Ground State Properties of an Asymmetric Hubbard Model for Unbalanced Ultracold Fermionic Quantum Gases

In order to describe unbalanced ultracold fermionic quantum gases on optical lattices in a harmonic trap, we investigate an attractive ($U<0$) asymmetric ($t_\uparrow\neq t_\downarrow$) Hubbard model with a Zeeman-like magnetic field. In view of the model's spatial inhomogeneity, we focus in this paper on the solution at Hartree-Fock level. The Hartree-Fock Hamiltonian is diagonalized with particular emphasis on superfluid phases. For the special case of spin-independent hopping we analytically determine the number of solutions of the resulting self-consistency equations and the nature of the possible ground states at weak coupling. Numerical results for unbalanced Fermi-mixtures are presented within the local density approximation. In particular, we find a fascinating shell structure, involving normal and superfluid phases. For the general case of spin-dependent hopping we calculate the density of states and the possible superfluid phases in the ground state. In particular, we find a new magnetized superfluid phase.Comment: 9 pages, 5 figure

Anderson impurity model at finite Coulomb interaction U: generalized Non-crossing Approximation

We present an extension of the non-crossing approximation (NCA), which is widely used to calculate properties of Anderson impurity models in the limit of infinite Coulomb repulsion $U\to\infty$, to the case of finite $U$. A self-consistent conserving pseudo-particle representation is derived by symmetrizing the usual NCA diagrams with respect to empty and doubly occupied local states. This requires an infinite summation of skeleton diagrams in the generating functional thus defining the ``Symmetrized finite-U NCA'' (SUNCA). We show that within SUNCA the low energy scale $T_K$ (Kondo temperature) is correctly obtained, in contrast to other simpler approximations discussed in the literature.Comment: 7 pages, 6 figure

Auxiliary particle theory of threshold singularities in photoemission and X-ray absorption spectra: Test of a conserving T-matrix approximation

We calculate the exponents of the threshold singularities in the photoemission spectrum of a deep core hole and its X-ray absorption spectrum in the framework of a systematic many-body theory of slave bosons and pseudofermions (for the empty and occupied core level). In this representation, photoemission and X-ray absorption can be understood on the same footing; no distinction between orthogonality catastrophe and excitonic effects is necessary. We apply the conserving slave particle T-matrix approximation (CTMA), recently developed to describe both Fermi and non-Fermi liquid behavior systems with strong local correlations, to the X-ray problem as a test case. The numerical results for both photoemission and X-ray absorption are found to be in agreement with the exact infrared powerlaw behavior in the weak as well as in the strong coupling regions. We point out a close relation of the CTMA with the parquet equation approach of Nozi{\`e}res et al.Comment: 10 pages, 9 figures, published versio

Symmetry breaking in the Hubbard model at weak coupling

The phase diagram of the Hubbard model is studied at weak coupling in two and three spatial dimensions. It is shown that the Neel temperature and the order parameter in d=3 are smaller than the Hartree-Fock predictions by a factor of q=0.2599. For d=2 we show that the self-consistent (sc) perturbation series bears no relevance to the behavior of the exact solution of the Hubbard model in the symmetry-broken phase. We also investigate an anisotropic model and show that the coupling between planes is essential for the validity of mean-field-type order parameters

Direct Observation of Single Amyloid-β(1-40) Oligomers on Live Cells: Binding and Growth at Physiological Concentrations

