103 research outputs found
Vortex Rings in Fast Rotating Bose-Einstein Condensates
When Bose-Eintein condensates are rotated sufficiently fast, a giant vortex
phase appears, that is the condensate becomes annular with no vortices in the
bulk but a macroscopic phase circulation around the central hole. In a former
paper [M. Correggi, N. Rougerie, J. Yngvason, {\it arXiv:1005.0686}] we have
studied this phenomenon by minimizing the two dimensional Gross-Pitaevskii
energy on the unit disc. In particular we computed an upper bound to the
critical speed for the transition to the giant vortex phase. In this paper we
confirm that this upper bound is optimal by proving that if the rotation speed
is taken slightly below the threshold there are vortices in the condensate. We
prove that they gather along a particular circle on which they are evenly
distributed. This is done by providing new upper and lower bounds to the GP
energy.Comment: to appear in Archive of Rational Mechanics and Analysi
The magnetic neutron scattering resonance of high-T_c superconductors in external magnetic fields: an SO(5) study
The magnetic resonance at 41 meV observed in neutron scattering studies of Y
Ba_2 Cu_3 O_7 holds a key position in the understanding of high-T_c
superconductivity. Within the SO(5) model for superconductivity and
antiferromagnetism, we have calculated the effect of an applied magnetic field
on the neutron scattering cross-section of the magnetic resonance. In the
presence of vortices, the neutron scattering cross-section shows clear
signatures of not only the fluctuations in the superconducting order parameter
\psi, but also the modulation of the phase of \psi due to vortices. In
reciprocal space we find that i) the scattering amplitude is zero at
(pi/a,pi/a), ii) the resonance peak is split into a ring with radius pi/d
centered at (pi/a,pi/a), d being the vortex lattice constant, and consequently,
iii) the splitting pi/d scales with the magnetic field as sqrt{B}.Comment: 4 pages including 3 eps-figures - minor changes and one reference
added. Accepted for publication in Phys. Rev.
About curvature, conformal metrics and warped products
We consider the curvature of a family of warped products of two
pseduo-Riemannian manifolds and furnished with metrics of
the form and, in particular, of the type , where are smooth
functions and is a real parameter. We obtain suitable expressions for the
Ricci tensor and scalar curvature of such products that allow us to establish
results about the existence of Einstein or constant scalar curvature structures
in these categories. If is Riemannian, the latter question involves
nonlinear elliptic partial differential equations with concave-convex
nonlinearities and singular partial differential equations of the
Lichnerowicz-York type among others.Comment: 32 pages, 3 figure
Vortex state in a doped Mott insulator
We analyze the recent vortex core spectroscopy experiments in cuprate
superconductor and discuss what can be learned from them about the nature of
the ground state in these compounds. We argue that the data are inconsistent
with the assumption of a simple metallic ground state and exhibit
characteristics of a doped Mott insulator. A theory for a vortex core in such a
doped Mott insulator is developed based on the U(1) gauge field slave boson
model and is shown to exhibit properties qualitatively consistent with the
experimental data.Comment: 11 pages REVTeX, 3 ps figures; version to appear in PR
Vortons in the SO(5) model of high temperature superconductivity
It has been shown that superconducting vortices with antiferromagnetic cores
arise within Zhang's SO(5) model of high temperature supercondictivity. Similar
phenomena where the symmetry is not restored in the core of the vortex was
discussed by Witten in the case of cosmic strings. It was also suggested that
such strings can form stable vortons, which are closed loops of such vortices.
Motivated by this analogy, in following we will show that loops of such
vortices in the SO(5) model of high T_c superconductivity can exist as
classically stable objects, stabilized by the presence of conserved charges
trapped on the vortex core. These objects carry angular momentum which
counteracts the effect of the string tension that causes the loops to shrink.
The existence of such quasiparticles, which are called vortons, could be
interesting for the physics of high temperature superconductors. We also
speculate that the phase transition between superconducting and
antiferromagnetic phases at zero external magnetic field when the doping
parameter changes is associated with vortons.Comment: 11 page
3D Morphology, Ultrastructure and Development of Ceratomyxa puntazzi Stages: First Insights into the Mechanisms of Motility and Budding in the Myxozoa
Free, amoeboid movement of organisms within media as well as substrate-dependent cellular crawling processes of cells and organisms require an actin cytoskeleton. This system is also involved in the cytokinetic processes of all eukaryotic cells. Myxozoan parasites are known for the disease they cause in economical important fishes. Usually, their pathology is related to rapid proliferation in the host. However, the sequences of their development are still poorly understood, especially with regard to pre-sporogonic proliferation mechanisms. The present work employs light microscopy (LM), electron microscopy (SEM, TEM) and confocal laser scanning microscopy (CLSM) in combination with specific stains (Nile Red, DAPI, Phalloidin), to study the three-dimensional morphology, motility, ultrastructure and cellular composition of Ceratomyxa puntazzi, a myxozoan inhabiting the bile of the sharpsnout seabream
Prolog Technology Reinforcement Learning Prover: (System Description)
We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus. The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP builds on the leanCoP Prolog implementation and adds learning-guided Monte-Carlo Tree Search as done in the rlCoP system. Other components include a Python interface to plCoP and machine learners, and an external proof checker that verifies the validity of plCoP proofs. The toolkit is evaluated on two benchmarks and we demonstrate its extendability by two additions: (1) guidance is extended to reduction steps and (2) the standard leanCoP calculus is extended with rewrite steps and their learned guidance. We argue that the Prolog setting is suitable for combining statistical and symbolic learning methods. The complete toolkit is publicly released. © 2020, Springer Nature Switzerland AG
ProofWatch: Watchlist Guidance for Large Theories in E
Watchlist (also hint list) is a mechanism that allows related proofs to guide
a proof search for a new conjecture. This mechanism has been used with the
Otter and Prover9 theorem provers, both for interactive formalizations and for
human-assisted proving of open conjectures in small theories. In this work we
explore the use of watchlists in large theories coming from first-order
translations of large ITP libraries, aiming at improving hammer-style
automation by smarter internal guidance of the ATP systems. In particular, we
(i) design watchlist-based clause evaluation heuristics inside the E ATP
system, and (ii) develop new proof guiding algorithms that load many previous
proofs inside the ATP and focus the proof search using a dynamically updated
notion of proof matching. The methods are evaluated on a large set of problems
coming from the Mizar library, showing significant improvement of E's standard
portfolio of strategies, and also of the previous best set of strategies
invented for Mizar by evolutionary methods.Comment: 19 pages, 10 tables, submitted to ITP 2018 at FLO
GRUNGE: A Grand Unified ATP Challenge
This paper describes a large set of related theorem proving problems obtained
by translating theorems from the HOL4 standard library into multiple logical
formalisms. The formalisms are in higher-order logic (with and without type
variables) and first-order logic (possibly with multiple types, and possibly
with type variables). The resultant problem sets allow us to run automated
theorem provers that support different logical formats on corresponding
problems, and compare their performances. This also results in a new "grand
unified" large theory benchmark that emulates the ITP/ATP hammer setting, where
systems and metasystems can use multiple ATP formalisms in complementary ways,
and jointly learn from the accumulated knowledge.Comment: CADE 27 -- 27th International Conference on Automated Deductio
- …