125,133 research outputs found
A metric property of umbilic points
In the space of cubic forms of surfaces, regarded as a
-space and endowed with a natural invariant metric, the ratio of the volumes
of those representing umbilic points with negative to those with positive
indexes is evaluated in terms of the asymmetry of the metric, defined here. A
connection of this ratio with that reported by Berry and Hannay (1977) in the
domain of Statistical Physics, is discussed.Comment: 8 pages, 1 figur
Stabilizing Entangled States with Quasi-Local Quantum Dynamical Semigroups
We provide a solution to the problem of determining whether a target pure
state can be asymptotically prepared using dissipative Markovian dynamics under
fixed locality constraints. Beside recovering existing results for a large
class of physically relevant entangled states, our approach has the advantage
of providing an explicit stabilization test solely based on the input state and
constraints of the problem. Connections with the formalism of frustration-free
parent Hamiltonians are discussed, as well as control implementations in terms
of a switching output-feedback law.Comment: 11 pages, no figure
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