2,006 research outputs found
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
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 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
Lattice Monte Carlo calculations for unitary fermions in a harmonic trap
We present a new lattice Monte Carlo approach developed for studying large
numbers of strongly interacting nonrelativistic fermions, and apply it to a
dilute gas of unitary fermions confined to a harmonic trap. Our lattice action
is highly improved, with sources of discretization and finite volume errors
systematically removed; we are able to demonstrate the expected volume scaling
of energy levels of two and three untrapped fermions, and to reproduce the high
precision calculations published previously for the ground state energies for N
= 3 unitary fermions in a box (to within our 0.3% uncertainty), and for N = 3,
. . ., 6 unitary fermions in a harmonic trap (to within our ~ 1% uncertainty).
We use this action to determine the ground state energies of up to 70
unpolarized fermions trapped in a harmonic potential on a lattice as large as
64^3 x 72; our approach avoids the use of importance sampling or calculation of
a fermion determinant and employs a novel statistical method for estimating
observables, allowing us to generate ensembles as large as 10^8 while requiring
only relatively modest computational resources.Comment: 48 pages, 19 figures, published version, some text revised, typos
corrected, title changed in journal; previously "Unitary fermions on the
lattice I: in a harmonic trap
Extended study for unitary fermions on a lattice using the cumulant expansion technique
A recently developed lattice method for large numbers of strongly interacting
nonrelativistic fermions exhibits a heavy tail in the distributions of
correlators for large Euclidean time {\tau} and large number of fermions N,
which only allows the measurement of ground state energies for a limited number
of fermions using standard techniques. In such cases, it is suggested that
measuring the log of the correlator is more efficient, and a cumulant expansion
of this quantity can be exactly related to the correlation function. The
cumulant expansion technique allows us to determine the ground state energies
of up to 66 unpolarized unitary fermions on lattices as large as
7214^3, and up to 70 unpolarized unitary fermions trapped in a harmonic
potential on lattices as large as 7264^3. We have also improved our
lattice action with a Galilean invariant form for the four-fermion interaction,
which results in predictive volume scaling of the lowest energy of three
fermions in a periodic box and in good agreement of our results for N \leq 6
trapped unitary fermions with those from other benchmark calculations.Comment: 7 pages, 6 figures, Presented at 29th International Symposium on
Lattice Field Theory (Lattice2011), Squaw Valley, Lake Tahoe, CA, USA, 10-16
July 201
The Chemical Compositions of Very Metal-Poor Stars HD 122563 and HD 140283; A View From the Infrared
From high resolution (R = 45,000), high signal-to-noise (S/N > 400) spectra
gathered with the Immersion Grating Infrared Spectrograph (IGRINS) in the H and
K photometric bands, we have derived elemental abundances of two bright,
well-known metal-poor halo stars: the red giant HD 122563 and the subgiant HD
140283. Since these stars have metallicities approaching [Fe/H] = -3, their
absorption features are generally very weak. Neutral-species lines of Mg, Si, S
and Ca are detectable, as well as those of the light odd-Z elements Na and Al.
The derived IR-based abundances agree with those obtained from
optical-wavelength spectra. For Mg and Si the abundances from the infrared
transitions are improvements to those derived from shorter wavelength data.
Many useful OH and CO lines can be detected in the IGRINS HD 122563 spectrum,
from which derived O and C abundances are consistent to those obtained from the
traditional [O I] and CH features. IGRINS high resolutions H- and K-band
spectroscopy offers promising ways to determine more reliable abundances for
additional metal-poor stars whose optical features are either not detectable,
or too weak, or are based on lines with analytical difficulties.Comment: Accepted for publication in ApJ (28 pages, 4 tables, 6 figures
Noise, sign problems, and statistics
We show how sign problems in simulations of many-body systems can manifest
themselves in the form of heavy-tailed correlator distributions, similar to
what is seen in electron propagation through disordered media. We propose an
alternative statistical approach for extracting ground state energies in such
systems, illustrating the method with a toy model and with lattice data for
unitary fermions.Comment: 4 pages, 4 figure
Supergravity at Colliders
We consider supersymmetric theories where the gravitino is the lightest
superparticle (LSP). Assuming that the long-lived next-to-lightest
superparticle (NSP) is a charged slepton, we investigate two complementary ways
to prove the existence of supergravity in nature. The first is based on the NSP
lifetime which in supergravity depends only on the Planck scale and the NSP and
gravitino masses. With the gravitino mass inferred from kinematics, the
measurement of the NSP lifetime will test an unequivocal prediction of
supergravity. The second way makes use of the 3-body NSP decay. The angular and
energy distributions and the polarizations of the final state photon and lepton
carry the information on the spin of the gravitino and on its couplings to
matter and radiation.Comment: 13 pages, 11 figures; v2: 3 references added, to appear in Physics
Letters
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