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

Generalized Ginsparg-Wilson relations

We give a general derivation of Ginsparg-Wilson relations for both Dirac and Majorana fermions in any dimension. These relations encode continuous and discrete chiral, parity and time reversal anomalies and will apply to the various classes of free fermion topological insulators and superconductors (in the framework of a relativistic quantum field theory in Euclidean spacetime). We show how to formulate the exact symmetries of the lattice action and the relevant index theorems for the anomalies.Comment: 14 pages. Submitted Version. Section III.D revised, and other minor improvement

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 $0.366^{+0.016}_{-0.011}$ 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

Endovascular stent grafting in the presence of aortic neck filling defects: Early clinical experience

AbstractObjective: Although endovascular grafts have been increasingly applied to the treatment of abdominal aortic aneurysms, their use in clinical trials is limited by well-defined anatomical exclusion criteria. One such criterion is the presence of thrombus within the infrarenal neck of an aneurysm, which is thought to (1) prevent the creation of a permanent watertight seal between the graft and the vessel wall, resulting in an endoleak; (2) contribute to stent migration; and (3) increase the risk of thromboembolism. This article summarizes our experience with endovascular abdominal aortic aneurysm exclusion in 19 patients with large aortic aneurysms, significant medical comorbidities, and apparent thrombus extending into the pararenal aortic neck. Methods: Of 268 patients undergoing abdominal aortic aneurysm repair, 19 (7%; 17 men; mean age, 71 years) demonstrated computed tomographic and angiographic evidence of intramural filling defects at the level of the aortic neck. In no instance did these filling defects extend above the renal arteries. Endovascular grafting was performed through use of a balloon-expandable Palmaz stent and an expanded polytetrafluoroethylene graft, delivered and deployed under fluoroscopic guidance. Follow-up at 3, 6, and 12 months and annually thereafter was performed with computed tomography and duplex ultrasound scan. Results: Spiral computed tomography and aortography revealed an irregular flow-limiting defect, occupying up to 75% of the aortic circumference, in every case. The mean aneurysm size, aortic neck diameter, and neck length before the procedure were 6.1, 2.43, and 1.4 cm, respectively; the mean aortic neck diameter after the procedure was 2.61 cm. No primary endoleaks were observed after graft insertion, and no delayed endoleaks have been detected during follow-up, which ranged from 7 to 48 months (mean, 23 months). In one patient, an asymptomatic renal artery embolus was detected on immediate follow-up computed tomography, and in another patient, an asymptomatic posterior tibial embolus occurred. Conclusion: No primary endoleaks, endograft migration, or significant distal embolization were observed after endografting in patients with aortic neck thrombus. The deployment of the fenestrated portion of the stent, above the thrombus and across the renal arteries, allows for effective renal perfusion, graft fixation, and exclusion of potential mural thrombus from the circulation. The presence of aortic neck thrombus may not necessarily be a contraindication to endovascular repair in select patients. (J Vasc Surg 2001;33:340-4.

Lattice formulation of (2,2) supersymmetric gauge theories with matter fields

We construct lattice actions for a variety of (2,2) supersymmetric gauge theories in two dimensions with matter fields interacting via a superpotential.Comment: 13 pages, 2 figures. Appendix added, references updated, typos fixe

Validation of deep learning-based markerless 3D pose estimation

Deep learning-based approaches to markerless 3D pose estimation are being adopted by researchers in psychology and neuroscience at an unprecedented rate. Yet many of these tools remain unvalidated. Here, we report on the validation of one increasingly popular tool (DeepLabCut) against simultaneous measurements obtained from a reference measurement system (Fastrak) with well-known performance characteristics. Our results confirm close (mm range) agreement between the two, indicating that under specific circumstances deep learning-based approaches can match more traditional motion tracking methods. Although more work needs to be done to determine their specific performance characteristics and limitations, this study should help build confidence within the research community using these new tools