542 research outputs found
Bautin-type bifurkations and stability of energy solutions for a delay differential equation modeling leukemia
In [3], [4] a mathematical model of chronic myelogenous leukemia is considered
Generating random density matrices
We study various methods to generate ensembles of random density matrices of
a fixed size N, obtained by partial trace of pure states on composite systems.
Structured ensembles of random pure states, invariant with respect to local
unitary transformations are introduced. To analyze statistical properties of
quantum entanglement in bi-partite systems we analyze the distribution of
Schmidt coefficients of random pure states. Such a distribution is derived in
the case of a superposition of k random maximally entangled states. For another
ensemble, obtained by performing selective measurements in a maximally
entangled basis on a multi--partite system, we show that this distribution is
given by the Fuss-Catalan law and find the average entanglement entropy. A more
general class of structured ensembles proposed, containing also the case of
Bures, forms an extension of the standard ensemble of structureless random pure
states, described asymptotically, as N \to \infty, by the Marchenko-Pastur
distribution.Comment: 13 pages in latex with 8 figures include
Interplay between Symmetric Exchange Anisotropy, Uniform Dzyaloshinskii-Moriya Interaction and Magnetic Fields in the Phase Diagram of Quantum Magnets and Superconductors
We theoretically study the joint influence of uniform Dzyaloshinskii-Moriya
(DM) interactions, symmetric exchange anisotropy (with its axis parallel to the
DM vector) and arbitrarily oriented magnetic fields on one-dimensional spin 1/2
antiferromagnets. We show that the zero-temperature phase diagram contains
three competing phases: (i) an antiferromagnet with Neel vector in the plane
spanned by the DM vector and the magnetic field, (ii) a {\em dimerized}
antiferromagnet with Neel vector perpendicular to both the DM vector and the
magnetic field, and (iii) a gapless Luttinger liquid. Phase (i) is destroyed by
a small magnetic field component along the DM vector and is furthermore
unstable beyond a critical value of easy-plane anisotropy, which we estimate
using Abelian and non-Abelian bosonization along with perturbative
renormalization group. We propose a mathematical equivalent of the spin model
in a one-dimensional Josephson junction (JJ) array located in proximity to a
bulk superconductor.
We discuss the analogues of the magnetic phases in the superconducting
context and comment on their experimental viability.Comment: 20 pages, 16 figures; submitted to Phys. Rev.
Symmetries of the Dirac operators associated with covariantly constant Killing-Yano tensors
The continuous and discrete symmetries of the Dirac-type operators produced
by particular Killing-Yano tensors are studied in manifolds of arbitrary
dimensions. The Killing-Yano tensors considered are covariantly constant and
realize certain square roots of the metric tensor. Such a Killing-Yano tensor
produces simultaneously a Dirac-type operator and the generator of a
one-parameter Lie group connecting this operator with the standard Dirac one.
The Dirac operators are related among themselves through continuous or discrete
transformations. It is shown that the groups of the continuous symmetry can be
only U(1) and SU(2), specific to (hyper-)Kahler spaces, but arising even in
cases when the requirements for these special geometries are not fulfilled. The
discrete symmetries are also studied obtaining the discrete groups Z_4 and Q.
The briefly presented examples are the Euclidean Taub-NUT space and the
Minkowski spacetime.Comment: 27 pages, latex, no figures, final version to be published in Class.
Quantum Gravit
Random matrix techniques in quantum information theory
The purpose of this review article is to present some of the latest
developments using random techniques, and in particular, random matrix
techniques in quantum information theory. Our review is a blend of a rather
exhaustive review, combined with more detailed examples -- coming from research
projects in which the authors were involved. We focus on two main topics,
random quantum states and random quantum channels. We present results related
to entropic quantities, entanglement of typical states, entanglement
thresholds, the output set of quantum channels, and violations of the minimum
output entropy of random channels
Observables of the Euclidean Supergravity
The set of constraints under which the eigenvalues of the Dirac operator can
play the role of the dynamical variables for Euclidean supergravity is derived.
These constraints arise when the gauge invariance of the eigenvalues of the
Dirac operator is imposed. They impose conditions which restrict the
eigenspinors of the Dirac operator.Comment: Revised version, some misprints in the ecuations (11), (13) and (17)
corrected. The errors in the published version will appear cortected in a
future erratu
Evolutionary Events in a Mathematical Sciences Research Collaboration Network
This study examines long-term trends and shifting behavior in the
collaboration network of mathematics literature, using a subset of data from
Mathematical Reviews spanning 1985-2009. Rather than modeling the network
cumulatively, this study traces the evolution of the "here and now" using
fixed-duration sliding windows. The analysis uses a suite of common network
diagnostics, including the distributions of degrees, distances, and clustering,
to track network structure. Several random models that call these diagnostics
as parameters help tease them apart as factors from the values of others. Some
behaviors are consistent over the entire interval, but most diagnostics
indicate that the network's structural evolution is dominated by occasional
dramatic shifts in otherwise steady trends. These behaviors are not distributed
evenly across the network; stark differences in evolution can be observed
between two major subnetworks, loosely thought of as "pure" and "applied",
which approximately partition the aggregate. The paper characterizes two major
events along the mathematics network trajectory and discusses possible
explanatory factors.Comment: 30 pages, 14 figures, 1 table; supporting information: 5 pages, 5
figures; published in Scientometric
Endo-sinus bone gain in case of lateral sinus floor elevation with immediate implant placement without grafting material
The superior ophthalmic vein approach for the treatment of carotid-cavernous fistulas: Our first experience
Complex cavernous sinus fistulae (CCF) are still a technical challenge to neurovascular team. The most commonly performed treatment consists in endovascular embolization of the lesion through an arterial or venous approach. Not always these conventional routes are feasible, requiring alternative routes. We report a case of a 44-year-old woman with a complex indirect (Barrow D) carotid cavernous sinus fistula treated by two interventional sessions that imposing a retrograde direct transvenous approach via the superior ophthalmic vein
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