75 research outputs found
Region Operators of Wigner Function: Transformations, Realizations and Bounds
An integral of the Wigner function of a wavefunction |psi >, over some region
S in classical phase space is identified as a (quasi) probability measure (QPM)
of S, and it can be expressed by the |psi > average of an operator referred to
as the region operator (RO). Transformation theory is developed which provides
the RO for various phase space regions such as point, line, segment, disk and
rectangle, and where all those ROs are shown to be interconnected by completely
positive trace increasing maps. The latter are realized by means of unitary
operators in Fock space extended by 2D vector spaces, physically identified
with finite dimensional systems. Bounds on QPMs for regions obtained by tiling
with discs and rectangles are obtained by means of majorization theory.Comment: 16 pages, 4 figures. Hurst Bracken Festschrift, Reports of
Mathematical Physics, Feb 2006, to appea
A Divide and Conquer Approximation Algorithm for Partitioning Rectangles
Given a rectangle with area and a set of areas
with , we consider the problem of partitioning into
sub-regions with areas in a way that the total
perimeter of all sub-regions is minimized. The goal is to create square-like
sub-regions, which are often more desired. We propose an efficient
--approximation algorithm for this problem based on a divide and conquer
scheme that runs in time. For the special case when the
aspect ratios of all rectangles are bounded from above by 3, the approximation
factor is . We also present a modified version of out
algorithm as a heuristic that achieves better average and best run times
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