566 research outputs found

### Boltzmann Collision Term

We derive the Boltzmann equation for scalar fields using the
Schwinger-Keldysh formalism. The focus lies on the derivation of the collision
term. We show that the relevant self-energy diagrams have a factorization
property. The collision term assumes the Boltzmann-like form of scattering
probability times statistical factors for those self-energy diagrams which
correspond to tree level scattering processes. Our proof covers scattering
processes with any number of external particles, which come from self-energy
diagrams with any number of loops.Comment: 17 pages, 4 figure

### Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting

In this paper we establish links between, and new results for, three problems
that are not usually considered together. The first is a matrix decomposition
problem that arises in areas such as statistical modeling and signal
processing: given a matrix $X$ formed as the sum of an unknown diagonal matrix
and an unknown low rank positive semidefinite matrix, decompose $X$ into these
constituents. The second problem we consider is to determine the facial
structure of the set of correlation matrices, a convex set also known as the
elliptope. This convex body, and particularly its facial structure, plays a
role in applications from combinatorial optimization to mathematical finance.
The third problem is a basic geometric question: given points
$v_1,v_2,...,v_n\in \R^k$ (where $n > k$) determine whether there is a centered
ellipsoid passing \emph{exactly} through all of the points.
We show that in a precise sense these three problems are equivalent.
Furthermore we establish a simple sufficient condition on a subspace $U$ that
ensures any positive semidefinite matrix $L$ with column space $U$ can be
recovered from $D+L$ for any diagonal matrix $D$ using a convex
optimization-based heuristic known as minimum trace factor analysis. This
result leads to a new understanding of the structure of rank-deficient
correlation matrices and a simple condition on a set of points that ensures
there is a centered ellipsoid passing through them.Comment: 20 page

### The kink Casimir energy in a lattice sine-Gordon model

The Casimir energy of quantum fluctuations about the classical kink
configuration is computed numerically for a recently proposed lattice
sine-Gordon model. This energy depends periodically on the kink position and is
found to be approximately sinusoidal.Comment: 10 pages, 4 postscript figure

### Micro-SQUID technique for studying the temperature dependence of switching fields of single nanoparticles

An improved micro-SQUID technique is presented allowing us to measure the
temperature dependence of the magnetisation switching fields of single
nanoparticles well above the critical superconducting temperature of the SQUID.
Our first measurements on 3 nm cobalt nanoparticle embedded in a niobium matrix
are compared to the Neel Brown model describing the magnetisation reversal by
thermal activation over a single anisotropy barrier.Comment: 3 pages, 4 figures; conference proceeding: 1st Joint European
Magnetic Symposia (JEMS'01), Grenoble (France), 28th August - 1st September,
200

### Blinking statistics of a molecular beacon triggered by end-denaturation of DNA

We use a master equation approach based on the Poland-Scheraga free energy
for DNA denaturation to investigate the (un)zipping dynamics of a denaturation
wedge in a stretch of DNA, that is clamped at one end. In particular, we
quantify the blinking dynamics of a fluorophore-quencher pair mounted within
the denaturation wedge. We also study the behavioural changes in the presence
of proteins, that selectively bind to single-stranded DNA. We show that such a
setup could be well-suited as an easy-to-implement nanodevice for sensing
environmental conditions in small volumes.Comment: 14 pages, 5 figures, LaTeX, IOP style. Accepted to J Phys Cond Mat
special issue on diffusio

### Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements

We introduce the problem of constructing weighted complex projective
2-designs from the union of a family of orthonormal bases. If the weight
remains constant across elements of the same basis, then such designs can be
interpreted as generalizations of complete sets of mutually unbiased bases,
being equivalent whenever the design is composed of d+1 bases in dimension d.
We show that, for the purpose of quantum state determination, these designs
specify an optimal collection of orthogonal measurements. Using highly
nonlinear functions on abelian groups, we construct explicit examples from d+2
orthonormal bases whenever d+1 is a prime power, covering dimensions d=6, 10,
and 12, for example, where no complete sets of mutually unbiased bases have
thus far been found.Comment: 28 pages, to appear in J. Math. Phy

### Nonlocality in mesoscopic Josephson junctions with strip geometry

We study the current in a clean superconductor-normal-metal-superconductor
junction of length d and width w in the presence of an applied magnetic field
H. We show that both the geometrical pattern of the current density and the
critical current as a function of the total flux in the junction, depend on the
ratio of the Josephson vortex distance a_0 and the range r of the nonlocal
electrodynamics. In particular, the critical current has the periodicity of the
superconducting flux quantum only for r<a_0 and acquires, due to boundary
effects, the double (pseudo-) periodicity for strong nonlocality, r>a_0.
Comparing our results to recent experiments of Heida et al. [Phys. Rev. B 57,
R5618 (1998)] we find good agreement.Comment: 4 pages, 5 figures, to be published in the RC section of Phys. Rev.

### Stepwise Projection: Toward Brane Setups for Generic Orbifold Singularities

The construction of brane setups for the exceptional series E6,E7,E8 of SU(2)
orbifolds remains an ever-haunting conundrum. Motivated by techniques in some
works by Muto on non-Abelian SU(3) orbifolds, we here provide an algorithmic
outlook, a method which we call stepwise projection, that may shed some light
on this puzzle. We exemplify this method, consisting of transformation rules
for obtaining complex quivers and brane setups from more elementary ones, to
the cases of the D-series and E6 finite subgroups of SU(2). Furthermore, we
demonstrate the generality of the stepwise procedure by appealing to Frobenius'
theory of Induced Representations. Our algorithm suggests the existence of
generalisations of the orientifold plane in string theory.Comment: 22 pages, 3 figure

### Hypervitaminosis A is prevalent in children with CKD and contributes to hypercalcemia.

Vitamin A accumulates in renal failure, but the prevalence of hypervitaminosis A in children with predialysis chronic kidney disease (CKD) is not known. Hypervitaminosis A has been associated with hypercalcemia. In this study we compared dietary vitamin A intake with serum retinoid levels and their associations with hypercalcemia

### The Bose Gas and Asymmetric Simple Exclusion Process on the Half-Line

In this paper we find explicit formulas for: (1) Green's function for a
system of one-dimensional bosons interacting via a delta-function potential
with particles confined to the positive half-line; and (2) the transition
probability for the one-dimensional asymmetric simple exclusion process (ASEP)
with particles confined to the nonnegative integers. These are both for systems
with a finite number of particles. The formulas are analogous to ones obtained
earlier for the Bose gas and ASEP on the line and integers, respectively. We
use coordinate Bethe Ansatz appropriately modified to account for confinement
of the particles to the half-line. As in the earlier work, the proof for the
ASEP is less straightforward than for the Bose gas.Comment: 14 Page

- â€¦