9,348 research outputs found
Quantum tomography for collider physics: Illustrations with lepton pair production
Quantum tomography is a method to experimentally extract all that is
observable about a quantum mechanical system. We introduce quantum tomography
to collider physics with the illustration of the angular distribution of lepton
pairs. The tomographic method bypasses much of the field-theoretic formalism to
concentrate on what can be observed with experimental data, and how to
characterize the data. We provide a practical, experimentally-driven guide to
model-independent analysis using density matrices at every step. Comparison
with traditional methods of analyzing angular correlations of inclusive
reactions finds many advantages in the tomographic method, which include
manifest Lorentz covariance, direct incorporation of positivity constraints,
exhaustively complete polarization information, and new invariants free from
frame conventions. For example, experimental data can determine the
of the production process, which is a
model-independent invariant that measures the degree of coherence of the
subprocess. We give reproducible numerical examples and provide a supplemental
standalone computer code that implements the procedure. We also highlight a
property of that guarantees in a least-squares type fit
that a local minimum of a statistic will be a global minimum: There
are no isolated local minima. This property with an automated implementation of
positivity promises to mitigate issues relating to multiple minima and
convention-dependence that have been problematic in previous work on angular
distributions.Comment: 25 pages, 3 figure
On the Hyperbolicity of Lorenz Renormalization
We consider infinitely renormalizable Lorenz maps with real critical exponent
and combinatorial type which is monotone and satisfies a long return
condition. For these combinatorial types we prove the existence of periodic
points of the renormalization operator, and that each map in the limit set of
renormalization has an associated unstable manifold. An unstable manifold
defines a family of Lorenz maps and we prove that each infinitely
renormalizable combinatorial type (satisfying the above conditions) has a
unique representative within such a family. We also prove that each infinitely
renormalizable map has no wandering intervals and that the closure of the
forward orbits of its critical values is a Cantor attractor of measure zero.Comment: 63 pages; 10 figure
Invariant measures for Cherry flows
We investigate the invariant probability measures for Cherry flows, i.e.
flows on the two-torus which have a saddle, a source, and no other fixed
points, closed orbits or homoclinic orbits. In the case when the saddle is
dissipative or conservative we show that the only invariant probability
measures are the Dirac measures at the two fixed points, and the Dirac measure
at the saddle is the physical measure. In the other case we prove that there
exists also an invariant probability measure supported on the quasi-minimal
set, we discuss some situations when this other invariant measure is the
physical measure, and conjecture that this is always the case. The main
techniques used are the study of the integrability of the return time with
respect to the invariant measure of the return map to a closed transversal to
the flow, and the study of the close returns near the saddle.Comment: 12 pages; updated versio
Transitions in a globalising world
The increasing complexity of our global society means that sustainable development cannot be addressed from a single perspective or scientific discipline. By using the concept of transitions, we examine current and future tensions between welfare, well-being and the environment, and focus on four major issues that are of global importance: two of our key natural resources, water and biodiversity; the health of human populations; and the developments related to global tourism. In our global assessment we base ourselves on the most recent scenario efforts of the Intergovernmental Panel on Climate Change (IPCC). Future developments are explored along the lines of four development paths (scenario groups), defined along two dimensions (global versus regional dynamics and emphasising economic objectives versus environmental and equity objectives
Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature
The definition of a nonequilibrium temperature through generalized
fluctuation-dissipation relations relies on the independence of the
fluctuation-dissipation temperature from the observable considered. We argue
that this observable independence is deeply related to the uniformity of the
phase-space probability distribution on the hypersurfaces of constant energy.
This property is shown explicitly on three different stochastic models, where
observable-dependence of the fluctuation-dissipation temperature arises only
when the uniformity of the phase-space distribution is broken. The first model
is an energy transport model on a ring, with biased local transfer rules. In
the second model, defined on a fully connected geometry, energy is exchanged
with two heat baths at different temperatures, breaking the uniformity of the
phase-space distribution. Finally, in the last model, the system is connected
to a zero temperature reservoir, and preserves the uniformity of the
phase-space distribution in the relaxation regime, leading to an
observable-independent temperature.Comment: 15 pages, 7 figure
A Phase Transition for Circle Maps and Cherry Flows
We study weakly order preserving circle maps with a flat interval.
The main result of the paper is about a sharp transition from degenerate
geometry to bounded geometry depending on the degree of the singularities at
the boundary of the flat interval. We prove that the non-wandering set has zero
Hausdorff dimension in the case of degenerate geometry and it has Hausdorff
dimension strictly greater than zero in the case of bounded geometry. Our
results about circle maps allow to establish a sharp phase transition in the
dynamics of Cherry flows
Streaming Tree Transducers
Theory of tree transducers provides a foundation for understanding
expressiveness and complexity of analysis problems for specification languages
for transforming hierarchically structured data such as XML documents. We
introduce streaming tree transducers as an analyzable, executable, and
expressive model for transforming unranked ordered trees in a single pass.
Given a linear encoding of the input tree, the transducer makes a single
left-to-right pass through the input, and computes the output in linear time
using a finite-state control, a visibly pushdown stack, and a finite number of
variables that store output chunks that can be combined using the operations of
string-concatenation and tree-insertion. We prove that the expressiveness of
the model coincides with transductions definable using monadic second-order
logic (MSO). Existing models of tree transducers either cannot implement all
MSO-definable transformations, or require regular look ahead that prohibits
single-pass implementation. We show a variety of analysis problems such as
type-checking and checking functional equivalence are solvable for our model.Comment: 40 page
Multithermal Analysis of a CDS Coronal Loop
The observations from 1998 April 20 taken with the Coronal Diagnostics
Spectrometer CDS on SOHO of a coronal loop on the limb have shown that the
plasma was multi-thermal along each line of sight investigated, both before and
after background subtraction. The latter result relied on Emission Measure Loci
plots, but in this Letter, we used a forward folding technique to produce
Differential Emission Measure curves. We also calculate DEM-weighted
temperatures for the chosen pixels and find a gradient in temperature along the
loop as a function of height that is not compatible with the flat profiles
reported by numerous authors for loops observed with EIT on SOHO and TRACE. We
also find discrepancies in excess of the mathematical expectation between some
of the observed and predicted CDS line intensities. We demonstrate that these
differences result from well-known limitations in our knowledge of the atomic
data and are to be expected. We further show that the precision of the DEM is
limited by the intrinsic width of the ion emissivity functions that are used to
calculate the DEM. Hence we conclude that peaks and valleys in the DEM, while
in principle not impossible, cannot be confirmed from the data.Comment: 12 pages, 3 figures, Accepted by ApJ Letter
Applying Quantum Tomography to Hadronic Interactions
A proper description of inclusive reactions is expressed with density matrices. Quantum tomography reconstructs density matrices from experimental observables. We review recent work that applies quantum tomography to practical experimental data analysis. Almost all field-theoretic formalism and modeling used in a traditional approach is circumvented with great efficiency. Tomographically-determined density matrices can express information about quantum systems which cannot in principle be expressed with distributions defined by classical probability. Topics such as entanglement and von Neumann entropy can be accessed using the same natural language where they are defined. A deep relation exists between {\it separability}, as defined in quantum information science, and {\it factorization}, as defined in high energyphysics. Factorization acquires a non-perturbative definition when expressed in terms of a conditional form of separability. An example illustrates how to go from data for momentum 4-vectors to a density matrix while bypassing almost all the formalism of the Standard Model
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