2,007 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
Phenomenology of chiral damping in noncentrosymmetric magnets
A phenomenology of magnetic chiral damping is proposed in the context of
magnetic materials lacking inversion symmetry breaking. We show that the
magnetic damping tensor adopts a general form that accounts for a component
linear in magnetization gradient in the form of Lifshitz invariants. We propose
different microscopic mechanisms that can produce such a damping in
ferromagnetic metals, among which spin pumping in the presence of anomalous
Hall effect and an effective "-" Dzyaloshinskii-Moriya antisymmetric
exchange. The implication of this chiral damping in terms of domain wall motion
is investigated in the flow and creep regimes. These predictions have major
importance in the context of field- and current-driven texture motion in
noncentrosymmetric (ferro-, ferri-, antiferro-)magnets, not limited to metals.Comment: 5 pages, 2 figure
Families of quasi-exactly solvable extensions of the quantum oscillator in curved spaces
We introduce two new families of quasi-exactly solvable (QES) extensions of
the oscillator in a -dimensional constant-curvature space. For the first
three members of each family, we obtain closed-form expressions of the energies
and wavefunctions for some allowed values of the potential parameters using the
Bethe ansatz method. We prove that the first member of each family has a hidden
sl(2,) symmetry and is connected with a QES equation of the first
or second type, respectively. One-dimensional results are also derived from the
-dimensional ones with , thereby getting QES extensions of the
Mathews-Lakshmanan nonlinear oscillator.Comment: 30 pages, 8 figures, published versio
Attractive Fermi gases with unequal spin populations in highly elongated traps
We investigate two-component attractive Fermi gases with imbalanced spin
populations in trapped one dimensional configurations. The ground state
properties are determined within local density approximation, starting from the
exact Bethe-ansatz equations for the homogeneous case. We predict that the
atoms are distributed according to a two-shell structure: a partially polarized
phase in the center of the trap and either a fully paired or a fully polarized
phase in the wings. The partially polarized core is expected to be a superfluid
of the FFLO type. The size of the cloud as well as the critical spin
polarization needed to suppress the fully paired shell, are calculated as a
function of the coupling strength.Comment: Final accepted versio
Hunting for open clusters in \textit{Gaia} DR2: the Galactic anticentre
The Gaia Data Release 2 (DR2) provided an unprecedented volume of precise
astrometric and excellent photometric data. In terms of data mining the Gaia
catalogue, machine learning methods have shown to be a powerful tool, for
instance in the search for unknown stellar structures. Particularly, supervised
and unsupervised learning methods combined together significantly improves the
detection rate of open clusters. We systematically scan Gaia DR2 in a region
covering the Galactic anticentre and the Perseus arm and
, with the goal of finding any open clusters that may
exist in this region, and fine tuning a previously proposed methodology
successfully applied to TGAS data, adapting it to different density regions.
Our methodology uses an unsupervised, density-based, clustering algorithm,
DBSCAN, that identifies overdensities in the five-dimensional astrometric
parameter space that may correspond
to physical clusters. The overdensities are separated into physical clusters
(open clusters) or random statistical clusters using an artificial neural
network to recognise the isochrone pattern that open clusters show in a colour
magnitude diagram. The method is able to recover more than 75% of the open
clusters confirmed in the search area. Moreover, we detected 53 open clusters
unknown previous to Gaia DR2, which represents an increase of more than 22%
with respect to the already catalogued clusters in this region. We find that
the census of nearby open clusters is not complete. Different machine learning
methodologies for a blind search of open clusters are complementary to each
other; no single method is able to detect 100% of the existing groups. Our
methodology has shown to be a reliable tool for the automatic detection of open
clusters, designed to be applied to the full Gaia DR2 catalogue.Comment: 8 pages, accepted by Astronomy and Astrophysics (A&A) the 14th May,
2019. Tables 1 and 2 available at the CD
A ring in a shell: the large-scale 6D structure of the Vela OB2 complex
The Vela OB2 association is a group of 10 Myr stars exhibiting a complex
spatial and kinematic substructure. The all-sky Gaia DR2 catalogue contains
proper motions, parallaxes (a proxy for distance) and photometry that allow us
to separate the various components of Vela OB2. We characterise the
distribution of the Vela OB2 stars on a large spatial scale, and study its
internal kinematics and dynamic history. We make use of Gaia DR2 astrometry and
published Gaia-ESO Survey data. We apply an unsupervised classification
algorithm to determine groups of stars with common proper motions and
parallaxes. We find that the association is made up of a number of small
groups, with a total current mass over 2330 Msun. The three-dimensional
distribution of these young stars trace the edge of the gas and dust structure
known as the IRAS Vela Shell across 180 pc and shows clear signs of expansion.
We propose a common history for Vela OB2 and the IRAS Vela Shell. The event
that caused the expansion of the shell happened before the Vela OB2 stars
formed, imprinted the expansion in the gas the stars formed from, and most
likely triggered star formation.Comment: Accepted by A&A (02 November 2018), 13 pages, 9+2 figure
On the exactly solvable pairing models for bosons
We propose the new exactly solvable model for bosons corresponding to the
attractive pairing interaction. Using the electrostatic analogy, the solution
of this model in thermodynamic limit is found. The transition from the
superfluid phase with the Bose condensate and the Bogoliubov - type spectrum of
excitations in the weak coupling regime to the incompressible phase with the
gap in the excitation spectrum in the strong coupling regime is observed.Comment: 19 page
A simple construction of elliptic -matrices
We show that Belavin's solutions of the quantum Yang--Baxter equation can be
obtained by restricting an infinite -matrix to suitable finite dimensional
subspaces. This infinite -matrix is a modified version of the
Shibukawa--Ueno -matrix acting on functions of two variables.Comment: 6 page
More on the exact solution of the O(n) model on a random lattice and an investigation of the case |n|>2
For the model on a random lattice has critical points to
which a scaling behaviour characteristic of 2D gravity interacting with
conformal matter fields with can be associated. Previously
we have written down an exact solution of this model valid at any point in the
coupling constant space and for any . The solution was parametrized in terms
of an auxiliary function. Here we determine the auxiliary function explicitly
as a combination of -functions, thereby completing the solution of the
model. Using our solution we investigate, for the simplest version of the
model, hitherto unexplored regions of the parameter space. For example we
determine in a closed form the eigenvalue density without any assumption of
being close to or at a critical point. This gives a generalization of the
Wigner semi-circle law to . We also study the model for . Both
for we find that the model is well defined in a certain region
of the coupling constant space. For we find no new critical points while
for we find new critical points at which the string susceptibility
exponent takes the value .Comment: 27 pages, LaTeX file (uses epsf) + 3 eps figures, formulas involving
the string susceptibility corrrected, no change in conclusion
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