Collisional Damping of the Collective Oscillations of a Trapped Fermi Gas

We consider a Fermi gas confined by a harmonic trapping potential and we highlight the role of the Fermi–Dirac statistics by studying frequency and damping of collective oscillations of quadrupole type in the framework of the quantum Boltzmann equation, in which statistical corrections are taken into account in the collisional integral. We are able to describe the crossover from the collisionless regime to the hydrodynamic one by introducing a temperature-dependent relaxation time _Q . We show that, in the degenerate regime, the relaxation rate ^–1 _Q exhibits a temperature dependence different from the collision rate . We finally compare the collisional properties of the Fermi gas with the ones of the Bose gas for temperatures above the Bose–Einstein condensation.     

Spin-charge separation and anomalous scaling in coupled chains

We use a bosonization approach to show that the three dimensional Coulomb interaction in coupled metallic chains leads to a Luttinger liquid for vanishing inter-chain hopping t, and to a Fermi liquid for any finite t. However, for small t 0 the Greens-function satisfies a homogeneity relation with a non-trivial exponent _cb in a large intermediate regime. Our results offer a simple explanation for the large values of _cb inferred from recent photoemission data from quasi one-dimensional conductors and might have some relevance for the understanding of the unusual properties of the high-temperature superconductors.     

An induced interaction model for arbitrarily polarized Fermi systems

A model for calculating the interactions in arbitrarily spin-polarized Fermi systems is presented. Starting from the four-point vertex functions, the induced part of the interactions is deduced by explicitly treating the one-particle, one-hole irreducible diagrams and using some general crossing symmetry relations. Extrapolation away from the Fermi surface is carried out by replacing the particle-hole phase space by Lindhard functions in the crossed channel; consequently, calculation of the necessary - phase space function is presented. The longitudinal spin-density and density responses for polarized systems are obtained by diagrammatic means. A possible way of treating the direct part of the interactions using Born approximation is also discussed. Finally, the limits of the model for zero and full polarization are given.     

Transverse Spin Diffusion in a Dilute Spin-Polarized Degenerate Fermi Gas

We re-examine the calculation of the transverse spin-diffusion coefficient in a dilute degenerate spin-polarized Fermi gas, for the case of s-wave scattering. The special feature of this limit is that the dependence of the spin diffusion coefficient on temperature and field can be calculated explicitly with no further approximations. This exact solution uncovers a novel intermediate behaviour between the high field spin-rotation dominated regime in which D H^–2 , D T^–2 , and the low-field isotropic, collision dominated regime with D = D T^–2 . In this intermediate regime, D_, T^–2 but D D. We emphasize that the low-field crossover cannot be described within the relaxation time approximation. We also present an analytical calculation of the self-energy in the s-wave approximation for a dilute spin-polarized Fermi gas, at zero temperature. This emphasizes the failure of the conventional Fermi-liquid phase space arguments for processes involving spin flips. We close by reviewing the evidence for the existence of the intermediate regime in experiments on weakly spin-polarized ³ He and ³ He– ⁴ He mixtures.     

Orbital dynamics of the Anderson-Brinkman-Morel phase of superfluid3He

The orbital dynamics of the Anderson-Brinkman-Morel (ABM) phase of helium 3 is studied in both the hydrodynamic and collisionless limits. The complete equations for the orbital motion in the hydrodynamic limit are written down and the important parameters are evaluated by simple arguments. In the collisionless limit the matrix kinetic equation, not including the dipole interaction or Fermi liquid corrections, is inverted exactly to give a form that explicitly displays the various collective modes possible. The existence of an intrinsic orbital angular momentum density of order _s (T _c/E _F) ₂ and the moment of intertia term suggested by Leggett and Takagi is confirmed, and a physical understanding of their origin is given. However, in both collisionless and hydrodynamic limits the interaction with the normal fluid dominates the motion except very near zero temperature.     

Numerical Calculation of the Flow Regimes of a Fluid Partially Filling a Horizontal Rotating Heat‐Exchange Cylinder

Consideration is given to a numerical determination of a twodimensional unsteady viscous flow with the free surface in a stationarily rotating horizontal cylinder in which heatexchange processes are carried out. The markerandcell method in a polar coordinate system is used. The features of modeling of the walllayer regime and the circulating flow regime that occur in rapid and slow rotation of the cylinder, respectively, are discussed. Based on the given results of numerical calculations, the influence of the Reynolds number on the character of flow is analyzed.     

