648 research outputs found
On the differential geometry of curves in Minkowski space
We discuss some aspects of the differential geometry of curves in Minkowski
space. We establish the Serret-Frenet equations in Minkowski space and use them
to give a very simple proof of the fundamental theorem of curves in Minkowski
space. We also state and prove two other theorems which represent Minkowskian
versions of a very known theorem of the differential geometry of curves in
tridimensional Euclidean space. We discuss the general solution for torsionless
paths in Minkowki space. We then apply the four-dimensional Serret-Frenet
equations to describe the motion of a charged test particle in a constant and
uniform electromagnetic field and show how the curvature and the torsions of
the four-dimensional path of the particle contain information on the
electromagnetic field acting on the particle.Comment: 10 pages. Typeset using REVTE
Dynamical laws of superenergy in General Relativity
The Bel and Bel-Robinson tensors were introduced nearly fifty years ago in an
attempt to generalize to gravitation the energy-momentum tensor of
electromagnetism. This generalization was successful from the mathematical
point of view because these tensors share mathematical properties which are
remarkably similar to those of the energy-momentum tensor of electromagnetism.
However, the physical role of these tensors in General Relativity has remained
obscure and no interpretation has achieved wide acceptance. In principle, they
cannot represent {\em energy} and the term {\em superenergy} has been coined
for the hypothetical physical magnitude lying behind them. In this work we try
to shed light on the true physical meaning of {\em superenergy} by following
the same procedure which enables us to give an interpretation of the
electromagnetic energy. This procedure consists in performing an orthogonal
splitting of the Bel and Bel-Robinson tensors and analysing the different parts
resulting from the splitting. In the electromagnetic case such splitting gives
rise to the electromagnetic {\em energy density}, the Poynting vector and the
electromagnetic stress tensor, each of them having a precise physical
interpretation which is deduced from the {\em dynamical laws} of
electromagnetism (Poynting theorem). The full orthogonal splitting of the Bel
and Bel-Robinson tensors is more complex but, as expected, similarities with
electromagnetism are present. Also the covariant divergence of the Bel tensor
is analogous to the covariant divergence of the electromagnetic energy-momentum
tensor and the orthogonal splitting of the former is found. The ensuing {\em
equations} are to the superenergy what the Poynting theorem is to
electromagnetism. See paper for full abstract.Comment: 27 pages, no figures. Typos corrected, section 9 suppressed and more
acknowledgments added. To appear in Classical and Quantum Gravit
Magnetic-film atom chip with 10 m period lattices of microtraps for quantum information science with Rydberg atoms
We describe the fabrication and construction of a setup for creating lattices
of magnetic microtraps for ultracold atoms on an atom chip. The lattice is
defined by lithographic patterning of a permanent magnetic film. Patterned
magnetic-film atom chips enable a large variety of trapping geometries over a
wide range of length scales. We demonstrate an atom chip with a lattice
constant of 10 m, suitable for experiments in quantum information science
employing the interaction between atoms in highly-excited Rydberg energy
levels. The active trapping region contains lattice regions with square and
hexagonal symmetry, with the two regions joined at an interface. A structure of
macroscopic wires, cut out of a silver foil, was mounted under the atom chip in
order to load ultracold Rb atoms into the microtraps. We demonstrate
loading of atoms into the square and hexagonal lattice sections simultaneously
and show resolved imaging of individual lattice sites. Magnetic-film lattices
on atom chips provide a versatile platform for experiments with ultracold
atoms, in particular for quantum information science and quantum simulation.Comment: 7 pages, 7 figure
Topics on the geometry of D-brane charges and Ramond-Ramond fields
In this paper we discuss some topics on the geometry of type II superstring
backgrounds with D-branes, in particular on the geometrical meaning of the
D-brane charge, the Ramond-Ramond fields and the Wess-Zumino action. We see
that, depending on the behaviour of the D-brane on the four non-compact
space-time directions, we need different notions of homology and cohomology to
discuss the associated fields and charge: we give a mathematical definition of
such notions and show their physical applications. We then discuss the problem
of corretly defining Wess-Zumino action using the theory of p-gerbes. Finally,
we recall the so-called *-problem and make some brief remarks about it.Comment: 29 pages, no figure
Bundle Theory of Improper Spin Transformations
{\it We first give a geometrical description of the action of the parity
operator () on non relativistic spin Pauli spinors in
terms of bundle theory. The relevant bundle, , is a
non trivial extension of the universal covering group .
