2,911 research outputs found
Generalized Boltzmann Equation in a Manifestly Covariant Relativistic Statistical Mechanics
We consider the relativistic statistical mechanics of an ensemble of
events with motion in space-time parametrized by an invariant ``historical
time'' We generalize the approach of Yang and Yao, based on the Wigner
distribution functions and the Bogoliubov hypotheses, to find the approximate
dynamical equation for the kinetic state of any nonequilibrium system to the
relativistic case, and obtain a manifestly covariant Boltzmann-type equation
which is a relativistic generalization of the Boltzmann-Uehling-Uhlenbeck (BUU)
equation for indistinguishable particles. This equation is then used to prove
the -theorem for evolution in In the equilibrium limit, the
covariant forms of the standard statistical mechanical distributions are
obtained. We introduce two-body interactions by means of the direct action
potential where is an invariant distance in the Minkowski
space-time. The two-body correlations are taken to have the support in a
relative -invariant subregion of the full spacelike region. The
expressions for the energy density and pressure are obtained and shown to have
the same forms (in terms of an invariant distance parameter) as those of the
nonrelativistic theory and to provide the correct nonrelativistic limit
Foundations of a spacetime path formalism for relativistic quantum mechanics
Quantum field theory is the traditional solution to the problems inherent in
melding quantum mechanics with special relativity. However, it has also long
been known that an alternative first-quantized formulation can be given for
relativistic quantum mechanics, based on the parametrized paths of particles in
spacetime. Because time is treated similarly to the three space coordinates,
rather than as an evolution parameter, such a spacetime approach has proved
particularly useful in the study of quantum gravity and cosmology. This paper
shows how a spacetime path formalism can be considered to arise naturally from
the fundamental principles of the Born probability rule, superposition, and
Poincar\'e invariance. The resulting formalism can be seen as a foundation for
a number of previous parametrized approaches in the literature, relating, in
particular, "off-shell" theories to traditional on-shell quantum field theory.
It reproduces the results of perturbative quantum field theory for free and
interacting particles, but provides intriguing possibilities for a natural
program for regularization and renormalization. Further, an important
consequence of the formalism is that a clear probabilistic interpretation can
be maintained throughout, with a natural reduction to non-relativistic quantum
mechanics.Comment: RevTex 4, 42 pages; V6 is as accepted for publication in the Journal
of Mathematical Physics, updated in response to referee comments; V7 includes
final editorial correction
Semigroup evolution in Wigner Weisskopf pole approximation with Markovian spectral coupling
We establish the relation between the Wigner-Weisskopf theory for the
description of an unstable system and the theory of coupling to an environment.
According to the Wigner-Weisskopf general approach, even within the pole
approximation (neglecting the background contribution) the evolution of a total
system subspace is not an exact semigroup for the multi-channel decay, unless
the projectors into eigesntates of the reduced evolution generator are
orthogonal. In this case these projectors must be evaluated at different pole
locations . Since the orthogonality relation does not
generally hold at different values of , for example, when there is symmetry
breaking, the semigroup evolution is a poor approximation for the multi-channel
decay, even for a very weak coupling. Nevertheless, there exists a possibility
not only to ensure the orthogonality of the projectors regardless the
number of the poles, but also to simultaneously suppress the effect of the
background contribution. This possibility arises when the theory is generalized
to take into account interactions with an environment. In this case , and
hence its eigenvectors as well, are {\it independent} of , which corresponds
to a structure of the coupling to the continuum spectrum associated with the
Markovian limit.Comment: 9 pages, 3 figure
Quantum Time and Spatial Localization: An Analysis of the Hegerfeldt Paradox
Two related problems in relativistic quantum mechanics, the apparent
superluminal propagation of initially localized particles and dependence of
spatial localization on the motion of the observer, are analyzed in the context
of Dirac's theory of constraints. A parametrization invariant formulation is
obtained by introducing time and energy operators for the relativistic particle
and then treating the Klein-Gordon equation as a constraint. The standard,
physical Hilbert space is recovered, via integration over proper time, from an
augmented Hilbert space wherein time and energy are dynamical variables. It is
shown that the Newton-Wigner position operator, being in this description a
constant of motion, acts on states in the augmented space. States with strictly
positive energy are non-local in time; consequently, position measurements
receive contributions from states representing the particle's position at many
times. Apparent superluminal propagation is explained by noting that, as the
particle is potentially in the past (or future) of the assumed initial place
and time of localization, it has time to propagate to distant regions without
exceeding the speed of light. An inequality is proven showing the Hegerfeldt
paradox to be completely accounted for by the hypotheses of subluminal
propagation from a set of initial space-time points determined by the quantum
time distribution arising from the positivity of the system's energy. Spatial
localization can nevertheless occur through quantum interference between states
representing the particle at different times. The non-locality of the same
system to a moving observer is due to Lorentz rotation of spatial axes out of
the interference minimum.Comment: This paper is identical to the version appearing in J. Math. Phys.
