12,466 research outputs found
New results on q-positivity
In this paper we discuss symmetrically self-dual spaces, which are simply
real vector spaces with a symmetric bilinear form. Certain subsets of the space
will be called q-positive, where q is the quadratic form induced by the
original bilinear form. The notion of q-positivity generalizes the classical
notion of the monotonicity of a subset of a product of a Banach space and its
dual. Maximal q-positivity then generalizes maximal monotonicity. We discuss
concepts generalizing the representations of monotone sets by convex functions,
as well as the number of maximally q-positive extensions of a q-positive set.
We also discuss symmetrically self-dual Banach spaces, in which we add a Banach
space structure, giving new characterizations of maximal q-positivity. The
paper finishes with two new examples.Comment: 18 page
A repulsive atomic gas in a harmonic trap on the border of itinerant ferromagnetism
Alongside superfluidity, itinerant (Stoner) ferromagnetism remains one of the
most well-characterized phases of correlated Fermi systems. A recent experiment
has reported the first evidence for novel phase behavior on the repulsive side
of the Feshbach resonance in a two-component ultracold Fermi gas. By adapting
recent theoretical studies to the atomic trap geometry, we show that an
adiabatic ferromagnetic transition would take place at a weaker interaction
strength than is observed in experiment. This discrepancy motivates a simple
non-equilibrium theory that takes account of the dynamics of magnetic defects
and three-body losses. The formalism developed displays good quantitative
agreement with experiment.Comment: 4 pages, 2 figure
SSDB spaces and maximal monotonicity
In this paper, we develop some of the theory of SSD spaces and SSDB spaces,
and deduce some results on maximally monotone multifunctions on a reflexive
Banach space.Comment: 16 pages. Written version of the talk given at IX ISORA in Lima,
Peru, October 200
Critical States in Disordered Superconducting Films
When subject to a pair-breaking perturbation, the pairing susceptibility of a
disordered superconductor exhibits substantial long-ranged mesoscopic
fluctuations. Focusing on a thin film subject to a parallel magnetic field, it
is proposed that the quantum phase transition to the bulk superconducting
condensate may be preempted by the formation of a glass-like phase with
multi-fractal correlations of a complex order parameter. Although not
universal, we argue that such behavior may be a common feature of quantum
critical phenomena in disordered environments.Comment: 7 pages, 1 eps figur
Theory of quantum paraelectrics and the metaelectric transition
We present a microscopic model of the quantum paraelectric-ferroelectric
phase transition with a focus on the influence of coupled fluctuating phonon
modes. These may drive the continuous phase transition first order through a
metaelectric transition and furthermore stimulate the emergence of a textured
phase that preempts the transition. We discuss two further consequences of
fluctuations, firstly for the heat capacity, and secondly we show that the
inverse paraelectric susceptibility displays T^2 quantum critical behavior, and
can also adopt a characteristic minimum with temperature. Finally, we discuss
the observable consequences of our results.Comment: 5 pages, 2 figure
Bayesian inversion for finite fault earthquake source models I—theory and algorithm
The estimation of finite fault earthquake source models is an inherently underdetermined
problem: there is no unique solution to the inverse problem of determining the rupture history
at depth as a function of time and space when our data are limited to observations at
the Earth’s surface. Bayesian methods allow us to determine the set of all plausible source
model parameters that are consistent with the observations, our a priori assumptions about the
physics of the earthquake source and wave propagation, and models for the observation errors
and the errors due to the limitations in our forward model. Because our inversion approach
does not require inverting any matrices other than covariance matrices, we can restrict our
ensemble of solutions to only those models that are physically defensible while avoiding the
need to restrict our class of models based on considerations of numerical invertibility. We
only use prior information that is consistent with the physics of the problem rather than some
artefice (such as smoothing) needed to produce a unique optimal model estimate. Bayesian inference
can also be used to estimate model-dependent and internally consistent effective errors
due to shortcomings in the forward model or data interpretation, such as poor Green’s functions
or extraneous signals recorded by our instruments. Until recently, Bayesian techniques
have been of limited utility for earthquake source inversions because they are computationally
intractable for problems with as many free parameters as typically used in kinematic
finite fault models. Our algorithm, called cascading adaptive transitional metropolis in parallel
(CATMIP), allows sampling of high-dimensional problems in a parallel computing framework.
CATMIP combines the Metropolis algorithm with elements of simulated annealing and
genetic algorithms to dynamically optimize the algorithm’s efficiency as it runs. The algorithm
is a generic Bayesian Markov Chain Monte Carlo sampler; it works independently of the
model design, a priori constraints and data under consideration, and so can be used for a wide
variety of scientific problems. We compare CATMIP’s efficiency relative to several existing
sampling algorithms and then present synthetic performance tests of finite fault earthquake
rupture models computed using CATMIP
Magnetic Properties of the Second Mott Lobe in Pairing Hamiltonians
We explore the Mott insulating state of single-band bosonic pairing
Hamiltonians using analytical approaches and large scale density matrix
renormalization group calculations. We focus on the second Mott lobe which
exhibits a magnetic quantum phase transition in the Ising universality class.
We use this feature to discuss the behavior of a range of physical observables
within the framework of the 1D quantum Ising model and the strongly anisotropic
Heisenberg model. This includes the properties of local expectation values and
correlation functions both at and away from criticality. Depending on the
microscopic interactions it is possible to achieve either antiferromagnetic or
ferromagnetic exchange interactions and we highlight the possibility of
observing the E8 mass spectrum for the critical Ising model in a longitudinal
magnetic field.Comment: 14 pages, 15 figure
Collaborative Research: Interactive Effects of Chronic N deposition, Acidification, and Phosphorus Limitation on Coupled Element Cycling in Streams
The overarching goal of this project is to understand how chronic acidification and nitrogen enrichment of watersheds influences coupled biogeochemical cycling in streams. Embedded in the project were two primary research elements: 1) examining nitrogen satuartion and the extent of coupling between nitrogen and phosphorus cycling and 2) resolving the interactions among acidification, phosphorus bioavailability and biotic demand for nitrogen and phosphorus. The research involved a series of stable isotope tracer experiments to document nitrogen uptake under ambient and elevated phosphrous conditions and examination of a suite of key microbial processes (denitrification, decomposition, microbial enzyme activity) at two whole-watershed experiment sites. A microcosm experiment was used to examine the influence of acidity stress on animal and microbial stoichiometry
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