is the non relativistic limit of the corresponding Dirac matrix
operator and obeys . Then, from the direct
product of O(3) by , naturally induced by the structure of the galilean
group, we identify, in its double cover, the time reversal operator ()
acting on spinors, and its product with . Both, and
, generate the group . As in the case of parity,
is the non relativistic limit of the corresponding Dirac matrix
operator , and obeys .}Comment: 8 pages, Plaintex; titled changed, minor text modifications, one
reference complete
The geometry of entanglement: metrics, connections and the geometric phase
Using the natural connection equivalent to the SU(2) Yang-Mills instanton on
the quaternionic Hopf fibration of over the quaternionic projective space
with an fiber the geometry of
entanglement for two qubits is investigated. The relationship between base and
fiber i.e. the twisting of the bundle corresponds to the entanglement of the
qubits. The measure of entanglement can be related to the length of the
shortest geodesic with respect to the Mannoury-Fubini-Study metric on between an arbitrary entangled state, and the separable state nearest to
it. Using this result an interpretation of the standard Schmidt decomposition
in geometric terms is given. Schmidt states are the nearest and furthest
separable ones lying on, or the ones obtained by parallel transport along the
geodesic passing through the entangled state. Some examples showing the
correspondence between the anolonomy of the connection and entanglement via the
geometric phase is shown. Connections with important notions like the
Bures-metric, Uhlmann's connection, the hyperbolic structure for density
matrices and anholonomic quantum computation are also pointed out.Comment: 42 page
Coset Construction of Gravitational Instantons
We study Ricci-flat metrics on non-compact manifolds with the exceptional
holonomy . We concentrate on the metrics which are defined on
. If the homogeneous coset spaces have weak ,
SU(3) holonomy, the manifold may have
holonomy metrics. Using the formulation with vector fields, we investigate the
metrics with holonomy on . We have found the explicit volume-preserving vector fields on
these manifold using the elementary coordinate parameterization. This
construction is essentially dual to solving the generalized self-duality
condition for spin connections. We present most general differential equations
for each coset. Then, we develop the similar formulation in order to calculate
metrics with holonomyComment: 29 pages, no figure; (v2) Errors are corrected ; (v3) Some
explanations are added. More general differential equations for SU(3)/U(1)
coset are give
Pregnancy-Associated Breast Cancers are Driven by Differences in Adipose Stromal Cells Present During Lactation
Introduction
The prognosis of breast cancer is strongly influenced by the developmental stage of the breast when the tumor is diagnosed. Pregnancy-associated breast cancers (PABCs), cancers diagnosed during pregnancy, lactation, or in the first postpartum year, are typically found at an advanced stage, are more aggressive and have a poorer prognosis. Although the systemic and microenvironmental changes that occur during post-partum involution have been best recognized for their role in the pathogenesis of PABCs, epidemiological data indicate that PABCs diagnosed during lactation have an overall poorer prognosis than those diagnosed during involution. Thus, the physiologic and/or biological events during lactation may have a significant and unrecognized role in the pathobiology of PABCs.
Methods
Syngeneic in vivo mouse models of PABC were used to examine the effects of system and stromal factors during pregnancy, lactation and involution on mammary tumorigenesis. Mammary adipose stromal cell (ASC) populations were isolated from mammary glands and examined by using a combination of in vitro and in vivo functional assays, gene expression analysis, and molecular and cellular assays. Specific findings were further investigated by immunohistochemistry in mammary glands of mice as well as in functional studies using ASCs from lactating mammary glands. Additional findings were further investigated using human clinical samples, human stromal cells and using in vivo xenograft assays.
Results
ASCs present during lactation (ASC-Ls), but not during other mammary developmental stages, promote the growth of carcinoma cells and angiogenesis. ASCs-Ls are distinguished by their elevated expression of cellular retinoic acid binding protein-1 (crabp1), which regulates their ability to retain lipid. Human breast carcinoma-associated fibroblasts (CAFs) exhibit traits of ASC-Ls and express crabp1. Inhibition of crabp1 in CAFs or in ASC-Ls abolished their tumor-promoting activity and also restored their ability to accumulate lipid.
Conclusions
These findings imply that (1) PABC is a complex disease, which likely has different etiologies when diagnosed during different stages of pregnancy; (2) both systemic and local factors are important for the pathobiology of PABCs; and (3) the stromal changes during lactation play a distinct and important role in the etiology and pathogenesis of PABCs that differ from those during post-lactational involution
Impurity and quaternions in nonrelativistic scattering from a quantum memory
Models of quantum computing rely on transformations of the states of a
quantum memory. We study mathematical aspects of a model proposed by Wu in
which the memory state is changed via the scattering of incoming particles.
This operation causes the memory content to deviate from a pure state, i.e.
induces impurity. For nonrelativistic particles scattered from a two-state
memory and sufficiently general interaction potentials in 1+1 dimensions, we
express impurity in terms of quaternionic commutators. In this context, pure
memory states correspond to null hyperbolic quaternions. In the case with point
interactions, the scattering process amounts to appropriate rotations of
quaternions in the frequency domain. Our work complements a previous analysis
by Margetis and Myers (2006 J. Phys. A 39 11567--11581).Comment: 16 pages, no figure
Remarks on the Configuration Space Approach to Spin-Statistics
The angular momentum operators for a system of two spin-zero
indistinguishable particles are constructed, using Isham's Canonical Group
Quantization method. This mathematically rigorous method provides a hint at the
correct definition of (total) angular momentum operators, for arbitrary spin,
in a system of indistinguishable particles. The connection with other
configuration space approaches to spin-statistics is discussed, as well as the
relevance of the obtained results in view of a possible alternative proof of
the spin-statistics theorem.Comment: 18 page
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