl-β- -glucopyranoside

Conventional relaxation parameters (T₁⁻¹, T₂⁻¹, and NOE), obtained at different temperatures and magnetic fields, are reported for the hydroxymethyl (C6) carbon in methyl-β- -glucopyranoside in a D₂O/DMSO cryosolvent. These data are interpreted with the Lipari–Szabo model. In addition, two-field measurements of longitudinal and spin-locked relaxation rates related to the cross-correlated carbon–proton dipole–dipole interactions for the same carbon are reported. The complete data set consisting the conventional and cross-correlated relaxation parameters is interpreted using a new “hybrid” approach, in which the Lipari–Szabo model for the auto-correlated spectral densities is combined with the two-site jump model for the cross-correlated spectral densities, with the global correlation time as a common parameter. The two-site jump rates thus obtained are in reasonable agreement with the ultrasonic relaxation measurements, and have reasonable temperature dependence.     

Spatial evolution of the generation and relaxation of excited carriers near the breakdown of the quantum Hall effect

We have measured the generation and relaxation of excited carriers along their drift direction near the breakdown of the quantum Hall effect (QHE). The dissipative resistivity ρ_xx(x) at current densities close to the critical value for the QHE breakdown was measured as a function of the distance x from the electron injection at x=0. By injecting “cold” electrons into constrictions at supercritical current levels, the evolution of the breakdown along the drift direction was monitored. After a smooth increase of the resistivity with the drifting distance, an avalanche-like rise towards a saturation value occurs. Drastic changes of the resistivity profiles with the applied current were found in a narrow range around the critical current. The observed behavior is attributed to impurity-assisted tunneling between Landau levels. By injecting hot electrons (excited in a periodic set of constrictions) into a region with subcritical current density, the relaxation process was analyzed. Inelastic relaxation lengths with typical values in the range from 0.3 to 4 μm were found, which agree within 10% with the elastic mean free path determined from the Hall mobility at zero magnetic field. We conclude that the energy relaxation process is triggered by scattering at impurity potentials.     

Compositionally asymmetrical multiquantum wells: “Pseudo-molecules” for giant optical nonlinearities in the infrared (9–11 μm)

Intersubband transitions in quantum well have extremely large oscillator strengths and induce strong nonlinear effects in structures where inversion symmetry is broken, realized by growing AlGaAs quantum wells with asymmetrical A1 gradients. These compositionally asymmetrical multiquantum wells may thus be viewed as giant “quasimolecules” optimized for optimal nonlinearities in the mid infrared. Optical rectification as well as second harmonic generation have been measured in those structures using a continuous CO₂ laser. At 10.6 μm the nonlinear coefficients are more than 3 orders of magnitude higher in these samples than for bulk GaAs (i.e. χ₀⁽²⁾ = 5.3 × 10⁻⁶m/V, χ_2ω⁽²⁾ = 7.2 × 10⁻⁷ m/V) and are in good agreement with theoretical predictions. We present more complex “pseudo-molecules” involving weakly coupled quantum wells. The optical rectification effects in these devices are so large χ₀⁽²⁾ = 1.6 × 10⁻³ m/V) that application to infrared detection may be envisioned.     

Zeroing of the OSL signal in quartz from young glaciofluvial sediments

The natural luminescence of quartz samples from recent (<200 yr old) glaciofluvial sediments collected from a range of distances from the snout of the Gangotri glacier in the Garhwal Himalaya, India, was measured. Six measured D_E (equivalent dose) values ranged from 35 to 175 Gy, strongly suggesting that these samples had been exposed to daylight only poorly before deposition. However, regenerated growth curves constructed after exposure to several hours of natural daylight gave apparent D_E values ranging from 10 to 30 Gy. Detailed measurements of one sample confirm that these observations are due to a huge recuperation effect. The “shine plateaux” observed in the majority of these D_E determinations showed little increase of D_E with increasing exposure time. The mechanisms of this unexpected behaviour, and the implications for the detection of partial bleaching, are discussed.     

