1,764 research outputs found
A Fermion-like description of condensed Bosons in a trap
A Bose-Einstein condensate of atoms, trapped in an axially symmetric harmonic
potential, is considered. By averaging the spatial density along the symmetry
direction over a length that preserves the aspect ratio, the system may be
mapped on to a zero temperature noninteracting Fermi-like gas. The ``mock
fermions'' have a state occupancy factor proportional to the ratio of
the coherance length to the ``hard-core'' radius of the atom. The mapping
reproduces the ground state properties of the condensate, and is used to
estimate the vortex excitation energy analytically. The ``mock-fermion''
description predicts some novel collective excitation in the condensed phase.Comment: 11 pages, REVTE
Cold atoms at unitarity and inverse square interaction
Consider two identical atoms in a spherical harmonic oscillator interacting
with a zero-range interaction which is tuned to produce an s-wave zero-energy
bound state. The quantum spectrum of the system is known to be exactly
solvable. We note that the same partial wave quantum spectrum is obtained by
the one-dimensional scale-invariant inverse square potential. Long known as the
Calogero-Sutherland-Moser (CSM) model, it leads to Fractional Exclusion
Statistics (FES) of Haldane and Wu. The statistical parameter is deduced from
the analytically calculated second virial coefficient. When FES is applied to a
Fermi gas at unitarity, it gives good agreement with experimental data without
the use of any free parameter.Comment: 11 pages, 3 figures, To appear in J. Phys. B. Atomic, Molecular and
Optical Physic
Ground state fluctuations in finite Fermi and Bose systems
We consider a small and fixed number of fermions (bosons) in a trap. The
ground state of the system is defined at T=0. For a given excitation energy,
there are several ways of exciting the particles from this ground state. We
formulate a method for calculating the number fluctuation in the ground state
using microcanonical counting, and implement it for small systems of
noninteracting fermions as well as bosons in harmonic confinement. This exact
calculation for fluctuation, when compared with canonical ensemble averaging,
gives considerably different results, specially for fermions. This difference
is expected to persist at low excitation even when the fermion number in the
trap is large.Comment: 20 pages (including 1 appendix), 3 postscript figures. An error was
found in one section of the paper. The corrected version is updated on
Sep/05/200
Evaluation of Spectrograms of High Speed Steels for Minor Elements Plate Calibration Method
Minor elements occurring in high speed steels do not exceed a total of two percent Such steels of our Works manufacture designated as T.H.S. a are of the conventional type 18-4-1. The time-scale method of plate calibration due to Smith
has been adopted and applied to the ferrous analysis of the above samples; the spectra evaluated and compared with the usual method of log ratio of galvanometer deflections against composition. The elements receiving attention were manganese, silicon and vanadium. Conventional spark technique for exciting spectra was used. The standard deviations of results which have been computed, do not exceed 2 to 3 per cent of contents
Haldane Exclusion Statistics and the Boltzmann Equation
We generalize the collision term in the one-dimensional Boltzmann-Nordheim
transport equation for quasiparticles that obey the Haldane exclusion
statistics. For the equilibrium situation, this leads to the ``golden rule''
factor for quantum transitions. As an application of this, we calculate the
density response function of a one-dimensional electron gas in a periodic
potential, assuming that the particle-hole excitations are quasiparticles
obeying the new statistics. We also calculate the relaxation time of a nuclear
spin in a metal using the modified golden rule.Comment: version accepted for publication in J. of Stat. Phy
Relativistic U(3) Symmetry and Pseudo-U(3) Symmetry of the Dirac Hamiltonian
The Dirac Hamiltonian with relativistic scalar and vector harmonic oscillator
potentials has been solved analytically in two limits. One is the spin limit
for which spin is an invariant symmetry of the the Dirac Hamiltonian and the
other is the pseudo-spin limit for which pseudo-spin is an invariant symmetry
of the the Dirac Hamiltonian. The spin limit occurs when the scalar potential
is equal to the vector potential plus a constant, and the pseudospin limit
occurs when the scalar potential is equal in magnitude but opposite in sign to
the vector potential plus a constant. Like the non-relativistic harmonic
oscillator, each of these limits has a higher symmetry. For example, for the
spherically symmetric oscillator, these limits have a U(3) and pseudo-U(3)
symmetry respectively. We shall discuss the eigenfunctions and eigenvalues of
these two limits and derive the relativistic generators for the U(3) and
pseudo-U(3) symmetry. We also argue, that, if an anti-nucleon can be bound in a
nucleus, the spectrum will have approximate spin and U(3) symmetry.Comment: Submitted to the Proceedings of "Tenth International Spring
Seminar-New Quests in Nuclear Structure", 6 page
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