Magnetic transitions and superconductivity in thet-J model

The spectrum of the 2D t-J model is shown to change drastically due to transitions from the long-range to short-range antiferromagnetic order at the hole concentration x 0.04 and from the short-range order to a completely disordered paramagnetic state at x 0.19. In the region 0.04 x 0.19 the obtained shape of the Fermi surface, the hole dispersion near the Fermi level, and the density of states on it are in satisfactory agreement with experiment in Bi2212. Based on the obtained spectral functions the Eliashberg formalism is used for calculating T_c. The hole-magnon interaction alone is found to be unable to give rise to superconductivity. By adding a moderate interaction with apex oxygen vibrations high T_c are obtained for even frequency pairing in the range 0.04 x 0.17. For larger hole concentrations the odd frequency s-wave solution becomes the leading one which can result in s-wave superconductivity in the overdoped regime with the participation of a hole-phonon interaction of the respective symmetry.     

Fermi liquid behaviour of the viscosity of3He-4He mixtures

We have investigated³He-⁴He mixtures at³He-concentrations 0.98%x9.5% by the vibrating wire technique in the temperature range 1 mKT 100 mK and at pressures 0 bar p 20 bar. In the degenerate regime of the mixtures the Landau theory of Fermi liquids predicts a temperature dependence of the viscosity proportionalT ^–2. We report on the first observation of this behaviour at 3 mKT 10 mK for all investigated concentrations and pressures. At temperatures below about 20 mK slip corrections had to be taken into account due to the increase of the quasiparticle mean free path at very low temperatures. The low-temperature cut-off in T ² = constant indicates the transition into the ballistic regime of the mixtures, where the mean free path of the quasiparticles exceeds the radius of the vibrating wire. Our results for the pressure dependence of the viscosity as well as for its magnitude show substantial differences from predictions based on pseudopotential theory. However, a calculation of with the quasiparticle interaction potential of recent solubility measurements in mixtures agrees well with our experimental data, in particular the pressure independence of .     

Magnetic field dependence of the density of states of YBa2Cu3O6.95: Implications for the vortex structure

The total specific heat of YBa₂Cu₃O_6.95 single crystals includes contributions from phonons and spin-1/2 particles, as well as electronic contributions. The electronic specific heat is described by a quadratic term T² in zero field and a linear term [(0)+(H)]T which is increased when a magnetic field H is applied perpendicular to the CuO₂ planes. In agreement with d-wave superconductivity, we find that _n/T_c and (H)_n(H/H_c2)^1/2, where _n is the coefficient of the normal-state linear term. The H^1/2 dependence of the density of states at the Fermi level was predicted by G. Volovik for lines of nodes in the gap: the quasiparticles which contribute to this density of states are close to the nodes in momentum space and are located outside the vortex core.     

Magnetothermal oscillations and the Fermi surface of β-tungsten V3Ge

Landau quantum oscillations have been observed for the first time in a high-critical-field superconductor with the -tungsten crystal structure. The data are associated with extremal orbits on three sheets of the Fermi surface, all three resembling 100-directed cylinders. The results are compared qualitatively with a Fermi surface model suggested by APW energy band calculations.     

Exactly solvable models for the radiofrequency size effect. II. Small-angle scattering

The effect of small-angle scattering on the line shape of the radiofrequency size effect is calculated for the Fermi surface models discussed in Part I. By considering a model scattering probability that is uniform up to a maximum angle and zero thereafter, it is shown that the line shape undergoes a pronounced narrowing as is varied from the effective regime ( > ) to the ineffective regime ( < ), where is the skin depth relative to the plate thickness. Further, it is shown that scattering by Debye phonons leads to similar results. In the effective regime the resonance amplitude is proportional to T ³and the width is temperature independent. In the ineffective regime the resonance structure is confined to a region about the onset with its amplitude and width varying as T ³and T, respectively. This structure is followed by an exponentially decaying tail whose amplitude varies as T ⁵. Because of the manner in which the scattering angles are distributed, the transition region between regimes is about an order of magnitude larger than predicted by the first scattering model and encompasses approximately two decades in temperature.Work supported by the National Science Foundation under grant number DMR-74-11961.     

