2,522 research outputs found
Effects of two dimensional plasmons on the tunneling density of states
We show that gapless plasmons lead to a universal
correction to the tunneling
density of states of a clean two dimensional Coulomb interacting electron gas.
We also discuss a counterpart of this effect in the "composite fermion metal"
which forms in the presence of a quantizing perpendicular magnetic field
corresponding to the half-filled Landau level. We argue that the latter
phenomenon might be relevant for deviations from a simple scaling observed by
A.Chang et al in the tunneling characteristics of Quantum Hall liquids.Comment: 12 pages, Latex, NORDITA repor
Density of states of a two-dimensional electron gas in a non-quantizing magnetic field
We study local density of electron states of a two-dimentional conductor with
a smooth disorder potential in a non-quantizing magnetic field, which does not
cause the standart de Haas-van Alphen oscillations. It is found, that despite
the influence of such ``classical'' magnetic field on the average electron
density of states (DOS) is negligibly small, it does produce a significant
effect on the DOS correlations. The corresponding correlation function exhibits
oscillations with the characteristic period of cyclotron quantum
.Comment: 7 pages, including 3 figure
Transumbilical venous access with small diameter silastic catheters in very low birth weight infants
Characterization of the Sequential Product on Quantum Effects
We present a characterization of the standard sequential product of quantum
effects. The characterization is in term of algebraic, continuity and duality
conditions that can be physically motivated.Comment: 11 pages. Accepted for publication in the Journal of Mathematical
Physic
Power of unentangled measurements on two antiparallel spins
We consider a pair of antiparallel spins polarized in a random direction to
encode quantum information. We wish to extract as much information as possible
on the polarization direction attainable by an unentangled measurement, i.e.,
by a measurement, whose outcomes are associated with product states. We develop
analytically the upper bound 0.7935 bits to the Shannon mutual information
obtainable by an unentangled measurement, which is definitely less than the
value 0.8664 bits attained by an entangled measurement. This proves our main
result, that not every ensemble of product states can be optimally
distinguished by an unentangled measurement, if the measure of
distinguishability is defined in the sense of Shannon. We also present results
from numerical calculations and discuss briefly the case of parallel spins.Comment: Latex file, 18 pages, 1 figure; published versio
A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula
Continuing our development of a mathematical theory of stochastic
microlensing, we study the random shear and expected number of random lensed
images of different types. In particular, we characterize the first three
leading terms in the asymptotic expression of the joint probability density
function (p.d.f.) of the random shear tensor at a general point in the lens
plane due to point masses in the limit of an infinite number of stars. Up to
this order, the p.d.f. depends on the magnitude of the shear tensor, the
optical depth, and the mean number of stars through a combination of radial
position and the stars' masses. As a consequence, the p.d.f.s of the shear
components are seen to converge, in the limit of an infinite number of stars,
to shifted Cauchy distributions, which shows that the shear components have
heavy tails in that limit. The asymptotic p.d.f. of the shear magnitude in the
limit of an infinite number of stars is also presented. Extending to general
random distributions of the lenses, we employ the Kac-Rice formula and Morse
theory to deduce general formulas for the expected total number of images and
the expected number of saddle images. We further generalize these results by
considering random sources defined on a countable compact covering of the light
source plane. This is done to introduce the notion of {\it global} expected
number of positive parity images due to a general lensing map. Applying the
result to microlensing, we calculate the asymptotic global expected number of
minimum images in the limit of an infinite number of stars, where the stars are
uniformly distributed. This global expectation is bounded, while the global
expected number of images and the global expected number of saddle images
diverge as the order of the number of stars.Comment: To appear in JM
Perturbation theorems for Hele-Shaw flows and their applications
In this work, we give a perturbation theorem for strong polynomial solutions
to the zero surface tension Hele-Shaw equation driven by injection or suction,
so called the Polubarinova-Galin equation. This theorem enables us to explore
properties of solutions with initial functions close to but are not polynomial.
Applications of this theorem are given in the suction or injection case. In the
former case, we show that if the initial domain is close to a disk, most of
fluid will be sucked before the strong solution blows up. In the later case, we
obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows
in terms of invariant Richardson complex moments. This rescaling behavior
result generalizes a recent result regarding large-time rescaling behavior for
small data in terms of moments. As a byproduct of a theorem in this paper, a
short proof of existence and uniqueness of strong solutions to the
Polubarinova-Galin equation is given.Comment: 25 page
Density of states of the interacting two-dimensional electron gas
We study the influence of electron-electron interactions on the density of
states (DOS) of clean 2D electron gas. We confirm the linear cusp in the DOS
around the Fermi level, which was obtained previously. The cusp crosses over to
a pure logarithmic dependence further away from the Fermi surface.Comment: RevTeX, 3 pages, no figure
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