Scalar length scales and spatial averaging effects in turbulent piloted methane/air jet flames

The effects of spatial averaging in measurements of scalar variance and scalar dissipation in three piloted methane/air jet flames (Sandia flames C, D, and E) are investigated. Line imaging of Raman scattering, Rayleigh scattering, and laser-induced CO fluorescence is applied to obtain simultaneous single-shot measurements of temperature, the mass fractions of all major species, and mixture fraction, ξ, along 7-mm segments. Spatial filters are applied to ensembles of instantaneous profiles to quantify effects of spatial averaging on the Favre mean and variance of mixture fraction and scalar dissipation at several locations in the three flames. The radial contribution to scalar dissipation, χ_r = 2D_ξ (∂ξ/∂r)², is calculated from the filtered instantaneous profiles. The variance of mixture fraction tends to decrease linearly with increasing filter width, while the mean and variance of scalar dissipation are observed to follow an exponential dependence. In each case, the observed functional dependence is used to extrapolate to zero filter width, yielding estimates of the “fully resolved” profiles of measured quantities. Length scales for resolution of scalar variance and scalar dissipation are also extracted from the spatial filtering analysis and compared with length scales obtained from spatial autocorrelations. These results provide new insights on the small scale structure of turbulent jet flames and on the spatial resolution requirements for measurements of scalar variance and scalar dissipation.     

Effective spin susceptibility, electron mass and Landé factor in two-dimensional (2D) Si inversion layers

We have studied the silicon (Si) band-structure, electron–electron and electron-ionized donor interaction effects on our accurate and approximate results (AcR and ApR) for renormalized effective spin susceptibitity (RESS), electron mass (EEM), Landé factor and spin polarization in the impure 2D Si (electron system), showing that:(i) our ApR, being strongly deviated from our AcR, reproduces approximately all the data obtained recently by Pudalov et al. (Phys. Rev. Lett. 88 (2002) 196404) [in particular, RESS =4.7 at the critical value of Wigner–Seitz radius r_s: r_s=r_c≈8.5 at which occur the “apparent” metal–insulator transition (MIT)] and can also be compared with other ApRs found in the recent literature,(ii) both the RESS and EEM produce physical singularities at the same critical value: r_s=r_c11.05661 (weakly disordered samples) at which occurs the “true” MIT; the existence of such two “apparent and true” critical values in this impure system agrees with a recent discussion by Abrahams et al. (Rev. Mod. Phys. 73 (2001) 251), and(iii) at r_s=r_c=8.5, at which occurs the “apparent” MIT, our AcR for effective spin polarization and the corresponding result, obtained using a disordered Hubbard model and a determinant quantum Monte Carlo method by Denteneer and Scalettar (Phys. Rev. Lett. 90 (2003) 246401), both give the same result: ξ_eff.=ξ_c0.31 at B0.4 T, which is found to be lower than the critical parallel magnetic field for full spin polarization, B_c=1.29 T, supporting thus the existence of such an “apparent” MIT.     

Improved quantification of alite and belite in anhydrous Portland cements by Si MAS NMR: Effects of paramagnetic ions

The applicability, reliability, and repeatability of ²⁹Si MAS NMR for determination of the quantities of alite (Ca₃SiO₅) and belite (Ca₂SiO₄) in anhydrous Portland cement was investigated in detail for 11 commercial Portland cements and the results compared with phase quantifications based on powder X-ray diffraction combined with Rietveld analysis and with Taylor–Bogue calculations. The effects from paramagnetic ions (Fe³⁺) on the spinning sideband intensities, originating from dipolar couplings between ²⁹Si and the spins of the paramagnetic electrons, were considered and analyzed in spectra recorded at four magnetic fields (4.7–14.1 T) and this has led to an improved quantification of alite and belite from ²⁹Si MAS NMR spectra recorded at “high” spinning speeds of ν_R=12.0–13.0 kHz using 4 or 5 mm rotors. Furthermore, the impact of Fe³⁺ ions on the spin-lattice relaxation was studied by inversion-recovery experiments and it was found that the relaxation is overwhelmingly dominated by the Fe³⁺ ions incorporated as guest-ions in alite and belite rather than the Fe³⁺ sites present in the intimately mixed ferrite phase (Ca₂Al_xFe_2−xO₅).     

