132,617 research outputs found
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
Flow equation for Halpern-Huang directions of scalar O(N) models
A class of asymptotically free scalar theories with O(N) symmetry, defined
via the eigenpotentials of the Gaussian fixed point (Halpern-Huang directions),
are investigated using renormalization group flow equations. Explicit solutions
for the form of the potential in the nonperturbative infrared domain are found
in the large-N limit. In this limit, potentials without symmetry breaking
essentially preserve their shape and undergo a mass renormalization which is
governed only by the renormalization group distance parameter; as a
consequence, these scalar theories do not have a problem of naturalness.
Symmetry-breaking potentials are found to be ``fine-tuned'' in the large-N
limit in the sense that the nontrivial minimum vanishes exactly in the limit of
vanishing infrared cutoff: therefore, the O(N) symmetry is restored in the
quantum theory and the potential becomes flat near the origin.Comment: 18 pages, 4 figures, LaTeX, references added, presentation improved,
final version to appear in Phys. Rev.
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
A pseudo-potential analog for zero-range photoassociation and Feshbach resonance
A zero-range approach to atom-molecule coupling is developed in analogy to
the Fermi-Huang pseudo-potential treatment of atom-atom interactions. It is
shown by explicit comparison to an exactly-solvable finite-range model that
replacing the molecular bound-state wavefunction with a regularized
delta-function can reproduce the exact scattering amplitude in the
long-wavelength limit. Using this approach we find an analytical solution to
the two-channel Feshbach resonance problem for two atoms in a spherical
harmonic trap
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