Mathematical simulation of the process of combustion of slightly gaseous porous compositions

A one-dimensional model of combustion of slightly gaseous porous compositions is considered. Using this model an analysis of the dependence of the combustion characteristics on the basic parameters such as the mass ratio of the gas-free and volatile components in the starting composition, initial porosity, position of the gas liberation source relative to the reaction front of the gas-free component, and degree of sample hermetic sealing is performed for different exothermicity and endothermicity levels of the chemical processes taking place.Deceased.Institute of Structural Macrokinetics of the Russian Academy of Sciences, Chernogolovka. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 4, pp. 461–465, October, 1993.     

Magnetic-field-induced semiconductor-semimetal transition in Bi-Sb alloys

Accurate and detailed measurements of the temperature dependence of the longitudinal magnetoresistance of single-crystal Bi-Sb alloys have been made, with static magnetic fields in the range 0–100 kG oriented parallel to the trigonal axis. Alloy concentrations were in the range 8–12 at.% Sb, and temperatures in the range 1–35 K. At very high fields the resistance increases with increasing temperature in a metallic manner with ideal and residual components, in contrast to the semiconductor behavior observed at zero field or low fields. For the high-field semimetal regime the electrical resistance behaves in a simple manner similar to a metal in zero field, in contrast to the complicated magnetoresistance phenomena for metals in low fields. This behavior can be understood in terms of a simple quasi-one-dimensional extreme-quantum-limit regime. The magnetic-field-induced semiconductor-semimetal transition is associated with an energy gap and changes of the energy-band structure which are of order 1 meV. Thermal activation energies for electrical conduction manifest this gap only at temperatures below approximately 20 K. Activation energies an order of magnitude larger which have been measured at considerably higher temperatures are apparently the direct gap at theL-point in the Brillouin zone and are not directly connected with the semiconductor-semimetal transition. Our results indicate that the zero-field indirectL-T energy gap increases from zero somewhere near 7–8 at. % Sb to values only as large as approximately 1.5 meV at 12 at. % Sb. At the magnetic-field induced transition there occurs evidence of an intermediate excitonic insulator phase, a resistance minimum below 10 K reminiscent of the Kondo alloy behavior. This anomalous regime is a property of the semiconductor-to-semimetal transition and cannot be associated with the well-known temperature and magnetic-field freeze-out of charge carriers in extrinsic semiconductors, or with magnetic ordering of the Kondo type.     

Resonant Tunneling of Holes in GaMnAs-Related Double-Barrier Structures

Using the multiband quantum transmitting boundary method (MQTBM), hole resonant tunneling through AlGaAs/GaMnAs junctions is investigated theoretically. Because of band-edge splitting in the DMS layer, the current for holes with different spins are tuned in resonance at different biases. The bound levels of the light hole in the quantum well region turned out to be dominant in the tunneling channel for both heavy and light holes. The resonant tunneling structure can be used as a spin filter for holes for adjusting the Fermi energy and the thickness of the junctions.     

On the dispersion of gases under the action of the medium

Some general regularities of dispersion of a gas emerging from a nozzle submerged in a liquid are considered. A condition for establishment of the so-called maximum dispersion state is formulated.Notation ₀ coefficient of surface tension at the liquidgas boundary - contact angle of wetting of the nozzle material surface by the liquid - p_at atmospheric pressure - p air pressure - density of the liquid - g gravitational acceleration - h height of the liquid column - ₁, and _g dynamic viscosity coefficients of the liquid and gas, respectively - R and r radii of the bubble and nozzle, respectively - Q and F dimensionless criteria - , , , , and undetermined coefficients - ratio of the circumference of a circle to its diameter     