Methods for correlating T1ρ and FID components in wideline H NMR studies of motionally heterogeneous polymer systems

We address the problem of correlating the observed FID and T_1ρ components in wideline ¹H relaxation measurements of motionally heterogeneous polymers, and show that different methods of data treatment can highlight different aspects of the correlations present. For a sample of polypropylene we find that the T_1ρ relaxation behaviour is driven by relaxation associated with the intermediate FID component, which strongly suggests a motionally inhomogeneous amorphous region in the sample.     

Observation of record flux pinning in melt-textured NEG-123 superconductor doped by Nb, Mo, and Ti nanoparticles

Flux pinning in melt-processed (Nd_0.33Eu_0.33Gd_0.33)Ba₂Cu₃O_y “NEG-123” + 35 mol% Gd₂BaCuO₅ “NEG-211” (70 nm in size) composite doped by TiO₃, MoO₃ and Nb₂O₅ achieved record values. The optimum values of all three dopands were found to be around 0.1 mol%. Transmission electron microscope (TEM) analysis found clouds of <10 nm sized particles in the NEG-123 matrix, shifting the pinning particle size distribution to significantly lower values. TEM by energy dispersive X-ray spectroscopy (EDX) analysis clarified that these nanoparticles contained a significant amount of Nb, Mo, and Ti. Appearance of nanometer-sized defects correlated with a significantly improved flux pining at low and medium magnetic fields, which was particularly significant at high temperatures. In the Nb-doped sample, a record J_c value of 925 kA/cm² at the secondary peak field (4.5 T) was achieved at 65 K, 640 kA/cm² at zero field at 77 K, and 100 kA/cm² at 90.2 K, the last value having been up to now considered as a good standard for REBa₂Cu₃O_y “RE-123” materials at 77 K. The greatly improved J_c–B performance in Nb/Mo/Ti doped samples can be easily translated to large-scale LRE-123 (LRE = light rare earths, Nd, Eu, Gd, Sm) blocks intended for real superconducting super-magnets applications.     

A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

Dielectric relaxation studies of methyl cellulose with phenol derivatives in non-polar solvents using time domain reflectometry

Dielectric relaxation measurements of methyl cellulose with substituted phenols p-cresol, m-cresol and o-cresol mixture in different non-polar solvents CCl₄, benzene and 1,4-dioxan for different concentrations over the frequency range of 10 MHz–20 GHz at 303 K have been carried out using Time Domain Reflectometry (TDR). Dielectric parameters such as static permittivity (ε₀) and relaxation time (τ) were determined and discussed to yield information on the molecular structure and dynamics of the mixture. The dielectric constant and relaxation time were found to be high for methyl cellulose with p-cresol in CCl₄ compared with the other mixtures.     

Improved Estimation of Protein Rotational Correlation Times fromN Relaxation Measurements

