11,812 research outputs found
On Chow Stability for algebraic curves
In the last decades there have been introduced different concepts of
stability for projective varieties. In this paper we give a natural and
intrinsic criterion of the Chow, and Hilbert, stability for complex irreducible
smooth projective curves .
Namely, if the restriction of the tangent bundle of
to is stable then is Chow stable,
and hence Hilbert stable. We apply this criterion to describe a smooth open set
of the irreducible component of the Hilbert scheme of
containing the generic smooth Chow-stable curve of genus
and degree Moreover, we
describe the quotient stack of such curves. Similar results are obtained for
the locus of Hilbert stable curves.Comment: Minor corrections and improvements to presentation. We add Theorem
4.
Dynamical phases for the evolution of the entanglement between two oscillators coupled to the same environment
We study the dynamics of the entanglement between two oscillators that are
initially prepared in a general two-mode Gaussian state and evolve while
coupled to the same environment. In a previous paper we showed that there are
three qualitatively different dynamical phases for the entanglement in the long
time limit: sudden death, sudden death and revival and no-sudden death [Paz &
Roncaglia, Phys. Rev. Lett. 100, 220401 (2008)]. Here we generalize and extend
those results along several directions: We analyze the fate of entanglement for
an environment with a general spectral density providing a complete
characterization of the corresponding phase diagrams for ohmic and sub--ohmic
environments (we also analyze the super-ohmic case showing that for such
environment the expected behavior is rather different). We also generalize
previous studies by considering two different models for the interaction
between the system and the environment (first we analyze the case when the
coupling is through position and then we examine the case where the coupling is
symmetric in position and momentum). Finally, we analyze (both numerically and
analytically) the case of non-resonant oscillators. In that case we show that
the final entanglement is independent of the initial state and may be non-zero
at very low temperatures. We provide a natural interpretation of our results in
terms of a simple quantum optics model.Comment: 18 pages, 13 figure
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