7,849 research outputs found
Frames of subspaces and operators
We study the relationship between operators, orthonormal basis of subspaces
and frames of subspaces (also called fusion frames) for a separable Hilbert
space . We get sufficient conditions on an orthonormal basis of
subspaces of a Hilbert space
and a surjective in order that
is a frame of subspaces with respect to a computable
sequence of weights. We also obtain generalizations of results in [J. A.
Antezana, G. Corach, M. Ruiz and D. Stojanoff, Oblique projections and frames.
Proc. Amer. Math. Soc. 134 (2006), 1031-1037], which related frames of
subspaces (including the computation of their weights) and oblique projections.
The notion of refinament of a fusion frame is defined and used to obtain
results about the excess of such frames. We study the set of admissible weights
for a generating sequence of subspaces. Several examples are given.Comment: 21 pages, LaTeX; added references and comments about fusion frame
Wigner function and coherence properties of cold and thermal neutrons
We analyze the coherence properties of a cold or a thermal neutron by
utilizing the Wigner quasidistribution function. We look in particular at a
recent experiment performed by Badurek {\em et al.}, in which a polarized
neutron crosses a magnetic field that is orthogonal to its spin, producing
highly non-classical states. The quantal coherence is extremely sensitive to
the field fluctuation at high neutron momenta. A "decoherence parameter" is
introduced in order to get quantitative estimates of the losses of coherence.Comment: 6 pages, 3 figures. Contribution to the Sixth Central-European
Workshop on Quantum Optics, Chudobin near Olomouc, Czech Republic, April-May
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