In the study of protein backbone dynamics by¹⁵N relaxation measurements, an initial estimation of the isotropic global correlation time, τ_m, is usually obtained from the averageT₁/T₂ratio of nuclear spins that do not exhibit slow internal motion and withT₂values not significantly shortened by chemical or conformational exchange processes. Different methods have been used for identification of the rates of internal motion. However, the number of nuclear spins included in the τ_mestimation is often larger than the number that ultimately can be fitted to a single-order parameter,S², implying that some nuclear spins involved in the initial τ_mestimation actually have an effective internal correlation time, τ_e, not as fast as assumed. As a consequence, τ_mis underestimated, since internal motion reduces theT₁/T₂ratio. This situation becomes more obvious if the molecule has a large τ_mvalue because the reduction inT₁/T₂ratio arising from internal motion is more significant than for molecules with smaller τ_mand the same degree of internal motion. This Communication describes a more reliable method for identifying nuclear spins which should be excluded from the τ_mestimation because of insufficiently rapid internal motion. This results in an improved τ_mvalue, giving a much better agreement between the number of nuclear spins fitted successfully to a single-order parameter,S², and those used in the τ_mestimation.     

An “instantaneous” distribution of the ionization-passive electrons and holes under irradiation of a dielectric by intense electron or laser beams

A method is worked out for calculation of an “instantaneous” energy distribution of the ionization-passive electrons and holes resulting from the electron-electron collisions before the onset of electron-phonon relaxation under 10⁻¹⁵–10⁻¹⁴ s irradiation of a dielectric by an intense electron or laser beam. The method is based on the solution of a system of integral-differential kinetic equations of general form. The Auger and impact ionization as well as hole recoil due to the momentum conservation law are taken into account in calculations. The “instantaneous” distribution is calculated in NaCl under irradiation of the sample by a high-density electron beam. The “instantaneous” distribution of ionization-passive electrons and holes is the initial one in solutions of all kinetic equations describing further relaxation of electron excitations in irradiated materials.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 15–22, November, 2004.     

No pre-critical enhancement observed in C(π, γ)N(g.s.) at q 2mπ

The cross section and angular distribution for the reaction ¹³C(π⁺, γ)¹³N(g.s.) have been measured from 37 to 85° in the laboratory, at a pion energy of 115.5 MeV. The observed cross section ranges from 320 to 660 nb/sr. These results do not show the large magnitude and wide-angle peaking expected if pre-critical effects due to nascent pion condensation were present. In addition, the observed cross section is less than one-half of the predictions of available theoretical calculations which do not include the pre-critical effect. Data on the reaction ¹H(π⁻, γ)n at T_π = 116.6 MeV were also obtained for calibration purposes. These data agree with expectations based on knowledge of the inverse reaction and previous measurements.     

The effects of thermal annealing on the relaxation of rubbing-induced birefringence in polystyrene

We have conducted a systematic study on the effects of post rubbing annealing on the relaxation of rubbing-induced birefringence of polystyrene. It is found that annealing at T₀ only affects the relaxation up to T₀ + T_Lag, where T_Lag is proportional to the logarithm of the annealing time t_A. A theoretical model based on the distribution of relaxation times due to the individual birefringence elements is proposed. To remove its contribution to the net birefringence each element must overcome an energy barrier E = (317 + 1.17ξ)×10³ J/mol, and therefore must have a characteristic relaxation time τ which depends on temperature T and a barrier height which ranges from 340.4 kJ/mol to 445.7 kJ/mol. The relaxation of birefringence is expressed by the equation NB(T, t) = N(ξ)e^-t/τ(T,ξ)dξ, in which both the relaxation time τ(T,ξ) and the distribution function N(ξ) can be extracted from experimental data. The predictions of the model agree well with all the experimental results presented in this work. The differences and similarities of the relaxation of birefringence with respect to the physical aging of quenched PS are discussed. In particular, similarities in terms of the general temperature lag phenomena are noted.     

Slow Dynamics Mapping of Large-Linewidth Solids by a MARF Spin-Lock Filter

A new method forT_1ρcontrast in solid-state imaging is presented. The method is based upon the addition of aT_1ρspin-lock pulse to the standard MARF pulse sequence and is able to provide relaxation contrast in dependence either on the lock time or on the intensity of the lock field, without having effects related to the line-narrowing procedure. The results on some large-linewidth solids show thatT_1ρvalues measured by the usual spin-lock pulse sequence agree with those measured on space-resolved lines.