281 research outputs found
Bosons in Rapid Rotation
Some recent progress in the mathematical physics of rapidly rotating, dilute
Bose gases in anharmonic traps is reviewed.Comment: 16 pages, lecture given at a symposium in honor of Michel
Dubois-Violette, Orsay, April 200
Ginzburg-Landau vortex dynamics with pinning and strong applied currents
We study a mixed heat and Schr\"odinger Ginzburg-Landau evolution equation on
a bounded two-dimensional domain with an electric current applied on the
boundary and a pinning potential term. This is meant to model a superconductor
subjected to an applied electric current and electromagnetic field and
containing impurities. Such a current is expected to set the vortices in
motion, while the pinning term drives them toward minima of the pinning
potential and "pins" them there. We derive the limiting dynamics of a finite
number of vortices in the limit of a large Ginzburg-Landau parameter, or \ep
\to 0, when the intensity of the electric current and applied magnetic field
on the boundary scale like \lep. We show that the limiting velocity of the
vortices is the sum of a Lorentz force, due to the current, and a pinning
force. We state an analogous result for a model Ginzburg-Landau equation
without magnetic field but with forcing terms. Our proof provides a unified
approach to various proofs of dynamics of Ginzburg-Landau vortices.Comment: 48 pages; v2: minor errors and typos correcte
Convergence of Ginzburg-Landau functionals in 3-d superconductivity
In this paper we consider the asymptotic behavior of the Ginzburg- Landau
model for superconductivity in 3-d, in various energy regimes. We rigorously
derive, through an analysis via {\Gamma}-convergence, a reduced model for the
vortex density, and we deduce a curvature equation for the vortex lines. In a
companion paper, we describe further applications to superconductivity and
superfluidity, such as general expressions for the first critical magnetic
field H_{c1}, and the critical angular velocity of rotating Bose-Einstein
condensates.Comment: 45 page
Vortex density models for superconductivity and superfluidity
We study some functionals that describe the density of vortex lines in
superconductors subject to an applied magnetic field, and in Bose-Einstein
condensates subject to rotational forcing, in quite general domains in 3
dimensions. These functionals are derived from more basic models via
Gamma-convergence, here and in a companion paper. In our main results, we use
these functionals to obtain descriptions of the critical applied magnetic field
(for superconductors) and forcing (for Bose-Einstein), above which ground
states exhibit nontrivial vorticity, as well as a characterization of the
vortex density in terms of a non local vector-valued generalization of the
classical obstacle problem.Comment: 34 page
Critical Rotational Speeds for Superfluids in Homogeneous Traps
We present an asymptotic analysis of the effects of rapid rotation on the
ground state properties of a superfluid confined in a two-dimensional trap. The
trapping potential is assumed to be radial and homogeneous of degree larger
than two in addition to a quadratic term. Three critical rotational velocities
are identified, marking respectively the first appearance of vortices, the
creation of a `hole' of low density within a vortex lattice, and the emergence
of a giant vortex state free of vortices in the bulk. These phenomena have
previously been established rigorously for a `flat' trap with fixed boundary
but the `soft' traps considered in the present paper exhibit some significant
differences, in particular the giant vortex regime, that necessitate a new
approach. These differences concern both the shape of the bulk profile and the
size of vortices relative to the width of the annulus where the bulk of the
superfluid resides. Close to the giant vortex transition the profile is of
Thomas-Fermi type in `flat' traps, whereas it is gaussian for soft traps, and
the `last' vortices to survive in the bulk before the giant vortex transition
are small relative to the width of the annulus in the former case but of
comparable size in the latter.Comment: To appear in J. Math. Phys, published versio
Ginzburg-Landau model with small pinning domains
We consider a Ginzburg-Landau type energy with a piecewise constant pinning
term in the potential . The function is different from
1 only on finitely many disjoint domains, called the {\it pinning domains}.
