Effective field theory (EFT) methods are applied to density functional theory (DFT) as part of a program to systematically go beyond mean-field approaches to medium and heavy nuclei. A system of fermions with short-range, natural interactions and an external confining potential (e.g., fermionic atoms in an optical trap) serves as a laboratory for studying DFT/EFT. An effective action formalism leads to a Kohn-Sham DFT by applying an inversion method order-by-order in the EFT expansion parameter. Representative results showing the convergence of Kohn-Sham calculations at zero temperature in the local density approximation (LDA) are compared to Thomas-Fermi calculations and to power-counting estimates.case, the explicit expansion parameter is the local Fermi momentum times the scattering length (and other effective range parameters). We assume a gradient expansion parameter that justifies a local density approximation, but the verification of this assumption is postponed to future work. Ultimately we are interested in calculating self-bound systems (e.g., nuclei), with spin-and isospin-dependent interactions and long-range forces (e.g., pion exchange). These are all significant but well-defined extensions of the model described here. In the meantime, the model provides a prototype for more complex systems and also has a physical realization in recent and forthcoming experiments on fermionic atoms in optical traps [17].The Kohn-Sham approach to DFT was proposed in Ref.[1]. Since then, the literature of DFT applications has grown exponentially, primarily in the areas of quantum chemistry and electronic structure [5]. A general introduction to density functional theory as conventionally applied is provided in the books by Dreizler and Gross [3] and Parr and Young [2], while Ref.[18] is a practitioners guide to DFT for quantum chemists. The connection of DFT to nonrelativistic mean-field approaches to nuclei (e.g., Skyrme models) was pointed out in Ref. [19] (and no doubt elsewhere) and was explored for covariant nuclear mean-field models in Refs. [20,21]. However, it has not led, to our knowledge, to new or systematically improved mean-field-type functionals for nuclei.The use of functional Legendre transformations for DFT with the effective action formalism was first detailed by Fukuda and collaborators [22,23], who also discuss the inversion and auxiliary field methods of constructing the effective action. The connection to Kohn-Sham DFT was shown by Valiev and Fernando [24,25,26,27] and later by other authors in Refs. [28,29,30]. Recent work by Polonyi and Sailer applies renormalization group methods and a cluster expansion to an effective-action formulation of generalized DFT for Coulomb systems [31]. To our knowledge, however, there is no prior work on merging the Kohn-Sham density functional approach and effective field theory.The plan of the paper is as follows. In Sect. II, we review effective field theory for a dilute system of fermions. In Sect. III, the effective action approach for determining a Kohn-Sham ...

This work continues a program to systematically generalize the Skyrme Hartree-Fock method for medium and heavy nuclei by applying effective field theory (EFT) methods to Kohn-Sham density functional theory (DFT). When conventional Kohn-Sham DFT for Coulomb systems is extended beyond the local density approximation, the kinetic energy density τ is sometimes included in energy functionals in addition to the fermion density. However, a local (semi-classical) expansion of τ is used to write the energy as a functional of the density alone, in contrast to the Skyrme approach. The difference is manifested in different single-particle equations, which in the Skyrme case include a spatially varying effective mass. Here we show how to generalize the EFT framework for DFT derived previously to reconcile these approaches. A dilute gas of fermions with short-range interactions confined by an external potential serves as a model system for comparisons and for testing power-counting estimates of new contributions to the energy functional.

Alternative promoters that are differentially used in various cellular contexts and tissue types add to the transcriptional complexity in mammalian genome. Identification of alternative promoters and the annotation of their activity in different tissues is one of the major challenges in understanding the transcriptional regulation of the mammalian genes and their isoforms. To determine the use of alternative promoters in different tissues, we performed ChIP-seq experiments using antibody against RNA Pol-II, in five adult mouse tissues (brain, liver, lung, spleen and kidney). Our analysis identified 38 639 Pol-II promoters, including 12 270 novel promoters, for both protein coding and non-coding mouse genes. Of these, 6384 promoters are tissue specific which are CpG poor and we find that only 34% of the novel promoters are located in CpG-rich regions, suggesting that novel promoters are mostly tissue specific. By identifying the Pol-II bound promoter(s) of each annotated gene in a given tissue, we found that 37% of the protein coding genes use alternative promoters in the five mouse tissues. The promoter annotations and ChIP-seq data presented here will aid ongoing efforts of characterizing gene regulatory regions in mammalian genomes.

We consider interacting Fermi systems close to the unitary regime and compute the corrections to the energy density that are due to a large scattering length and a small effective range. Our approach exploits the universality of the density functional and determines the corrections from the analyical results for the harmonically trapped two-body system. The corrections due to the finite scattering length compare well with the result of Monte Carlo simulations. We also apply our results to symmetric neutron matter.PACS numbers: 03.75. Ss,03.75.Hh,05.30.Fk,21.65.+f Ultracold fermionic atom gases have attracted a lot of interest since Fermi degeneracy was achieved by DeMarco and Jin [1]. These systems are in the metastable gas phase, as three-body recombinations are rare. Most interestingly, the effective two-body interaction itself can be controlled via external magnetic fields. This makes it possible to study the system as it evolves from a dilute Fermi gas with weak attractive interactions to a bosonic gas of diatomic molecules. This transition from a superfluid BCS state to Bose Einstein condensation (BEC) has been the subject of many experimental [2,3,4,5,6,7,8,9,10,11,12] and theoretical works [13,14,15,16,17,18,19,20,21,22,23].At the midpoint of this transition, the two-body system has a zero-energy bound state, and the scattering length diverges. If other parameters as the effective range of the interaction can be neglected, the interparticle spacing becomes the only relevant length scale. This defines the unitary limit. In this limit, the energy density is proportional of that of a free Fermi gas, the proportionality constant denoted by ξ. Close to the unitary limit, corrections are due to a finite, large scattering length a and a small effective range r 0 of the potential. Within the local density approximation (LDA), the energy density is given asHere,is the energy density of the free Fermi gas. . We are not aware of any estimate for the constant c 2 in Eq. (1) that concerns the correction due to a small effective range. It is the purpose of this work to fill this gap. This is particularly interesting as experiments also have control over the effective range. Note that the regime of a large effective range has recently been discussed by Schwenk and Pethick [20].In this work, we determine the coefficients c 1 , and c 2 via density functional theory. Recall that the density functional is supposed to be universal, i.e. it can be used to solve the N -fermion system for any particle number N , and for any external potential. Exploiting the universality of the density functional, the parameters c 1 and c 2 can be obtained from a fit to an analytically known solution, i.e. the harmonically trapped two-fermion system [33]. This simple approach has recently been applied [27] to determine the universal constant ξ, and will be followed and extended below.Let us briefly turn to the harmonically trapped twofermion system. The wave function u(r) in the relative coordinate r = r 1 − r 2 of the spin-singlet state is ...