3,436 research outputs found
Examining Servant Leadership Behaviors in Higher Education: Explorations of a Compassion-Based Leadership Model through the Lens of University Leaders
A capstone submitted in partial fulfillment of the requirements for the degree of Doctor of Education in the Ernst and Sara Lane Volgenau College of Education at Morehead State University by Karol A. D. Johansen on March 31, 2023
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
Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive
We investigate the set a) of positive, trace preserving maps acting on
density matrices of size N, and a sequence of its nested subsets: the sets of
maps which are b) decomposable, c) completely positive, d) extended by identity
impose positive partial transpose and e) are superpositive. Working with the
Hilbert-Schmidt (Euclidean) measure we derive tight explicit two-sided bounds
for the volumes of all five sets. A sample consequence is the fact that, as N
increases, a generic positive map becomes not decomposable and, a fortiori, not
completely positive.
Due to the Jamiolkowski isomorphism, the results obtained for quantum maps
are closely connected to similar relations between the volume of the set of
quantum states and the volumes of its subsets (such as states with positive
partial transpose or separable states) or supersets. Our approach depends on
systematic use of duality to derive quantitative estimates, and on various
tools of classical convexity, high-dimensional probability and geometry of
Banach spaces, some of which are not standard.Comment: 34 pages in Latex including 3 figures in eps, ver 2: minor revision
Spectral density of generalized Wishart matrices and free multiplicative convolution
We investigate the level density for several ensembles of positive random
matrices of a Wishart--like structure, , where stands for a
nonhermitian random matrix. In particular, making use of the Cauchy transform,
we study free multiplicative powers of the Marchenko-Pastur (MP) distribution,
, which for an integer yield Fuss-Catalan
distributions corresponding to a product of independent square random
matrices, . New formulae for the level densities are derived
for and . Moreover, the level density corresponding to the
generalized Bures distribution, given by the free convolution of arcsine and MP
distributions is obtained. We also explain the reason of such a curious
convolution. The technique proposed here allows for the derivation of the level
densities for several other cases.Comment: 10 latex pages including 4 figures, Ver 4, minor improvements and
references updat
CP^n, or, entanglement illustrated
We show that many topological and geometrical properties of complex
projective space can be understood just by looking at a suitably constructed
picture. The idea is to view CP^n as a set of flat tori parametrized by the
positive octant of a round sphere. We pay particular attention to submanifolds
of constant entanglement in CP^3 and give a few new results concerning them.Comment: 28 pages, 9 figure
Temperature dependence of the resonance and low energy spin excitations in superconducting FeTeSe
We use inelastic neutron scattering to study the temperature dependence of
the low-energy spin excitations in single crystals of superconducting
FeTeSe ( K). In the low-temperature superconducting
state, the imaginary part of the dynamic susceptibility at the electron and
hole Fermi surfaces nesting wave vector ,
, has a small spin gap, a two-dimensional
neutron spin resonance above the spin gap, and increases linearly with
increasing for energies above the resonance. While the intensity
of the resonance decreases like an order parameter with increasing temperature
and disappears at temperature slightly above , the energy of the mode is
weakly temperature dependent and vanishes concurrently above . This
suggests that in spite of its similarities with the resonance in electron-doped
superconducting BaFe(Co,Ni)As, the mode in
FeTeSe is not directly associated with the superconducting
electronic gap.Comment: 7 pages, 6 figure
Fast chromatin immunoprecipitation assay
Chromatin immunoprecipitation (ChIP) is a widely used method to explore in vivo interactions between proteins and DNA. The ChIP assay takes several days to complete, involves several tube transfers and uses either phenolâchlorophorm or spin columns to purify DNA. The traditional ChIP method becomes a challenge when handling multiple samples. We have developed an efficient and rapid Chelex resin-based ChIP procedure that dramatically reduces time of the assay and uses only a single tube to isolate PCR-ready DNA. This method greatly facilitates the probing of chromatin changes over many time points with several antibodies in one experiment
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