The transverse acoustic impedance of dilute solutions of3He in superfluid4He

The transverse acoustic impedanceZ=R–iX of dilute solutions of³He in superfluid⁴He has been measured at a frequency (/2) of 20.5 MHz at temperaturesT from 30 mK to the transition at T. The³He concentrations studied werec=0.014, 0.031, 0.053, 0.060, and 0.092 below 1 K, thoughc decreased slightly near the point. The impedance was found from the temperature dependence of the quality factor and the resonant frequency of anAT-cut quartz crystal resonator immersed in the liquid. Below 1 K,Z is due to the Fermi gas of³He quasiparticles, and in the collisionless limit, 1 ( is a relaxation time),R remains constant whileX goes to zero. Measurements ofR(c, T) andX(c, T) were analyzed to determine the momentum accommodation coefficient (c, T) and (c, T). The relaxation times were in good agreement with previous work, while (c, T) was independent ofc, but increased from 0.29±0.03 below 0.1 K to 1.0±0.1 above 0.8 K. Various mechanisms are suggested to explain this. Between 1.0 and 1.5 K the³He quasiparticles and the thermally excited rotons are in the hydrodynamic region, 1. Values of the total viscosity (c, T) were obtained and analyzed to give the³He gas viscosity and the³He-³He and roton-³He scattering rates, both of which were energy-dependent. The superfluid healing length a was also measured. Near the point we founda=(0.1±0.03)^–2/3 nm, where =1–T/T, proportional to the phase coherence length . Our data are consistent with the hypothesis that _s/T is a universal constant for superfluid dilute solutions, where _s is the superfluid density. Between 1.0 and 1.8 K we found thata(c, T) was comparable to measurements in³He-⁴He films.     

Numerical simulation of the flow of a supersonic stream of viscous compressible gas over a cavity

Numerical simulation of the flow of a supersonic stream of viscous, compressible, heat-conducting gas over a cavity is carried out on the basis of kinetically consistent difference schemes. Different types of flow (open and closed cavities) are considered, the heat fluxes to the walls of the recess are determined, and a nonsteady regime of flow over a cavity is simulated. The results obtained are compared with known experimental relationships.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 61, No. 4, pp. 570–577, October, 1991.     

Inertial‐Capillary Surface Waves and their Influence on Crystal Growth in Zero Gravity

The results of the numerical calculations of oscillations of the liquid column free surface under the action on it of axial vibration in zero gravity are presented. On the basis of these calculations, an analytical model of the surface standing wave named the inertialcapillary wave has been developed. Comparison of the analytical calculations with the data of the numerical calculations and the experiment performed in microgravity under the TEXUS program has been made. The numerical study of the thermocapillary convection stability in the presence of inertialcapillary waves has shown that the change to the oscillation regime is very sharp upon reaching certain values of the vibration frequency and amplitude. The heatandmass transfer in growing semiconductor crystals by the floatingzone method in zero gravity under the action of vibration with allowance for the surface waves has been investigated. The possibility of measuring vibrational accelerations onboard space vehicles by means of oscillations of the liquidcolumn free surface are discussed.     

Elevated temperature deformation behaviour of multi-phase Ni-20 at % Al-30 at % Fe and its constituent phases

The mechanical behaviour of the multi-phase ( + /) alloy Ni-20 at % Al-30 at % Fe and alloys similar to its constituent and / phases, Ni-30 at % Al-20 at % Fe and Ni-12 at % Al-40 at % Fe, respectively, were investigated. When tested in tension at 300 K, the alloys exhibited 20%, 2% and 28% elongation, respectively. At elevated test temperatures (700, 900 and 1100 K), the multi-phase alloy exhibited increased ductility, reaching an elongation in excess of 70% at 1100 K without necking or fracture. Similarly, the alloy demonstrated increased ductility with increasing test temperatures. In contrast, the / alloy showed greatly reduced ductility with increasing temperature and was quite brittle both at 900 and 1100 K. Thus, whilst at room temperature the / phase improved the ductility of the + / aggregate, at elevated temperatures the phase alleviated the brittleness of the / phase, thereby preventing any embrittlement of the multi-phase alloy over the temperature range 300–1100 K. Also, whilst the phase improved the room-temperature strength of the multi-phase alloy, at elevated temperatures where the phase is known to be weak, the / phase improved the strength of the multi-phase alloy up to 900 K, beyond which the strength deteriorated due to disordering and lack of anomalous strengthening in the / component.     

Anisotropy in μ* for superconducting aluminum

Using two models for an anisotropic Coulomb pseudopotential parameter *(k), we have calculated approximate upper and lower limits for the anisotropic gap edge of superconducting aluminum as a function of wavevector direction over the Fermi surface. We consider all sources of anisotropy, i.e., anisotropic phonon dispersion curves and anisotropic Fermi surface, to determine the electron-phonon spectral functions _k ² ()F _k() and the matrix elements of the screened Coulomb repulsion. We find values of the gap anisotropy parameter a² and of the ratio between the pure single-crystal and isotropic dirty limit critical temperatures that agree better with experimental results than the values found using a constant *. Disagreement between theory and experiment remains for the variation of _o(k) itself over the Fermi surface.