20,554 research outputs found
Collapse models with non-white noises
We set up a general formalism for models of spontaneous wave function
collapse with dynamics represented by a stochastic differential equation driven
by general Gaussian noises, not necessarily white in time. In particular, we
show that the non-Schrodinger terms of the equation induce the collapse of the
wave function to one of the common eigenstates of the collapsing operators, and
that the collapse occurs with the correct quantum probabilities. We also
develop a perturbation expansion of the solution of the equation with respect
to the parameter which sets the strength of the collapse process; such an
approximation allows one to compute the leading order terms for the deviations
of the predictions of collapse models with respect to those of standard quantum
mechanics. This analysis shows that to leading order, the ``imaginary'' noise
trick can be used for non-white Gaussian noise.Comment: Latex, 20 pages;references added and minor revisions; published as J.
Phys. A: Math. Theor. {\bf 40} (2007) 15083-1509
Schwinger Algebra for Quaternionic Quantum Mechanics
It is shown that the measurement algebra of Schwinger, a characterization of
the properties of Pauli measurements of the first and second kinds, forming the
foundation of his formulation of quantum mechanics over the complex field, has
a quaternionic generalization. In this quaternionic measurement algebra some of
the notions of quaternionic quantum mechanics are clarified. The conditions
imposed on the form of the corresponding quantum field theory are studied, and
the quantum fields are constructed. It is shown that the resulting quantum
fields coincide with the fermion or boson annihilation-creation operators
obtained by Razon and Horwitz in the limit in which the number of particles in
physical states .Comment: 20 pages, Plain Te
Breaking quantum linearity: constraints from human perception and cosmological implications
Resolving the tension between quantum superpositions and the uniqueness of
the classical world is a major open problem. One possibility, which is
extensively explored both theoretically and experimentally, is that quantum
linearity breaks above a given scale. Theoretically, this possibility is
predicted by collapse models. They provide quantitative information on where
violations of the superposition principle become manifest. Here we show that
the lower bound on the collapse parameter lambda, coming from the analysis of
the human visual process, is ~ 7 +/- 2 orders of magnitude stronger than the
original bound, in agreement with more recent analysis. This implies that the
collapse becomes effective with systems containing ~ 10^4 - 10^5 nucleons, and
thus falls within the range of testability with present-day technology. We also
compare the spectrum of the collapsing field with those of known cosmological
fields, showing that a typical cosmological random field can yield an efficient
wave function collapse.Comment: 13 pages, LaTeX, 3 figure
Rain estimation from satellites: An examination of the Griffith-Woodley technique
The Griffith-Woodley Technique (GWT) is an approach to estimating precipitation using infrared observations of clouds from geosynchronous satellites. It is examined in three ways: an analysis of the terms in the GWT equations; a case study of infrared imagery portraying convective development over Florida; and the comparison of a simplified equation set and resultant rain map to results using the GWT. The objective is to determine the dominant factors in the calculation of GWT rain estimates. Analysis of a single day's convection over Florida produced a number of significant insights into various terms in the GWT rainfall equations. Due to the definition of clouds by a threshold isotherm the majority of clouds on this day did not go through an idealized life cycle before losing their identity through merger, splitting, etc. As a result, 85% of the clouds had a defined life of 0.5 or 1 h. For these clouds the terms in the GWT which are dependent on cloud life history become essentially constant. The empirically derived ratio of radar echo area to cloud area is given a singular value (0.02) for 43% of the sample, while the rainrate term is 20.7 mmh-1 for 61% of the sample. For 55% of the sampled clouds the temperature weighting term is identically 1.0. Cloud area itself is highly correlated (r=0.88) with GWT computed rain volume. An important, discriminating parameter in the GWT is the temperature defining the coldest 10% cloud area. The analysis further shows that the two dominant parameters in rainfall estimation are the existence of cold cloud and the duration of cloud over a point
Comment about pion electro-production and the axial form factors
The claim by Haberzettl (Phys.Rev.Lett.85 (2000) 3576) that the axial form
factor of the nucleon cannot be accessed through threshold pion
electroproduction is unfounded
Representations of U(1,q) and Constructive Quaternion Tensor Products
The representation theory of the group U(1,q) is discussed in detail because
of its possible application in a quaternion version of the Salam-Weinberg
theory.
As a consequence, from purely group theoretical arguments we demonstrate that
the eigenvalues must be right-eigenvalues and that the only consistent scalar
products are the complex ones. We also define an explicit quaternion tensor
product which leads to a set of additional group representations for integer
``spin''.Comment: 28 pages, Latex, Dipartimento di Fisica, Universita di Lecce
INFN-Sezione di Lecc
Formal Design of Asynchronous Fault Detection and Identification Components using Temporal Epistemic Logic
Autonomous critical systems, such as satellites and space rovers, must be
able to detect the occurrence of faults in order to ensure correct operation.
This task is carried out by Fault Detection and Identification (FDI)
components, that are embedded in those systems and are in charge of detecting
faults in an automated and timely manner by reading data from sensors and
triggering predefined alarms. The design of effective FDI components is an
extremely hard problem, also due to the lack of a complete theoretical
foundation, and of precise specification and validation techniques. In this
paper, we present the first formal approach to the design of FDI components for
discrete event systems, both in a synchronous and asynchronous setting. We
propose a logical language for the specification of FDI requirements that
accounts for a wide class of practical cases, and includes novel aspects such
as maximality and trace-diagnosability. The language is equipped with a clear
semantics based on temporal epistemic logic, and is proved to enjoy suitable
properties. We discuss how to validate the requirements and how to verify that
a given FDI component satisfies them. We propose an algorithm for the synthesis
of correct-by-construction FDI components, and report on the applicability of
the design approach on an industrial case-study coming from aerospace.Comment: 33 pages, 20 figure
Phonon-modulated magnetic interactions and spin Tomonaga-Luttinger liquid in the p-orbital antiferromagnet CsO2
The magnetic response of antiferromagnetic CsO2, coming from the p-orbital
S=1/2 spins of anionic O2- molecules, is followed by 133Cs nuclear magnetic
resonance across the structural phase transition occuring at Ts1=61 K on
cooling. Above Ts1, where spins form a square magnetic lattice, we observe a
huge, nonmonotonic temperature dependence of the exchange coupling originating
from thermal librations of O2- molecules. Below Ts1, where antiferromagnetic
spin chains are formed as a result of p-orbital ordering, we observe a spin
Tomonaga-Luttinger-liquid behavior of spin dynamics. These two interesting
phenomena, which provide rare simple manifestations of the coupling between
spin, lattice and orbital degrees of freedom, establish CsO2 as a model system
for molecular solids.Comment: 9 pages, 5 figures (with Supplemental Material), to appear in
Physical Review Letter
Non-colliding Brownian Motions and the extended tacnode process
We consider non-colliding Brownian motions with two starting points and two
endpoints. The points are chosen so that the two groups of Brownian motions
just touch each other, a situation that is referred to as a tacnode. The
extended kernel for the determinantal point process at the tacnode point is
computed using new methods and given in a different form from that obtained for
a single time in previous work by Delvaux, Kuijlaars and Zhang. The form of the
extended kernel is also different from that obtained for the extended tacnode
kernel in another model by Adler, Ferrari and van Moerbeke. We also obtain the
correlation kernel for a finite number of non-colliding Brownian motions
starting at two points and ending at arbitrary points.Comment: 38 pages. In the revised version a few arguments have been expanded
and many typos correcte
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