These pinning domains model small impurities in a homogeneous superconductor
and shrink to single points in the limit ; here, \v is the inverse of
the Ginzburg-Landau parameter. We study the energy minimization in a smooth
simply connected domain with Dirichlet boundary
condition on \d \O, with topological degree {\rm deg}_{\d \O} (g) = d
>0. Our main result is that, for small \v, minimizers have distinct
zeros (vortices) which are inside the pinning domains and they have a degree
equal to 1. The question of finding the locations of the pinning domains with
vortices is reduced to a discrete minimization problem for a finite-dimensional
functional of renormalized energy. We also find the position of the vortices
inside the pinning domains and show that, asymptotically, this position is
determined by {\it local renormalized energy} which does not depend on the
external boundary conditions.Comment: 39 page
Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates
We consider a 2D rotating Bose gas described by the Gross-Pitaevskii (GP)
theory and investigate the properties of the ground state of the theory for
rotational speeds close to the critical speed for vortex nucleation. While one
could expect that the vortex distribution should be homogeneous within the
condensate we prove by means of an asymptotic analysis in the strongly
interacting (Thomas-Fermi) regime that it is not. More precisely we rigorously
derive a formula due to Sheehy and Radzihovsky [Phys. Rev. A 70, 063620(R)
(2004)] for the vortex distribution, a consequence of which is that the vortex
distribution is strongly inhomogeneous close to the critical speed and
gradually homogenizes when the rotation speed is increased. From the
mathematical point of view, a novelty of our approach is that we do not use any
compactness argument in the proof, but instead provide explicit estimates on
the difference between the vorticity measure of the GP ground state and the
minimizer of a certain renormalized energy functional.Comment: 41 pages, journal ref: Communications in Mathematical Physics: Volume
321, Issue 3 (2013), Page 817-860, DOI : 10.1007/s00220-013-1697-
The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate
We study the Gross-Pitaevskii (GP) energy functional for a fast rotating
Bose-Einstein condensate on the unit disc in two dimensions. Writing the
coupling parameter as 1 / \eps^2 we consider the asymptotic regime \eps
\to 0 with the angular velocity proportional to
(\eps^2|\log\eps|)^{-1} . We prove that if \Omega = \Omega_0
(\eps^2|\log\eps|)^{-1} and then a minimizer of
the GP energy functional has no zeros in an annulus at the boundary of the disc
that contains the bulk of the mass. The vorticity resides in a complementary
`hole' around the center where the density is vanishingly small. Moreover, we
prove a lower bound to the ground state energy that matches, up to small
errors, the upper bound obtained from an optimal giant vortex trial function,
and also that the winding number of a GP minimizer around the disc is in accord
with the phase of this trial function.Comment: 52 pages, PDFLaTex. Minor corrections, sign convention modified. To
be published in Commun. Math. Phy
Quality of Maternal and Neonatal Care in Albania, Turkmenistan and Kazakhstan: A Systematic, Standard-Based, Participatory Assessment
BACKGROUND: Progress in maternal and neonatal mortality has been slow in many countries despite increasing access to institutional births, suggesting deficiencies in the quality of care. We carried out a systematic assessment of the quality of maternal and newborn care in three CEE/CIS countries, using an innovative approach to identify priority issues and promote action. METHODS: A standard-based tool, covering over 400 items grouped in 13 main areas ranging from support services to case management, was used to assess a sample of ten maternity hospitals in Albania, Kazakhstan and Turkmenistan. Sources of information were visit to services, medical records, observation of cases, and interviews with staff and mothers. A score (range 0 to 3) was attributed to each item and area of care. The assessment was carried out by a multidisciplinary team of international and national professionals. Local managers and staff provided the necessary information and were involved in discussing the findings and the priority actions. RESULTS: Quality of care was found to be substandard in all 13 areas. The lowest scores (between one and two) were obtained by: management of normal labour, delivery, obstetric complications and sick babies; infection prevention; use of guidelines and audits; monitoring and follow-up. Neonatal care as a whole scored better than obstetric care. Interviewed mothers identified lack of information, insufficient support during labour and lack of companionship as main issues. Actions to improve quality of care were identified at facility as well as at central level and framed according to main health system functions. CONCLUSIONS: Quality of care is a key issue to improve maternal and neonatal outcomes, particularly in countries such as CEE/CIS where access to institutional births is nearly universal. Approaches that involve health professionals and managers in comprehensive, action-oriented assessments of quality of care are promising and should be further supported
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