41; 6093 (Sept. 2000). The published version will be found at
http://ojps.aip.org/jmp/. The paper (40 page PDF file) has been completely
revised since the last posting to this archiv
Scaling Bounded Model Checking By Transforming Programs With Arrays
Bounded Model Checking is one the most successful techniques for finding bugs
in program. However, model checkers are resource hungry and are often unable to
verify programs with loops iterating over large arrays.We present a
transformation that enables bounded model checkers to verify a certain class of
array properties. Our technique transforms an array-manipulating (ANSI-C)
program to an array-free and loop-free (ANSI-C) program thereby reducing the
resource requirements of a model checker significantly. Model checking of the
transformed program using an off-the-shelf bounded model checker simulates the
loop iterations efficiently. Thus, our transformed program is a sound
abstraction of the original program and is also precise in a large number of
cases - we formally characterize the class of programs for which it is
guaranteed to be precise. We demonstrate the applicability and usefulness of
our technique on both industry code as well as academic benchmarks
On Locality in Quantum General Relativity and Quantum Gravity
The physical concept of locality is first analyzed in the special
relativistic quantum regime, and compared with that of microcausality and the
local commutativity of quantum fields. Its extrapolation to quantum general
relativity on quantum bundles over curved spacetime is then described. It is
shown that the resulting formulation of quantum-geometric locality based on the
concept of local quantum frame incorporating a fundamental length embodies the
key geometric and topological aspects of this concept. Taken in conjunction
with the strong equivalence principle and the path-integral formulation of
quantum propagation, quantum-geometric locality leads in a natural manner to
the formulation of quantum-geometric propagation in curved spacetime. Its
extrapolation to geometric quantum gravity formulated over quantum spacetime is
described and analyzed.Comment: Mac-Word file translated to postscript for submission. The author may
be reached at: [email protected] To appear in Found. Phys. vol. 27,
199
A simple and robust method for connecting small-molecule drugs using gene-expression signatures
Interaction of a drug or chemical with a biological system can result in a
gene-expression profile or signature characteristic of the event. Using a
suitably robust algorithm these signatures can potentially be used to connect
molecules with similar pharmacological or toxicological properties. The
Connectivity Map was a novel concept and innovative tool first introduced by
Lamb et al to connect small molecules, genes, and diseases using genomic
signatures [Lamb et al (2006), Science 313, 1929-1935]. However, the
Connectivity Map had some limitations, particularly there was no effective
safeguard against false connections if the observed connections were considered
on an individual-by-individual basis. Further when several connections to the
same small-molecule compound were viewed as a set, the implicit null hypothesis
tested was not the most relevant one for the discovery of real connections.
Here we propose a simple and robust method for constructing the reference
gene-expression profiles and a new connection scoring scheme, which importantly
allows the valuation of statistical significance of all the connections
observed. We tested the new method with the two example gene-signatures (HDAC
inhibitors and Estrogens) used by Lamb et al and also a new gene signature of
immunosuppressive drugs. Our testing with this new method shows that it
achieves a higher level of specificity and sensitivity than the original
method. For example, our method successfully identified raloxifene and
tamoxifen as having significant anti-estrogen effects, while Lamb et al's
Connectivity Map failed to identify these. With these properties our new method
has potential use in drug development for the recognition of pharmacological
and toxicological properties in new drug candidates.Comment: 8 pages, 2 figures, and 2 tables; supplementary data supplied as a
ZIP fil
Propagation of an Earth-directed coronal mass ejection in three dimensions
Solar coronal mass ejections (CMEs) are the most significant drivers of
adverse space weather at Earth, but the physics governing their propagation
through the heliosphere is not well understood. While stereoscopic imaging of
CMEs with the Solar Terrestrial Relations Observatory (STEREO) has provided
some insight into their three-dimensional (3D) propagation, the mechanisms
governing their evolution remain unclear due to difficulties in reconstructing
their true 3D structure. Here we use a new elliptical tie-pointing technique to
reconstruct a full CME front in 3D, enabling us to quantify its deflected
trajectory from high latitudes along the ecliptic, and measure its increasing
angular width and propagation from 2-46 solar radii (approximately 0.2 AU).
Beyond 7 solar radii, we show that its motion is determined by an aerodynamic
drag in the solar wind and, using our reconstruction as input for a 3D
magnetohydrodynamic simulation, we determine an accurate arrival time at the
Lagrangian L1 point near Earth.Comment: 5 figures, 2 supplementary movie
Single cell profiling of COVID-19 patients: an international data resource from multiple tissues
In late 2019 and through 2020, the COVID-19 pandemic swept the world, presenting both scientific and medical challenges associated with understanding and treating a previously unknown disease. To help address the need for great understanding of COVID-19, the scientific community mobilized and banded together rapidly to characterize SARS-CoV-2 infection, pathogenesis and its distinct disease trajectories. The urgency of COVID-19 provided a pressing use-case for leveraging relatively new tools, technologies, and nascent collaborative networks. Single-cell biology is one such example that has emerged over the last decade as a powerful approach that provides unprecedented resolution to the cellular and molecular underpinnings of biological processes. Early foundational work within the single-cell community, including the Human Cell Atlas, utilized published and unpublished data to characterize the putative target cells of SARS-CoV-2 sampled from diverse organs based on expression of the viral receptor ACE2 and associated entry factors TMPRSS2 and CTSL (Muus et al., 2020; Sungnak et al., 2020; Ziegler et al., 2020). This initial characterization of reference data provided an important foundation for framing infection and pathology in the airway as well as other organs. However, initial community analysis was limited to samples derived from uninfected donors and other previously-sampled disease indications. This report provides an overview of a single-cell data resource derived from samples from COVID-19 patients along with initial observations and guidance on data reuse and exploration
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