3,116 research outputs found
Zooming in on local level statistics by supersymmetric extension of free probability
We consider unitary ensembles of Hermitian NxN matrices H with a confining
potential NV where V is analytic and uniformly convex. From work by
Zinn-Justin, Collins, and Guionnet and Maida it is known that the large-N limit
of the characteristic function for a finite-rank Fourier variable K is
determined by the Voiculescu R-transform, a key object in free probability
theory. Going beyond these results, we argue that the same holds true when the
finite-rank operator K has the form that is required by the Wegner-Efetov
supersymmetry method of integration over commuting and anti-commuting
variables. This insight leads to a potent new technique for the study of local
statistics, e.g., level correlations. We illustrate the new technique by
demonstrating universality in a random matrix model of stochastic scattering.Comment: 38 pages, 3 figures, published version, minor changes in Section
Quantum tunneling on graphs
We explore the tunneling behavior of a quantum particle on a finite graph, in
the presence of an asymptotically large potential. Surprisingly the behavior is
governed by the local symmetry of the graph around the wells.Comment: 18 page
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Comprehensive transcriptomic analysis of cell lines as models of primary tumors across 22 tumor types.
Cancer cell lines are a cornerstone of cancer research but previous studies have shown that not all cell lines are equal in their ability to model primary tumors. Here we present a comprehensive pan-cancer analysis utilizing transcriptomic profiles from The Cancer Genome Atlas and the Cancer Cell Line Encyclopedia to evaluate cell lines as models of primary tumors across 22 tumor types. We perform correlation analysis and gene set enrichment analysis to understand the differences between cell lines and primary tumors. Additionally, we classify cell lines into tumor subtypes in 9 tumor types. We present our pancreatic cancer results as a case study and find that the commonly used cell line MIA PaCa-2 is transcriptionally unrepresentative of primary pancreatic adenocarcinomas. Lastly, we propose a new cell line panel, the TCGA-110-CL, for pan-cancer studies. This study provides a resource to help researchers select more representative cell line models
Some Comments on Gravitational Entropy and the Inverse Mean Curvature Flow
The Geroch-Wald-Jang-Huisken-Ilmanen approach to the positive energy problem
to may be extended to give a negative lower bound for the mass of
asymptotically Anti-de-Sitter spacetimes containing horizons with exotic
topologies having ends or infinities of the form , in
terms of the cosmological constant. We also show how the method gives a lower
bound for for the mass of time-symmetric initial data sets for black holes with
vectors and scalars in terms of the mass, of the double extreme
black hole with the same charges. I also give a lower bound for the area of an
apparent horizon, and hence a lower bound for the entropy in terms of the same
function . This shows that the so-called attractor behaviour extends
beyond the static spherically symmetric case. and underscores the general
importance of the function . There are hints that higher dimensional
generalizations may involve the Yamabe conjectures.Comment: 13pp. late
Quantum rings as electron spin beam splitters
Quantum interference and spin-orbit interaction in a one-dimensional
mesoscopic semiconductor ring with one input and two output leads can act as a
spin beam splitter. Different polarization can be achieved in the two output
channels from an originally totally unpolarized incoming spin state, very much
like in a Stern-Gerlach apparatus. We determine the relevant parameters such
that the device has unit efficiency.Comment: 4 pages, 3 figures; minor change
Giant planar Hall effect in colossal magnetoresistive La0.84Sr0.16MnO3 thin films
The transverse resistivity in thin films of La0.84Sr0.16MnO3 (LSMO) exhibits sharp field-symmetric jumps below TC . We show that a likely source of this behavior is the giant planar Hall effect combined with biaxial magnetic anisotropy. The effect is comparable in magnitude to that observed recently in the magnetic semiconductor Ga(Mn)As. It can be potentially used in applications such as magnetic sensors and nonvolatile memory devices
Spintronic single qubit gate based on a quantum ring with spin-orbit interaction
In a quantum ring connected with two external leads the spin properties of an
incoming electron are modified by the spin-orbit interaction resulting in a
transformation of the qubit state carried by the spin. The ring acts as a one
qubit spintronic quantum gate whose properties can be varied by tuning the
Rashba parameter of the spin-orbit interaction, by changing the relative
position of the junctions, as well as by the size of the ring. We show that a
large class of unitary transformations can be attained with already one ring --
or a few rings in series -- including the important cases of the Z, X, and
Hadamard gates. By choosing appropriate parameters the spin transformations can
be made unitary, which corresponds to lossless gates.Comment: 4 pages, 4 figure
Deformation Quantization of Bosonic Strings
Deformation quantization of bosonic strings is considered. We show that the
light-cone gauge is the most convenient classical description to perform the
quantization of bosonic strings in the deformation quantization formalism.
Similar to the field theory case, the oscillator variables greatly facilitates
the analysis. The mass spectrum, propagators and the Virasoro algebra are
finally described within this deformation quantization scheme.Comment: 33+1 pages, harvmac file, no figure
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