14,008 research outputs found
Explanation and observability of diffraction in time
Diffraction in time (DIT) is a fundamental phenomenon in quantum dynamics due
to time-dependent obstacles and slits. It is formally analogous to diffraction
of light, and is expected to play an increasing role to design coherent matter
wave sources, as in the atom laser, to analyze time-of-flight information and
emission from ultrafast pulsed excitations, and in applications of coherent
matter waves in integrated atom-optical circuits. We demonstrate that DIT
emerges robustly in quantum waves emitted by an exponentially decaying source
and provide a simple explanation of the phenomenon, as an interference of two
characteristic velocities. This allows for its controllability and
optimization.Comment: 4 pages, 6 figure
Another convex combination of product states for the separable Werner state
In this paper, we write down the separable Werner state in a two-qubit system
explicitly as a convex combination of product states, which is different from
the convex combination obtained by Wootters' method. The Werner state in a
two-qubit system has a single real parameter and varies from inseparable state
to separable state according to the value of its parameter. We derive a hidden
variable model that is induced by our decomposed form for the separable Werner
state. From our explicit form of the convex combination of product states, we
understand the following: The critical point of the parameter for separability
of the Werner state comes from positivity of local density operators of the
qubits.Comment: 7 pages, Latex2e; v2: 9 pages, title changed, an appendix and a
reference added, minor correction
Normalizations of Eisenstein integrals for reductive symmetric spaces
We construct minimal Eisenstein integrals for a reductive symmetric space G/H
as matrix coefficients of the minimal principal series of G. The Eisenstein
integrals thus obtained include those from the \sigma-minimal principal series.
In addition, we obtain related Eisenstein integrals, but with different
normalizations. Specialized to the case of the group, this wider class includes
Harish-Chandra's minimal Eisenstein integrals.Comment: 66 pages. Minor revisions. To be published in Journal of Functional
Analysi
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