From bare interactions, low--energy constants and unitary gas to nuclear density functionals without free parameters: application to neutron matter

We further progress along the line of Ref. [Phys. Rev. {\bf A 94}, 043614 (2016)] where a functional for Fermi systems with anomalously large $s$-wave scattering length $a_s$ was proposed that has no free parameters. The functional is designed to correctly reproduce the unitary limit in Fermi gases together with the leading-order contributions in the s- and p-wave channels at low density. The functional is shown to be predictive up to densities $\sim0.01$ fm$^{-3}$ that is much higher densities compared to the Lee-Yang functional, valid for $\rho < 10^{-6}$ fm$^{-3}$. The form of the functional retained in this work is further motivated. It is shown that the new functional corresponds to an expansion of the energy in $(a_s k_F)$ and $(r_e k_F)$ to all orders, where $r_e$ is the effective range and $k_F$ is the Fermi momentum. One conclusion from the present work is that, except in the extremely low--density regime, nuclear systems can be treated perturbatively in $-(a_s k_F)^{-1}$ with respect to the unitary limit. Starting from the functional, we introduce density--dependent scales and show that scales associated to the bare interaction are strongly renormalized by medium effects. As a consequence, some of the scales at play around saturation are dominated by the unitary gas properties and not directly to low-energy constants. For instance, we show that the scale in the s-wave channel around saturation is proportional to the so-called Bertsch parameter $\xi_0$ and becomes independent of $a_s$. We also point out that these scales are of the same order of magnitude than those empirically obtained in the Skyrme energy density functional. We finally propose a slight modification of the functional such that it becomes accurate up to the saturation density $\rho\simeq 0.16$ fm$^{-3}$

Generation and decay of Higgs mode in a strongly interacting Fermi gas

We investigate the life cycle of the large amplitude Higgs mode in strongly interacting superfluid Fermi gas. Through numerical simulations with time-dependent density-functional theory and the technique of the interaction quench, we verify the previous theoretical predictions on the mode's frequency. Next, we demonstrate that the mode is dynamically unstable against external perturbation and qualitatively examine the emerging state after the mode decays. The post-decay state is characterized by spatial fluctuations of the order parameter and density at scales comparable to the superfluid coherence length scale. We identify similarities with FFLO states, which become more prominent at higher dimensionalities and nonzero spin imbalances.Comment: Ancillary files contain reproducibility packs of numerical calculation

Gaspard2 UML profile documentation

This document describes the current UML profile of Gaspard2. This profile extends the UML semantics to allow the user to describe a SoC (System-on-Chip) in three steps: the application (behavior of the Soc), the hardware architecture, and the association of the application to the hardware architecture. The application is represented following a data flow model, but additional mechanisms permit the usage of control flow on those applications. In addition to those notions, the profile contains a package introducing factorization mechanisms to enable the compact description of massively parallel and repetitive systems

Cabbage and fermented vegetables : From death rate heterogeneity in countries to candidates for mitigation strategies of severe COVID-19

Large differences in COVID-19 death rates exist between countries and between regions of the same country. Some very low death rate countries such as Eastern Asia, Central Europe, or the Balkans have a common feature of eating large quantities of fermented foods. Although biases exist when examining ecological studies, fermented vegetables or cabbage have been associated with low death rates in European countries. SARS-CoV-2 binds to its receptor, the angiotensin-converting enzyme 2 (ACE2). As a result of SARS-CoV-2 binding, ACE2 downregulation enhances the angiotensin II receptor type 1 (AT(1)R) axis associated with oxidative stress. This leads to insulin resistance as well as lung and endothelial damage, two severe outcomes of COVID-19. The nuclear factor (erythroid-derived 2)-like 2 (Nrf2) is the most potent antioxidant in humans and can block in particular the AT(1)R axis. Cabbage contains precursors of sulforaphane, the most active natural activator of Nrf2. Fermented vegetables contain many lactobacilli, which are also potent Nrf2 activators. Three examples are: kimchi in Korea, westernized foods, and the slum paradox. It is proposed that fermented cabbage is a proof-of-concept of dietary manipulations that may enhance Nrf2-associated antioxidant effects, helpful in mitigating COVID-19 severity.Peer reviewe

Nrf2-interacting nutrients and COVID-19 : time for research to develop adaptation strategies

