1,926 research outputs found
Laughlin's wave functions, Coulomb gases and expansions of the discriminant
In the context of the fractional quantum Hall effect, we investigate
Laughlin's celebrated ansatz for the groud state wave function at fractional
filling of the lowest Landau level. Interpreting its normalization in terms of
a one component plasma, we find the effect of an additional quadrupolar field
on the free energy, and derive estimates for the thermodynamically equivalent
spherical plasma. In a second part, we present various methods for expanding
the wave function in terms of Slater determinants, and obtain sum rules for the
coefficients. We also address the apparently simpler question of counting the
number of such Slater states using the theory of integral polytopes.Comment: 97 pages, using harvmac (with big option recommended) and epsf, 7
figures available upon request, Saclay preprint Spht 93/12
The spin 1/2 Calogero-Gaudin System and its q-Deformation
The spin 1/2 Calogero-Gaudin system and its q-deformation are exactly solved:
a complete set of commuting observables is diagonalized, and the corresponding
eigenvectors and eigenvalues are explicitly calculated. The method of solution
is purely algebraic and relies on the co-algebra simmetry of the model.Comment: 15 page
Noise correlations of the ultra-cold Fermi gas in an optical lattice
In this paper we study the density noise correlations of the two component
Fermi gas in optical lattices. Three different type of phases, the BCS-state
(Bardeen, Cooper, and Schieffer), the FFLO-state (Fulde, Ferrel, Larkin, and
Ovchinnikov), and BP (breach pair) state, are considered. We show how these
states differ in their noise correlations. The noise correlations are
calculated not only at zero temperature, but also at non-zero temperatures
paying particular attention to how much the finite temperature effects might
complicate the detection of different phases. Since one-dimensional systems
have been shown to be very promising candidates to observe FFLO states, we
apply our results also to the computation of correlation signals in a
one-dimensional lattice. We find that the density noise correlations reveal
important information about the structure of the underlying order parameter as
well as about the quasiparticle dispersions.Comment: 25 pages, 11 figures. Some figures are updated and text has been
modifie
Abundances and kinematics for ten anticentre open clusters
Open clusters are distributed all across the disk and are convenient tracers
of its properties. In particular, outer disk clusters bear a key role for the
investigation of the chemical evolution of the Galactic disk. The goal of this
study is to derive homogeneous elemental abundances for a sample of ten outer
disk OCs, and investigate possible links with disk structures such as the
Galactic Anticenter Stellar Structure. We analyse high-resolution spectra of
red giants, obtained from the HIRES@Keck and UVES@VLT archives. We derive
elemental abundances and stellar atmosphere parameters by means of the
classical equivalent width method. We also performed orbit integrations using
proper motions. The Fe abundances we derive trace a shallow negative radial
metallicity gradient of slope -0.027+/-0.007 dex.kpc-1 in the outer 12 kpc of
the disk. The [alpha/Fe] gradient appears flat, with a slope of 0.006+/-0.007
dex.kpc-1 . The two outermost clusters (Be 29 and Sau 1) appear to follow
elliptical orbits. Be 20 also exhibits a peculiar orbit with a large excursion
above the plane. The irregular orbits of the three most metal-poor clusters (of
which two are located at the edge of the Galactic disk), if confirmed by more
robust astrometric measurements such as those of the Gaia mission, are
compatible with an inside-out formation scenario for the Milky Way, in which
extragalactic material is accreted onto the outer disk. We cannot determine if
Be 20, Be 29,and Sau 1 are of extragalactic origin, as they may be old genuine
Galactic clusters whose orbits were perturbed by accretion events or minor
mergers in the past 5 Gyr, or they may be representants of the thick disk
population. The nature of these objects is intriguing and deserves further
investigations in the near future.Comment: 17 pages, 9 figures; accepted for publication in A&
Plasmon channels in the electronic relaxation of diamond under high-order harmonics femtosecond irradiation
We used high order harmonics of a femtosecond titanium-doped sapphire system
(pulse duration 25 fs) to realise Ultraviolet Photoelectron Spectroscopy (UPS)
measurements on diamond. The UPS spectra were measured for harmonics in the
range 13 to 27. We also made ab initio calculations of the electronic lifetime
of conduction electrons in the energy range produced in the UPS experiment.
Such calculations show that the lifetime suddenly diminishes when the
conduction electron energy reaches the plasmon energy, whereas the UPS spectra
show evidence in this range of a strong relaxation mechanism with an increased
production of low energy secondary electrons. We propose that in this case the
electronic relaxation proceeds in two steps : excitation of a plasmon by the
high energy electron, the latter decaying into individual electron-hole pairs,
as in the case of metals. This process is observed for the first time in an
insulator and, on account of its high efficiency, should be introduced in the
models of laser breakdown under high intensity
Local density approximation for a perturbative equation of state
The knowledge of a series expansion of the equation of state provides a deep
insight into the physical nature of a quantum system. Starting from a generic
``perturbative'' equation of state of a homogeneous ultracold gas we make
predictions for the properties of the gas in the presence of harmonic
confinement. The local density approximation is used to obtain the chemical
potential, total and release energies, Thomas-Fermi size and density profile of
a trapped system in three-, two-, and one- dimensional geometries. The
frequencies of the lowest breathing modes are calculated using scaling and
sum-rule approaches and could be used in an experiment as a high precision tool
for obtaining the expansion terms of the equation of state. The derived
formalism is applied to dilute Bose and Fermi gases in different dimensions and
to integrable one-dimensional models. Physical meaning of expansion terms in a
number of systems is discussed.Comment: 3 Figure
The BCS model and the off shell Bethe ansatz for vertex models
We study the connection between the BCS pairing model and the inhomogeneous
vertex model. The two spectral problems coincide in the quasi-classical limit
of the off-shell Bethe Ansatz of the disordered six vertex model. The latter
problem is transformed into an auxiliary spectral problem which corresponds to
the diagonalization of the integrals of motion of the BCS model. A generating
functional whose quasi classical expansion leads to the constants of motion of
the BCS model and in particular the Hamiltonian, is identified.Comment: 10 pages, 1 figure. To be published in J. Phys.
Emergence of Wigner molecules in one-dimensional systems of repulsive fermions under harmonic confinement
A Bethe-Ansatz spin-density functional approach is developed to evaluate the
ground-state density profile in a system of repulsively interacting spin-1/2
fermions inside a quasi-one-dimensional harmonic well. The approach allows for
the formation of antiferromagnetic quasi-order with increasing coupling
strength and reproduces with high accuracy the exact solution that is available
for the two-fermion system.Comment: 3 pages, 2 figures, submitte
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