6,206 research outputs found
The Chern-Simons Action in Non-Commutative Geometry
A general definition of Chern-Simons actions in non-commutative geometry is
proposed and illustrated in several examples. These are based on
``space-times'' which are products of even-dimensional, Riemannian spin
manifolds by a discrete (two-point) set. If the *algebras of operators
describing the non-commutative spaces are generated by functions over such
``space-times'' with values in certain Clifford algebras the Chern-Simons
actions turn out to be the actions of topological gravity on the
even-dimensional spin manifolds. By contrasting the space of field
configurations in these examples in an appropriate manner one is able to
extract dynamical actions from Chern-Simons actions.Comment: 40 page
Long range order for lattice dipoles
We consider a system of classical Heisenberg spins on a cubic lattice in
dimensions three or more, interacting via the dipole-dipole interaction. We
prove that at low enough temperature the system displays orientational long
range order, as expected by spin wave theory. The proof is based on reflection
positivity methods. In particular, we demonstrate a previously unproven
conjecture on the dispersion relation of the spin waves, first proposed by
Froehlich and Spencer, which allows one to apply infrared bounds for estimating
the long distance behavior of the spin-spin correlation functions.Comment: 9 page
Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction
We show that, in a model where a non-relativistic particle is coupled to a
quantized relativistic scalar Bose field, the embedded mass shell of the
particle dissolves in the continuum when the interaction is turned on, provided
the coupling constant is sufficiently small. More precisely, under the
assumption that the fiber eigenvectors corresponding to the putative mass shell
are differentiable as functions of the total momentum of the system, we show
that a mass shell could exist only at a strictly positive distance from the
unperturbed embedded mass shell near the boundary of the energy-momentum
spectrum.Comment: Revised version: a remark added at the end of Section
Dynamics of Sound Waves in an Interacting Bose Gas
We consider a non-relativistic quantum gas of bosonic atoms confined to a
box of volume in physical space. The atoms interact with each other
through a pair potential whose strength is inversely proportional to the
density, , of the gas. We study the time evolution of
coherent excitations above the ground state of the gas in a regime of large
volume and small ratio . The initial state of
the gas is assumed to be close to a \textit{product state} of one-particle wave
functions that are approximately constant throughout the box. The initial
one-particle wave function of an excitation is assumed to have a compact
support independent of . We derive an effective non-linear equation
for the time evolution of the one-particle wave function of an excitation and
establish an explicit error bound tracking the accuracy of the effective
non-linear dynamics in terms of the ratio . We conclude
with a discussion of the dispersion law of low-energy excitations, recovering
Bogolyubov's well-known formula for the speed of sound in the gas, and a
dynamical instability for attractive two-body potentials.Comment: 42 page
Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas
We study a system consisting of a heavy quantum particle, called tracer
particle, coupled to an ideal gas of light Bose particles, the ratio of masses
of the tracer particle and a gas particle being proportional to the gas
density. All particles have non-relativistic kinematics. The tracer particle is
driven by an external potential and couples to the gas particles through a pair
potential. We compare the quantum dynamics of this system to an effective
dynamics given by a Newtonian equation of motion for the tracer particle
coupled to a classical wave equation for the Bose gas. We quantify the
closeness of these two dynamics as the mean-field limit is approached (gas
density ). Our estimates allow us to interchange the thermodynamic
with the mean-field limit.Comment: 27 pages, typos corrected, a few more explanations adde
The Pierre Auger Project and Enhancements
The current status of the scientific results of the Auger Observatory will be
discussed which include spectrum, anisotropy in arrival directions, chemical
composition analyses, and limits on neutrino and photon fluxes. A review of the
Observatory detection systems will be presented. Auger has started the
construction of its second phase which encompasses antennae for radio detection
of cosmic rays, high-elevation telescopes, and surface plus muon detectors.
Details will be presented on the latter, AMIGA (Auger Muons and Infill for the
Ground Array), an Auger project consisting of 85 detector pairs each one
composed of a surface water-Cherenkov detector and a buried muon counter. The
detector pairs are arranged in an array with spacings of 433 and 750 m in order
to perform a detailed study of the 10^17 eV to 10^19 eV spectrum region.
Preliminary results on the performance of the 750 m array of surface detectors
and the first muon counter prototype will be presented.Comment: 10 pages, 8 figures, VIII Latin American Symposium on Nuclear Physics
and Applications December 15-19, 2009, Santiago, Chil
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