27,707 research outputs found
Non-ergodic states induced by impurity levels in quantum spin chains
The semi-infinite XY spin chain with an impurity at the boundary has been
chosen as a prototype of interacting many-body systems to test for non-ergodic
behavior. The model is exactly solvable in analytic way in the thermodynamic
limit, where energy eigenstates and the spectrum are obtained in closed form.
In addition of a continuous band, localized states may split off from the
continuum, for some values of the impurity parameters. In the next step, after
the preparation of an arbitrary non-equilibrium state, we observe the time
evolution of the site magnetization. Relaxation properties are described by the
long-time behavior, which is estimated using the stationary phase method.
Absence of localized states defines an ergodic region in parameter space, where
the system relaxes to a homogeneous magnetization. Out of this region, impurity
levels split from the band, and localization phenomena may lead to
non-ergodicity.Comment: 10 pages, 5 figures. arXiv admin note: substantial text overlap with
arXiv:1703.0344
Betti numbers of the moduli space of rank 3 parabolic Higgs bundles
We compute the Betti numbers of the moduli space of rank 3 parabolic Higgs
bundles, using Morse theory. A key point is that certain critical submanifolds
of the Morse function can be identified with moduli spaces of parabolic
triples. These moduli spaces come in families depending on a real parameter and
we study their variation with this parameter.Comment: 78 pages. Extended version. Added a section with the fixed
determinant case. To appear in Memoirs of the AM
Towards Noncommutative Linking Numbers Via the Seiberg-Witten Map
In the present work some geometric and topological implications of
noncommutative Wilson loops are explored via the Seiberg-Witten map. In the
abelian Chern-Simons theory on a three dimensional manifold, it is shown that
the effect of noncommutativity is the appearance of new knots at the
-th order of the Seiberg-Witten expansion. These knots are trivial homology
cycles which are Poincar\'e dual to the high-order Seiberg-Witten potentials.
Moreover the linking number of a standard 1-cycle with the Poincar\'e dual of
the gauge field is shown to be written as an expansion of the linking number of
this 1-cycle with the Poincar\'e dual of the Seiberg-Witten gauge fields. In
the process we explicitly compute the noncommutative 'Jones-Witten' invariants
up to first order in the noncommutative parameter. Finally in order to exhibit
a physical example, we apply these ideas explicitly to the Aharonov-Bohm
effect. It is explicitly displayed at first order in the noncommutative
parameter, we also show the relation to the noncommutative Landau levels.Comment: 19 pages, 1 figur
Classical Bianchi type I cosmology in K-essence theory
We use one of the simplest forms of the K-essence theory and we apply it to
the classical anisotropic Bianchi type I cosmological model, with a barotropic
perfect fluid modeling the usual matter content and with cosmological constant.
The classical solutions for any but the stiff fluid and without cosmological
constant are found in closed form, using a time transformation. We also present
the solution whith cosmological constant and some particular values of the
barotropic parameter. We present the possible isotropization of the
cosmological model, using the ratio between the anisotropic parameters and the
volume of the universe and show that this tend to a constant or to zero for
different cases. We include also a qualitative analysis of the analog of the
Friedmann equation.Comment: 15 pages with one figure, accepted in Advances in High Energy Physic
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