Revised Huang-Yang multipolar pseudopotential

A number of authors have recently pointed out inconsistencies of results obtained with the Huang-Yang multipolar pseudo-potential for low-energy scattering [K. Huang and K. C. Yang, Phys. Rev. A, v 105, 767 (1957); later revised in K. Huang, ``Statistical Mechanics'', (Wiley, New York, 1963)]. The conceptual validity of their original derivation has been questioned. Here I show that these inconsistencies are rather due to an {\em algebraic} mistake made by Huang and Yang. With the corrected error, I present the revised version of the multipolar pseudo-potential

Universality in ultradilute liquid Bose-Bose mixtures

We have studied dilute Bose-Bose mixtures of atoms with attractive interspecies and repulsive intraspecies interactions using quantum Monte Carlo methods at T=0. Using a number of models for interactions, we determine the range of validity of the universal equation of state of the symmetric liquid mixture as a function of two parameters: the s-wave scattering length and the effective range of the interaction potential. It is shown that the Lee-Huang-Yang correction is sufficient only for extremely dilute liquids with the additional restriction that the range of the potential is small enough. Based on the quantum Monte Carlo equation of state we develop a density functional which goes beyond the Lee-Huang-Yang term and use it together with the local density approximation to determine density profiles of realistic self-bound drops.Postprint (published version

Effects of Disorder in a Dilute Bose Gas

We discuss the effects of a weak random external potential on the properties of the dilute Bose gas at zero temperature. The results recently obtained by Huang and Meng for the depletion of the condensate and of the superfluid density are recovered. Results for the shift of the velocity of sound as well as for its damping due to collisions with the external field are presented. The damping of phonons is calculated also for dense superfluids. (submitted to Phys.Rev.B)Comment: 21 pages, Plain Tex, 2 figures available upon request, preprint UTF 31

PHONON COUPLING AND PHOTOIONIZATION CROSS-SECTIONS IN SEMICONDUCTORS

The coupling to lattice vibrations affects the photoionisation spectra of defects in semiconductors. This is especially important for deep defects. The effects are characterised mainly by a Huang-Rhys factor S0 and by a spectral moment. These are calculated for a variety of electron-photon coupling mechanisms as a function of the observable ionisation energy EI rather than the unobservable effective radius used by previous workers. For Frohlich coupling a good approximation for the Huang-Rhys factor is S0(x)/S0(0)=X/ square root ((5+x)/6) with x=EI/(effective Ryd for purely hydrogenic centre)

Transition Temperature of a Uniform Imperfect Bose Gas

We calculate the transition temperature of a uniform dilute Bose gas with repulsive interactions, using a known virial expansion of the equation of state. We find that the transition temperature is higher than that of an ideal gas, with a fractional increase K_0(na^3)^{1/6}, where n is the density and a is the S-wave scattering length, and K_0 is a constant given in the paper. This disagrees with all existing results, analytical or numerical. It agrees exactly in magnitude with a result due to Toyoda, but has the opposite sign.Comment: Email correspondence to [email protected] ; 2 pages using REVTe

Elementary excitations in trapped Bose gases beyond mean field approximation

Using hydrodynamic theory of superfluids and the Lee-Huang-Yang equation of state for interacting Bose gases we derive the first correction to the collective frequencies of a trapped gas, due to effects beyond mean field approximation. The corresponding frequency shift, which is calculated at zero temperature and for large N, is compared with other corrections due to finite size, non-linearity and finite temperature. We show that for reasonable choices of the relevant parameters of the system, the non-mean field correction is the leading contribution and amounts to about 1%. The role of the deformation of the trap is also discussed.Comment: 4 pages, 1 Postscript figur