1,166 research outputs found
A Perturbative Approach to the Relativistic Harmonic Oscillator
A quantum realization of the Relativistic Harmonic Oscillator is realized in
terms of the spatial variable and {\d\over \d x} (the minimal canonical
representation). The eigenstates of the Hamiltonian operator are found (at
lower order) by using a perturbation expansion in the constant . Unlike
the Foldy-Wouthuysen transformed version of the relativistic hydrogen atom,
conventional perturbation theory cannot be applied and a perturbation of the
scalar product itself is required.Comment: 9 pages, latex, no figure
Bell inequalities from variable elimination methods
Tight Bell inequalities are facets of Pitowsky's correlation polytope and are
usually obtained from its extreme points by solving the hull problem. Here we
present an alternative method based on a combination of algebraic results on
extensions of measures and variable elimination methods, e.g., the
Fourier-Motzkin method. Our method is shown to overcome some of the
computational difficulties associated with the hull problem in some non-trivial
cases. Moreover, it provides an explanation for the arising of only a finite
number of families of Bell inequalities in measurement scenarios where one
experimenter can choose between an arbitrary number of different measurements
A robust pseudo-inverse spectral filter applied to the Earth Radiation Budget Experiment (ERBE) scanning channels
Computer simulations of a least squares estimator operating on the ERBE scanning channels are discussed. The estimator is designed to minimize the errors produced by nonideal spectral response to spectrally varying and uncertain radiant input. The three ERBE scanning channels cover a shortwave band a longwave band and a ""total'' band from which the pseudo inverse spectral filter estimates the radiance components in the shortwave band and a longwave band. The radiance estimator draws on instantaneous field of view (IFOV) scene type information supplied by another algorithm of the ERBE software, and on a priori probabilistic models of the responses of the scanning channels to the IFOV scene types for given Sun scene spacecraft geometry. It is found that the pseudoinverse spectral filter is stable, tolerant of errors in scene identification and in channel response modeling, and, in the absence of such errors, yields minimum variance and essentially unbiased radiance estimates
On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables
In this paper we explore further the connections between convex bodies
related to quantum correlation experiments with dichotomic variables and
related bodies studied in combinatorial optimization, especially cut polyhedra.
Such a relationship was established in Avis, Imai, Ito and Sasaki (2005 J.
Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show
that several well known bodies related to cut polyhedra are equivalent to
bodies such as those defined by Tsirelson (1993 Hadronic J. S. 8 329-45) to
represent hidden deterministic behaviors, quantum behaviors, and no-signalling
behaviors. Among other things, our results allow a unique representation of
these bodies, give a necessary condition for vertices of the no-signalling
polytope, and give a method for bounding the quantum violation of Bell
inequalities by means of a body that contains the set of quantum behaviors.
Optimization over this latter body may be performed efficiently by semidefinite
programming. In the second part of the paper we apply these results to the
study of classical correlation functions. We provide a complete list of tight
inequalities for the two party case with (m,n) dichotomic observables when
m=4,n=4 and when min{m,n}<=3, and give a new general family of correlation
inequalities.Comment: 17 pages, 2 figure
Drawing Planar Graphs with a Prescribed Inner Face
Given a plane graph (i.e., a planar graph with a fixed planar embedding)
and a simple cycle in whose vertices are mapped to a convex polygon, we
consider the question whether this drawing can be extended to a planar
straight-line drawing of . We characterize when this is possible in terms of
simple necessary conditions, which we prove to be sufficient. This also leads
to a linear-time testing algorithm. If a drawing extension exists, it can be
computed in the same running time
Looking for symmetric Bell inequalities
Finding all Bell inequalities for a given number of parties, measurement
settings, and measurement outcomes is in general a computationally hard task.
We show that all Bell inequalities which are symmetric under the exchange of
parties can be found by examining a symmetrized polytope which is simpler than
the full Bell polytope. As an illustration of our method, we generate 238885
new Bell inequalities and 1085 new Svetlichny inequalities. We find, in
particular, facet inequalities for Bell experiments involving two parties and
two measurement settings that are not of the
Collins-Gisin-Linden-Massar-Popescu type.Comment: Joined the associated website as an ancillary file, 17 pages, 1
figure, 1 tabl
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