There are large between- and within-country variations in COVID-19 death rates. Some very low death rate settings such as Eastern Asia, Central Europe, the Balkans and Africa have a common feature of eating large quantities of fermented foods whose intake is associated with the activation of the Nrf2 (Nuclear factor (erythroid-derived 2)-like 2) anti-oxidant transcription factor. There are many Nrf2-interacting nutrients (berberine, curcumin, epigallocatechin gallate, genistein, quercetin, resveratrol, sulforaphane) that all act similarly to reduce insulin resistance, endothelial damage, lung injury and cytokine storm. They also act on the same mechanisms (mTOR: Mammalian target of rapamycin, PPAR gamma:Peroxisome proliferator-activated receptor, NF kappa B: Nuclear factor kappa B, ERK: Extracellular signal-regulated kinases and eIF2 alpha:Elongation initiation factor 2 alpha). They may as a result be important in mitigating the severity of COVID-19, acting through the endoplasmic reticulum stress or ACE-Angiotensin-II-AT(1)R axis (AT(1)R) pathway. Many Nrf2-interacting nutrients are also interacting with TRPA1 and/or TRPV1. Interestingly, geographical areas with very low COVID-19 mortality are those with the lowest prevalence of obesity (Sub-Saharan Africa and Asia). It is tempting to propose that Nrf2-interacting foods and nutrients can re-balance insulin resistance and have a significant effect on COVID-19 severity. It is therefore possible that the intake of these foods may restore an optimal natural balance for the Nrf2 pathway and may be of interest in the mitigation of COVID-19 severity

Théorie fonctionnelle de la densité pour les systèmes de fermions en interaction forte : application à la physique atomique et à la physique nucléaire

In the present work, a density functional theory (DFT) is developed for systems interacting through an anomalously large s-wave scattering length as. Examples of such systems are atomic gas or neutron matter. The Many-Body Perturbation Theory (MBPT) is first discussed to describe dilute Fermi systems. This approach leads to the well-known Lee-Yang functional valid in a very narrow range of density when the s-wave scattering length is large. To extend the domain of validity of the perturbative approach, resummation techniques with the ladder approximation is used. This leads to compact expressions for both the energy and/or the on-shell self-energy in infinite spin-degenerated systems that can be applied from diluted to dense systems. It also leads to finite energy in atomic gas at the unitary limit, i.e. when |askF|→+∞. The deduced functionals remain rather complex and lacks of predictive power in general. To simplify the functional, approximations called phase-space or partial phase-space approximations respectively for the energy or for the self-energy, are proposed. These approximations not only simplify the form of the functionals, but also improve their predictive power at various density while properly reproducing the low density limit. Guided by the non-perturbative resummation technique developed in this thesis, several novel functionals are proposed as well as extensions of them to include effective range effects. These non-empirical functionals, that essentially contain no free parameters, are tested against cold atom and/or neutron matter properties. A very good reproduction of ab initio and experimental observations in cold atom is obtained. The equation of state obtained for neutron matter is also reproduced up to ρ = 0.01 fm⁻³. The static response of neutron matter, recently obtained from ab initio theory, is also better reproduced compared to standardly used empirical nuclear DFT. This study has also pointed out the necessity to better understand quasi-particle properties like the effective mass. To further progress, starting from resummed expressions of the self-energy together with partial phase-space approximation, compact expressions of the chemical potential and effective masses are obtained that are eventually compatible with the DFTs proposed in the first part of this thesis. These expressions are anticipated to significantly extend the domain of validity compared to the perturbative approach. We finally show that the developments made in this work are also useful to reconcile the parameters generally used in the empirical nuclear DFT with the properties of the strong nuclear interaction.Dans ce travail de thèse, des théories de type fonctionnelle de la densité sont développées pour des systèmes en interaction forte possédant une longueur de diffusion en onde s, notée as, anormalement grande. Les gaz atomiques ou la matière neutronique sont des exemples physiques de tels systèmes. La théorie des perturbations à N-corps est tout d'abord utilisée pour décrire les systèmes de fermions dilués. Cette approche conduit par exemple à la fonctionnelle de Lee-Yang qui est valide dans une plage de densité très restreinte lorsque la longueur de diffusion en onde s devient grande. Pour étendre le domaine de validité de l’approche perturbative, des techniques de resommation associées à l’approximation dite en échelle sont utilisée. Cette approche conduit à des expressions compactes pour l'énergie et/ou la self-énergie on-shell dans des systèmes infinis pouvant être appliquées à des systèmes plus ou moins denses. Cela conduit également à une énergie finie du gaz atomique à la limite unitaire, i.e. lorsque |askF|→+∞. Les fonctionnelles ainsi déduites restent assez complexes et manquent en général de pouvoir prédictif. Pour simplifier ces fonctionnelles, des approximations appelées respectivement approximations de “l’espace des phases” ou de “l'espace des phases partiel” sont proposées pour l'énergie ou la self-énergie. Ces approximations simplifient non seulement la forme des fonctionnelles, mais améliorent également leur pouvoir prédictif tout en reproduisant correctement la limite de basse densité. Guidé par les techniques de resommation non-perturbatives développées dans cette thèse, plusieurs nouvelles fonctionnelles sont proposées ainsi que leurs extensions permettant d’inclure des effets de portée effective. Ces fonctionnelles non empiriques, qui ne contiennent aucun paramètre libre, sont testées par rapport aux propriétés des systèmes d'atomes froids et/ou de la matière neutronique. Ces fonctionnelles reproduisent très bien les propriétés obtenues dans les calculs ab-initio ou observées expérimentalement dans les systèmes d'atomes froids. L'équation d'état de la matière neutronique est également reproduite jusqu'à ρ = 0.01 fm⁻³. La réponse statique de la matière neutronique, récemment calculée dans des théories ab-initio, est également mieux reproduite par rapport aux fonctionnelles empiriques utilisées généralement en physique nucléaire. Cette étude a aussi mis en évidence la nécessité de mieux comprendre les propriétés des quasi-particules telle que la masse effective. Pour progresser sur ce point, en partant des expressions resommées de la self-énergie et de l’approximation de l’espace des phases partiel, des expressions compactes du potentiel chimique et de la masse effective ont été obtenues ; ces expressions étant compatibles avec les fonctionnelles proposées dans la première partie de cette thèse. Ces expressions devraient élargir considérablement le domaine de validité des fonctionnelles non-empiriques par rapport aux théories perturbatives. Enfin, il est montré que les développements de ce travail sont également utiles pour réconcilier les paramètres généralement utilisés dans les fonctionnelles empiriques de la physique nucléaire avec les propriétés de l’interaction nucléaire forte

Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory

International audienceIn the present work, we start from a minimal Hamiltonian for Fermi systems where the s-wave scattering is the only low energy constant (LEC) at play. The many-body perturbative approach that is usually valid at rather low density is first discussed. We then use the resummation technique with the ladder approximation to obtain compact expressions for both the energy and/or the on-shell self-energy in infinite spin-degenerated systems. The diagrammatic resummation technique has the advantage in general to be predictive in a region of density larger compared to many-body perturbation theory. It also leads to a non-diverging limit as . Still, the obtained expressions are a rather complex function of the Fermi momentum k F. We introduce the full phase-space or the partial phase-space approximations respectively applied to the energy or to the self-energy to simplify their dependences in terms of (a s k F) while keeping the correct limit at low density and the non-diverging property at large . Quasi-particle properties of the Fermi system in various regimes of density and scattering length are then illustrated. Our conclusion is that such simplified expressions where the direct link is made with the LEC without fine-tuning can provide a clear guidance to obtain density functional theory (DFT) beyond the perturbative regime. However, quasi-particle properties close or near unitarity cannot be reproduced unless this limit is explicitly used as a constraint. We finally discuss how such approximate treatment of quasi-particles can guide the development of DFT for strongly interacting Fermi systems

Static response, collective frequencies and ground state thermodynamical properties of spin saturated two-component cold atoms and neutron matter

International audienceThe thermodynamical ground-state properties and static response in both cold atoms at or close to unitarity and neutron matter are determined using a recently proposed density functional theory (DFT) based on the s-wave scattering length as, effective range re, and unitary gas limit. In cold atoms, when the effective range may be neglected, we show that the pressure, chemical potential, compressibility modulus, and sound velocity obtained with the DFT are compatible with experimental observations or exact theoretical estimates. The static response in homogeneous infinite systems is also obtained and a possible influence of the effective range on the response is analyzed. The neutron matter differs from unitary gas due to the noninfinite scattering length and to a significant influence of effective range, which affects all thermodynamical quantities as well as the static response. In particular, we show for neutron matter that the latter response recently obtained in auxiliary-field diffusion Monte Carlo (AFDMC) can be qualitatively reproduced when the p-wave contribution is added to the functional. Our study indicates that the close similarity between the exact AFDMC static response and the free-gas response might stem from the compensation of the as effect by the effective range and p-wave contributions. We finally consider the dynamical response of both atoms or neutron droplets in anisotropic traps. Assuming the hydrodynamical regime and a polytropic equation of state, a reasonable description of the radial and axial collective frequencies in cold atoms is obtained. Following a similar strategy, we estimate the equivalent collective frequencies of neutron drops in anisotropic traps