Tunable high-temperature thermodynamics of weakly-interacting dipolar gases

We consider dilute gases of dipolar bosons or fermions in the high-temperature limit in a spherically symmetric harmonic trapping potential. We examine the system using a virial expansion up to second order in the fugacity. Using the Born approximation and assuming purely dipolar interactions, we find that the second-order virial coefficient for both bosons and fermions depends quadratically on the dipole length and is negative at high temperature, indicating that to lowest order in the dipole-dipole interactions the dipolar single-component quantum gases are repulsive. If the $s$-wave scattering length for the bosonic system is tunable and its absolute value is made small, then the $s$-wave interactions dominate and the dipolar as behaves like a weakly-interacting Bose gas with isotropic $s$-wave interactions. If the generalized scattering lengths for the fermionic system are tunable, then the dipole length can enter linearly in the virial equation of state, enhancing the dipole-dipole effects in the thermodynamic observables.Comment: 9 pages, 6 figure

Occupation numbers of the harmonically trapped few-boson system

We consider a harmonically trapped dilute $N$-boson system described by a low-energy Hamiltonian with pairwise interactions. We determine the condensate fraction, defined in terms of the largest occupation number, of the weakly-interacting $N$-boson system ($N \ge 2$) by employing a perturbative treatment within the framework of second quantization. The one-body density matrix and the corresponding occupation numbers are compared with those obtained by solving the two-body problem with zero-range interactions exactly. Our expressions are also compared with high precision {\em{ab initio}} calculations for Bose gases with $N=2-4$ that interact through finite-range two-body model potentials. Non-universal corrections are identified to enter at subleading order, confirming that different low-energy Hamiltonians, constructed to yield the same energy, may yield different occupation numbers. Lastly, we consider the strongly-interacting three-boson system under spherically symmetric harmonic confinement and determine its occupation numbers as a function of the three-body "Efimov parameter".Comment: 16 pages, 7 figure

Alfven wave refraction by interplanetary inhomogeneities

Pioneer 6 magnetic data reveals that the propagation direction of Alfven waves in the interplanetary medium is strongly oriented along the ambient field. Magnetic fluctuations of frequencies up to 1/30 sec in the spacecraft frame are shown to satisfy a necessary condition for Alfven wave normal. It appears from this analysis that geometrical hydromagnetics may satisfactorily describe deviation of the wave normal from the background field. The rotational discontinuity is likely also to propagate along the field lines

Ultracold neutral plasma expansion in two dimensions

We extend an isothermal thermal model of ultracold neutral plasma expansion to systems without spherical symmetry, and use this model to interpret new fluorescence measurements on these plasmas. By assuming a self-similar expansion, it is possible to solve the fluid equations analytically and to include velocity effects to predict the fluorescence signals. In spite of the simplicity of this approach, the model reproduces the major features of the experimental data

Iron abundance and magnetic permeability of the moon

A larger set of simultaneous data from the Apollo 12 lunar surface magnetometer and the Explorer 35 Ames magnetometer are used to construct a whole-moon hysteresis curve, from which a new value of global lunar permeability is determined to be mu = 1.012 + or - 0.006. The corresponding global induced dipole moment is 2.1 x 10 to the 18th power gauss-cu cm for typical inducing fields of .0001 gauss in the lunar environment. From the permeability measurement, lunar free iron abundance is determined to be 2.5 + or - 2.0 wt. %. Total iron abundance (sum of iron in the ferromagnetic and paramagnetic states) is calculated for two assumed compositional models of the lunar interior: a free iron/orthopyroxene lunar composition and a free iron/olivine composition. The overall lunar total iron abundance is determined to be 9.0 + or - 4.7 wt. %. Other lunar models with a small iron core and with a shallow iron-rich layer are discussed in light of the measured global permeability

Thermodynamics of the two-component Fermi gas with unequal masses at unitarity

We consider mass-imbalanced two-component Fermi gases for which the unequal-mass atoms interact via a zero-range model potential with a diverging s-wave scattering length $a_s$, i.e., with $1/a_s=0$. The high temperature thermodynamics of the harmonically trapped and homogeneous systems are examined using a virial expansion approach up to third order in the fugacity. We find that the universal part of the third-order virial coefficient associated with two light atoms and one heavy atom is negative, while that associated with two heavy and one light atom changes sign from negative to positive as the mass ratio $\kappa$ increases, and diverges when Efimov physics sets in at $\kappa=13.61$. By examining the Helmholtz free energy, we find that the equilibrium polarization of the trapped and homogeneous systems is 0 for $\kappa=1$, but finite for $\kappa \ne 1$ (with a majority of heavy particles). Compared to the equilibrium polarization of the non-interacting system, the equilibrium polarization at unitarity is increased for the trapped system and decreased for the homogeneous system. We find that unequal-mass Fermi gases are stable for all polarizations.Comment: 14+2 pages, 14 figure

Magnetism and the interior of the moon

The application of lunar magnetic field measurements to the study of properties of the lunar crust and deep interior is reviewed. Following a brief description of lunar magnetometers and the lunar magnetic environment, measurements of lunar remanent fields and their interaction with the solar plasma are discussed. The magnetization induction mode is considered with reference to lunar magnetic permeability and iron abundance calculations. Finally, electrical conductivity and temperature calculations from analyses of poloidal induction, for data taken in both the solar wind and in the geomagnetic tail, are reviewed

Crustal evolution inferred from Apollo magnetic measurements

Magnetic field and solar wind plasma density measurements were analyzed to determine the scale size characteristics of remanent fields at the Apollo 12, 15, and 16 landing sites. Theoretical model calculations of the field-plasma interaction, involving diffusion of the remanent field into the solar plasma, were compared to the data. The information provided by all these experiments shows that remanent fields over most of the lunar surface are characterized by spatial variations as small as a few kilometers. Large regions (50 to 100 km) of the lunar crust were probably uniformly magnetized during early crustal evolution. Bombardment and subsequent gardening of the upper layers of these magnetized regions left randomly oriented, smaller scale (5 to 10 km) magnetic sources close to the surface. The larger scale size fields of magnitude approximately 0.1 gammas are measured by the orbiting subsatellite experiments and the small scale sized remanent fields of magnitude approximately 100 gammas are measured by the surface experiments