1,265 research outputs found
Efficient and Perfect domination on circular-arc graphs
Given a graph , a \emph{perfect dominating set} is a subset of
vertices such that each vertex is
dominated by exactly one vertex . An \emph{efficient dominating set}
is a perfect dominating set where is also an independent set. These
problems are usually posed in terms of edges instead of vertices. Both
problems, either for the vertex or edge variant, remains NP-Hard, even when
restricted to certain graphs families. We study both variants of the problems
for the circular-arc graphs, and show efficient algorithms for all of them
Control of the geometric phase and pseudo-spin dynamics on coupled Bose-Einstein condensates
We describe the behavior of two coupled Bose-Einstein condensates in
time-dependent (TD) trap potentials and TD Rabi (or tunneling) frequency, using
the two-mode approach. Starting from Bloch states, we succeed to get analytical
solutions for the TD Schroedinger equation and present a detailed analysis of
the relative and geometric phases acquired by the wave function of the
condensates, as well as their population imbalance. We also establish a
connection between the geometric phases and constants of motion which
characterize the dynamic of the system. Besides analyzing the affects of
temporality on condensates that differs by hyperfine degrees of freedom
(internal Josephson effect), we also do present a brief discussion of a one
specie condensate in a double-well potential
(external Josephson effect).Comment: 1 tex file and 11 figures in pdf forma
Collisional Semiclassical Aproximations in Phase-Space Representation
The Gaussian Wave-Packet phase-space representation is used to show that the
expansion in powers of of the quantum Liouville propagator leads, in
the zeroth order term, to results close to those obtained in the statistical
quasiclassical method of Lee and Scully in the Weyl-Wigner picture. It is also
verified that propagating the Wigner distribution along the classical
trajectories the amount of error is less than that coming from propagating the
Gaussian distribution along classical trajectories.Comment: 20 pages, REVTEX, no figures, 3 tables include
An Optimal Self-Stabilizing Firing Squad
Consider a fully connected network where up to processes may crash, and
all processes start in an arbitrary memory state. The self-stabilizing firing
squad problem consists of eventually guaranteeing simultaneous response to an
external input. This is modeled by requiring that the non-crashed processes
"fire" simultaneously if some correct process received an external "GO" input,
and that they only fire as a response to some process receiving such an input.
This paper presents FireAlg, the first self-stabilizing firing squad algorithm.
The FireAlg algorithm is optimal in two respects: (a) Once the algorithm is
in a safe state, it fires in response to a GO input as fast as any other
algorithm does, and (b) Starting from an arbitrary state, it converges to a
safe state as fast as any other algorithm does.Comment: Shorter version to appear in SSS0
Multi-Dimensional Hermite Polynomials in Quantum Optics
We study a class of optical circuits with vacuum input states consisting of
Gaussian sources without coherent displacements such as down-converters and
squeezers, together with detectors and passive interferometry (beam-splitters,
polarisation rotations, phase-shifters etc.). We show that the outgoing state
leaving the optical circuit can be expressed in terms of so-called
multi-dimensional Hermite polynomials and give their recursion and
orthogonality relations. We show how quantum teleportation of photon
polarisation can be modelled using this description.Comment: 10 pages, submitted to J. Phys. A, removed spurious fil
Optical bistability in sideband output modes induced by squeezed vacuum
We consider two-level atoms in a ring cavity interacting with a broadband
squeezed vacuum centered at frequency and an input monochromatic
driving field at frequency . We show that, besides the central mode
(at \o), many other {\em sideband modes} are produced at the output, with
frequencies shifted from by multiples of .
Here we analyze the optical bistability of the two nearest sideband modes, one
red-shifted and the other blue-shifted.Comment: Replaced with final published versio
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