30,202 research outputs found
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
Luttinger liquid superlattices: realization of gapless insulating phases
We investigate Luttinger Liquid superlattices, a periodic structure composed
of two kinds of one-dimensional systems of interacting electrons. We calculate
several properties of the low-energy sector: the effective charge and spin
velocities, the compressibility, various correlation functions, the Landauer
conductance and the Drude weight. The low-energy properties are subsumed into
effective parameters, much like homogeneous one-dimensional systems. A generic
result is the weighted average nature of these parameters, in proportion to the
spatial extent of the underlying subunits, pointing to the possibility of
``engineered'' structures. As a specific realization, we consider a
one-dimensional Hubbard superlattice, which consists of a periodic arrangement
of two long Hubbard chains with different coupling constants and different
hopping amplitudes. This system exhibits a rich phase diagram with several
phases, both metallic and insulating. We have found that gapless insulating
phases are present over a wide range of parameters.Comment: 16 pages, 15 figures, RevTeX
Jeans' gravitational instability and nonextensive kinetic theory
The concept of Jeans gravitational instability is rediscussed in the
framework of nonextensive statistics and its associated kinetic theory. A
simple analytical formula generalizing the Jeans criterion is derived by
assuming that the unperturbed self- gravitating collisionless gas is
kinetically described by the -parameterized class of power law velocity
distributions. It is found that the critical values of wavelength and mass
depend explicitly on the nonextensive -parameter. The standard Jeans
wavelength derived for a Maxwellian distribution is recovered in the limiting
case =1. For power-law distributions with cutoff, the instability condition
is weakened with the system becoming unstable even for wavelengths of the
disturbance smaller than the standard Jeans length .Comment: 5 pages, including 3 figures. Accepted for publication in A&
Disorder and the effective Mn-Mn exchange interaction in GaMnAs diluted magnetic semiconductors
We perform a theoretical study, using {\it ab initio} total energy
density-functional calculations, of the effects of disorder on the
exchange interactions for diluted semiconductors. For a 128
atoms supercell, we consider a variety of configurations with 2, 3 and 4 Mn
atoms, which correspond to concentrations of 3.1%, 4.7%, and 6.3%,
respectively. In this way, the disorder is intrinsically considered in the
calculations. Using a Heisenberg Hamiltonian to map the magnetic excitations,
and {\it ab initio} total energy calculations, we obtain the effective \JMn,
from first () all the way up to sixth () neighbors. Calculated
results show a clear dependence in the magnitudes of the \JMn with the Mn
concentration . Also, configurational disorder and/or clustering effects
lead to large dispersions in the Mn-Mn exchange interactions, in the case of
fixed Mn concentration. Moreover, theoretical results for the ground-state
total energies for several configurations indicate the importance of a proper
consideration of disorder in treating temperature and annealing effects
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