Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo

The term analytic continuation emerges in many branches of Mathematics, Physics, and, more generally, applied Science. Generally speaking, in many situations, given some amount of information that could arise from experimental or numerical measurements, one is interested in extending the domain of such information, to infer the values of some variables which are central for the study of a given problem. For example, focusing on Condensed Matter Physics, state-of-the-art methodologies to study strongly correlated quantum physical systems are able to yield accurate estimations of dynamical correlations in imaginary time. Those functions have to be extended to the whole complex plane, via analytic continuation, in order to infer real-time properties of those physical systems. In this review, we will present the Genetic Inversion via Falsification of Theories method, which allowed us to compute dynamical properties of strongly interacting quantum many-body systems with very high accuracy. Even though the method arose in the realm of Condensed Matter Physics, it provides a very general framework to face analytic continuation problems that could emerge in several areas of applied Science. Here, we provide a pedagogical review that elucidates the approach we have developed. [GRAPHICS]

Dynamical structure factor of a fermionic supersolid on an optical lattice

Interfacing unbiased quantum Monte Carlo simulations with state-of-art analytic continuation techniques, we obtain exact numerical results for dynamical density and spin correlations in the attractive Hubbard model, describing a spin-balanced two-dimensional cold Fermi gas on an optical lattice. We focus on half-filling, where on average one fermion occupies each lattice site, and the system displays an intriguing supersolid phase: a superfluid with a checkerboard density modulation. The coexistence of $U(1)$ broken symmetry and the density modulations makes this regime very challenging and interesting for the calculation of dynamical properties. We compare our unbiased results with state-of-the-art Generalized Random Phase Approximation calculations: both approaches agree on a well-defined low-energy Nambu-Goldstone collective mode in the density correlations, while the higher energy structures appear to differ significantly. We also observe an interesting high-energy spin mode. We argue that our results provide a robust benchmark for Generalized Random Phase Approximation techniques, which are widely considered to be the method of choice for dynamical correlations in Fermi gases. Also, our calculations yield new physical insight in the high-energy behavior of the dynamical structure factor of the attractive Hubbard model, which is a well known prototype lattice model for superconductors and is a fertile field to target the observation of collective modes in strongly correlated systems.Comment: 12 pages, 6 figures, post-print versio

Is aortic wall degeneration related to bicuspid aortic valve anatomy in patients with valvular disease?

ObjectivePatients with bicuspid aortic valve are at increased risk for aortic complications.MethodsA total of 115 consecutive patients with bicuspid aortic valve disease underwent surgery of the ascending aorta. We classified the cusp configuration by 3 types: fusion of left coronary and right coronary cusps (type A), fusion of right coronary and noncoronary cusps (type B), and fusion of left coronary and noncoronary cusps (type C). Histopathologic changes in the ascending aortic wall were graded (aortic wall score).ResultsWe observed type A fusion in 85 patients (73.9%), type B fusion in 28 patients (24.3%), and type C fusion in 2 patients (1.8%). Patients with type A fusion were younger at operation than patients with type B fusion (51.3 ± 15.5 years vs 58.7 ± 7.6 years, respectively; P = .034). The mean ascending aorta diameter was 48.9 ± 5.0 mm and 48.7 ± 5.7 mm in type A and type B fusion groups, respectively (P = .34). The mean aortic root diameter was significantly larger in type A fusion (4.9 ± 6.7 mm vs 32.7 ± 2.8 mm; P < .0001). The aortic wall score was significantly higher in type A fusion than in type B fusion (P = .02). The prevalence of aortic wall histopathologic changes was significantly higher in type A fusion. Moreover, there were no statistically significant differences between type A and type B fusion in terms of prevalence of bicuspid aortic valve stenosis, regurgitation, or mixed disease.ConclusionIn diseased bicuspid aortic valves, there was a statistically significant association between type A valve anatomy and a more severe degree of wall degeneration in the ascending aorta and dilatation of the aortic root at younger age compared with type B valve anatomy