2,539 research outputs found
Lattice study of trapped fermions at unitarity
We present a lattice study of up to N=20 unitary fermions confined to a
harmonic trap. Our preliminary results show better than 1% agreement with high
precision solutions to the many-body Schrodinger equation for up to N=6. We are
able to make predictions for larger N which were inaccessible by the
Hamiltonian approach due to computational limitations. Harmonic traps are used
experimentally to study cold atoms tuned to a Feshbach resonance. We show that
they also provide certain benefits to numerical studies of many-body
correlators on the lattice. In particular, we anticipate that the methods
described here could be used for studying nuclear physics.Comment: 7 pages, 5 figures, presented at the XXVIII International Symposium
on Lattice Field Theory (Lattice 2010), Villasimius, Italy, June 14-19 201
Lattice calculation for unitary fermions in a finite box
A fundamental constant in systems of unitary fermions is the so-called
Bertsch parameter, the ratio of the ground state energy for spin paired unitary
fermions to that for free fermions at the same density. I discuss how we
computed this parameter as well as the pairing gap using a recently developed
lattice construction for unitary fermions, by measuring correlation functions
for up to 38 fermions in a finite box. Our calculation illustrates interesting
issues facing the study of many-body states on the lattice, which may
eventually be confronted in QCD calculations as well.Comment: 7 pages, 6 figures, The XXVIII International Symposium on Lattice
Field Theory, Lattice2010, June 14-19, 2010, Villasimius, Ital
Sign problems, noise, and chiral symmetry breaking in a QCD-like theory
The Nambu-Jona-Lasinio model reduced to 2+1 dimensions has two different path
integral formulations: at finite chemical potential one formulation has a
severe sign problem similar to that found in QCD, while the other does not. At
large N, where N is the number of flavors, one can compute the probability
distributions of fermion correlators analytically in both formulations. In the
former case one finds a broad distribution with small mean; in the latter one
finds a heavy tailed positive distribution amenable to the cumulant expansion
techniques developed in earlier work. We speculate on the implications of this
model for QCD.Comment: 16 pages, 5 figures; Published version with minor changes from the
origina
Lattice Monte Carlo calculations for unitary fermions in a finite box
We perform lattice Monte Carlo simulations for up to 66 unitary fermions in a
finite box using a highly improved lattice action for nonrelativistic spin 1/2
fermions. We obtain a value of for the Bertsch
parameter, defined as the energy of the unitary Fermi gas measured in units of
the free gas energy in the thermodynamic limit. In addition, for up to four
unitary fermions, we compute the spectrum of the lattice theory by exact
diagonalization of the transfer matrix projected onto irreducible
representations of the octahedral group for small to moderate size lattices,
providing an independent check of our few-body simulation results. We compare
our exact numerical and simulation results for the spectrum to benchmark
studies of other research groups, as well as perform an extended analysis of
our lattice action improvement scheme, including an analysis of the errors
associated with higher partial waves and finite temporal discretization.Comment: Significant revisions from previous version. Included data at a
larger volume and performed an infinite volume extrapolation of the Bertsch
parameter. Published versio
Fossil gaps inferred from phylogenies alter the apparent nature of diversification in dragonflies and their relatives
<p>Abstract</p> <p>Background</p> <p>The fossil record has suggested that clade growth may differ in marine and terrestrial taxa, supporting equilibrial models in the former and expansionist models in the latter. However, incomplete sampling may bias findings based on fossil data alone. To attempt to correct for such bias, we assemble phylogenetic supertrees on one of the oldest clades of insects, the Odonatoidea (dragonflies, damselflies and their extinct relatives), using MRP and MRC. We use the trees to determine when, and in what clades, changes in taxonomic richness have occurred. We then test whether equilibrial or expansionist models are supported by fossil data alone, and whether findings differ when phylogenetic information is used to infer gaps in the fossil record.</p> <p>Results</p> <p>There is broad agreement in family-level relationships between both supertrees, though with some uncertainty along the backbone of the tree regarding dragonflies (Anisoptera). "Anisozygoptera" are shown to be paraphyletic when fossil information is taken into account. In both trees, decreases in net diversification are associated with species-poor extant families (Neopetaliidae, Hemiphlebiidae), and an upshift is associated with Calopterygidae + Polythoridae. When ghost ranges are inferred from the fossil record, many families are shown to have much earlier origination dates. In a phylogenetic context, the number of family-level lineages is shown to be up to twice as high as the fossil record alone suggests through the Cretaceous and Cenozoic, and a logistic increase in richness is detected in contrast to an exponential increase indicated by fossils alone.</p> <p>Conclusions</p> <p>Our analysis supports the notion that taxa, which appear to have diversified exponentially using fossil data, may in fact have diversified more logistically. This in turn suggests that one of the major apparent differences between the marine and terrestrial fossil record may simply be an artifact of incomplete sampling. Our results also support previous notions that adult colouration plays an important role in odonate radiation, and that Anisozygoptera should be grouped in a single inclusive taxon with Anisoptera, separate from Zygoptera.</p
High Dimensional Forecasting via Interpretable Vector Autoregression
Vector autoregression (VAR) is a fundamental tool for modeling multivariate
time series. However, as the number of component series is increased, the VAR
model becomes overparameterized. Several authors have addressed this issue by
incorporating regularized approaches, such as the lasso in VAR estimation.
Traditional approaches address overparameterization by selecting a low lag
order, based on the assumption of short range dependence, assuming that a
universal lag order applies to all components. Such an approach constrains the
relationship between the components and impedes forecast performance. The
lasso-based approaches work much better in high-dimensional situations but do
not incorporate the notion of lag order selection.
We propose a new class of hierarchical lag structures (HLag) that embed the
notion of lag selection into a convex regularizer. The key modeling tool is a
group lasso with nested groups which guarantees that the sparsity pattern of
lag coefficients honors the VAR's ordered structure. The HLag framework offers
three structures, which allow for varying levels of flexibility. A simulation
study demonstrates improved performance in forecasting and lag order selection
over previous approaches, and a macroeconomic application further highlights
forecasting improvements as well as HLag's convenient, interpretable output
A Brief History of Prohibition and Treatment Solutions for Substance Abusers
The predominant policy of prohibition (i.e. "War on Drugs") emerged in the early Twentieth Century. It has been expanded on since that time to become the primary thrust of drug policy in almost every nation today. We will examine how this came about and the ways in which it has contributed to the maltreatment of substance abuse disorders
- …