4,316 research outputs found
On the classical limit of quantum mechanics, fundamental graininess and chaos: compatibility of chaos with the correspondence principle
The aim of this paper is to review the classical limit of Quantum Mechanics
and to precise the well known threat of chaos (and fundamental graininess)to
the correspondence principle. We will introduce a formalism for this classical
limit that allows us to find the surfaces defined by the constants of the
motion in phase space. Then in the integrable case we will find the classical
trajectories, and in the non-integrable one the fact that regular initial cells
become "amoeboid-like". This deformations and their consequences can be
considered as a threat to the correspondence principle unless we take into
account the characteristic timescales of quantum chaos. Essentially we present
an analysis of the problem similar to the one of Omn\`{e}s [10,11], but with a
simpler mathematical structure.Comment: 27 pages, 6 figure
Gaussian ensembles distributions from mixing quantum systems
In the context of the mixing dynamical systems we present a derivation of the
Gaussian ensembles distributions from mixing quantum systems having a classical
analog that is mixing. We find that mixing factorization property is satisfied
for the mixing quantum systems expressed as a factorization of quantum mean
values. For the case of the kicked rotator and in its fully chaotic regime, the
factorization property links decoherence by dephasing with Gaussian ensembles
in terms of the weak limit, interpreted as a decohered state. Moreover, a
discussion about the connection between random matrix theory and quantum
chaotic systems, based on some attempts made in previous works and from the
viewpoint of the mixing quantum systems, is presented
Projective moduli space of semistable principal sheaves for a reductive group
Let X be a smooth projective complex variety, and let G be an algebraic
reductive complex group. We define the notion of principal G-sheaf, that
generalises the notion of principal G-bundle. Then we define a notion of
semistability, and construct the projective moduli space of semistable
principal G-sheaves on X. This is a natural compactification of the moduli
space of principal G-bundles.
This is the announcement note presented by the second author in the
conference held at Catania (11-13 April 2001), dedicated to the 60th birthday
of Silvio Greco. Detailed proofs will appear elsewhere.Comment: 10 pages, LaTeX2e. Submitted to the conference proceedings of
"Commutative Algebra and Algebraic Geometry", Catania, April 200
- …