942 research outputs found
Boundary behavior of the Kobayashi distance in pseudoconvex Reinhardt domains
We prove that the Kobayashi distance near boundary of a pseudoconvex
Reinhardt domain increases asymptotically at most like .
Moreover, for boundary points from the growth does not
exceed . The lower estimate by is
obtained under additional assumptions of -smoothness of a domain
and a non-tangential convergence.Comment: 16 pages. To appear in Mich. Math.
(Weak) -extremals and -geodesics
We present a collection of results on (weak) -extremals and -geodesics,
concerning general properties, the planar case, quasi-balanced pseudoconvex
domains, complex ellipsoids, the Euclidean ball and boundary properties. We
prove -geodesity of -extremals in the Euclidean ball. Equivalence of weak
-extremality and -extremality in some class of convex complex ellipsoids,
containing symmetric ones and -smooth ones is showed. Moreover,
first examples of -extremals being not -geodesics in convex domains are
given.Comment: 25 pages. In this version equivalence of weak m-extremality and
m-extremality is proved for a bigger family of convex complex ellipsoid
Geometric properties of semitube domains
In the paper we study the geometry of semitube domains in . In
particular, we extend the result of Burgu\'es and Dwilewicz for semitube
domains dropping out the smoothness assumption. We also prove various
properties of non-smooth pseudoconvex semitube domains obtaining among others a
relation between pseudoconvexity of a semitube domain and the number of
connected components of its vertical slices.
Finally, we present an example showing that there is a non-convex domain in
such that its image under arbitrary isometry is pseudoconvex.Comment: 6 page
Quantum Trajectories for Realistic Detection
Quantum trajectories describe the stochastic evolution of an open quantum
system conditioned on continuous monitoring of its output, such as by an ideal
photodetector. Here we derive (non-Markovian) quantum trajectories for
realistic photodetection, including the effects of efficiency, dead time,
bandwidth, electronic noise, and dark counts. We apply our theory to a
realistic cavity QED scenario and investigate the impact of such detector
imperfections on the conditional evolution of the system state. A practical
theory of quantum trajectories with realistic detection will be essential for
experimental and technological applications of quantum feedback in many areas.Comment: 5 pages, 4 figures (3 .eps included, 1 jpeg as an additional file).
To be published in Phys. Rev.
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