Understanding how amyloid-β peptide interacts with living cells on a molecular level is critical to development of targeted treatments for Alzheimer's disease. Evidence that oligomeric Aβ interacts with neuronal cell membranes has been provided, but the mechanism by which membrane binding occurs and the exact stoichiometry of the neurotoxic aggregates remain elusive. Physiologically relevant experimentation is hindered by the high Aβ concentrations required for most biochemical analyses, the metastable nature of Aβ aggregates, and the complex variety of Aβ species present under physiological conditions. Here we use single molecule microscopy to overcome these challenges, presenting direct optical evidence that small Aβ(1-40) oligomers bind to living neuroblastoma cells at physiological Aβ concentrations. Single particle fluorescence intensity measurements indicate that cell-bound Aβ species range in size from monomers to hexamers and greater, with the majority of bound oligomers falling in the dimer-to-tetramer range. Furthermore, while low-molecular weight oligomeric species do form in solution, the membrane-bound oligomer size distribution is shifted towards larger aggregates, indicating either that bound Aβ oligomers can rapidly increase in size or that these oligomers cluster at specific sites on the membrane. Calcium indicator studies demonstrate that small oligomer binding at physiological concentrations induces only mild, sporadic calcium leakage. These findings support the hypothesis that small oligomers are the primary Aβ species that interact with neurons at physiological concentrations

Assessment of the dynamics of atrial signals and local atrial period series during atrial fibrillation: effects of isoproterenol administration

BACKGROUND: The autonomic nervous system (ANS) plays an important role in the genesis and maintenance of atrial fibrillation (AF), but quantification of its electrophysiologic effects is extremely complex and difficult. Aim of the study was to evaluate the capability of linear and non-linear indexes to capture the fine changing dynamics of atrial signals and local atrial period (LAP) series during adrenergic activation induced by isoproterenol (a sympathomimetic drug) infusion. METHODS: Nine patients with paroxysmal or persistent AF (aged 60 ± 6) underwent electrophysiological study in which isoproterenol was administered to patients. Atrial electrograms were acquired during i) sinus rhythm (SR); ii) sinus rhythm during isoproterenol (SRISO) administration; iii) atrial fibrillation (AF) and iv) atrial fibrillation during isoproterenol (AFISO) administration. The level of organization between two electrograms was assessed by the synchronization index (S), whereas the degree of recurrence of a pattern in a signal was defined by the regularity index (R). In addition, the level of predictability (LP) and regularity of LAP series were computed. RESULTS: LAP series analysis shows a reduction of both LP and R index during isoproterenol infusion in SR and AF (R(SR )= 0.75 ± 0.07 R(SRISO )= 0.69 ± 0.10, p < 0.0001; R(AF )= 0.31 ± 0.08 R(AFISO )= 0.26 ± 0.09, p < 0.0001; LP(SR )= 99.99 ± 0.001 LP(SRISO )= 99.97 ± 0.03, p < 0.0001; LP(AF )= 69.46 ± 21.55 LP(AFISO )= 55 ± 24.75; p < 0.0001). Electrograms analysis shows R index reductions both in SR (R(SR )= 0.49 ± 0.08 R(SRISO )= 0.46 ± 0.09 p < 0.0001) and in AF (R(AF )= 0.29 ± 0.09 R(AFISO )= 0.28 ± 0.08 n.s.). CONCLUSIONS: The proposed parameters succeeded in discriminating the subtle changes due to isoproterenol infusion during both the rhythms especially when considering LAP series analysis. The reduced value of analyzed parameters after isoproterenol administration could reflect an important pro-arrhythmic influence of adrenergic activation on favoring maintenance of AF

Fish-Specific Duplicated dmrt2b Contributes to a Divergent Function through Hedgehog Pathway and Maintains Left-Right Asymmetry Establishment Function

Gene duplication is thought to provide raw material for functional divergence and innovation. Fish-specific dmrt2b has been identified as a duplicated gene of the dmrt2a/terra in fish genomes, but its function has remained unclear. Here we reveal that Dmrt2b knockdown zebrafish embryos display a downward tail curvature and have U-shaped somites. Then, we demonstrate that Dmrt2b contributes to a divergent function in somitogenesis through Hedgehog pathway, because Dmrt2b knockdown reduces target gene expression of Hedgehog signaling, and also impairs slow muscle development and neural tube patterning through Hedgehog signaling. Moreover, the Dmrt2b morphants display defects in heart and visceral organ asymmetry, and, some lateral-plate mesoderm (LPM) markers expressed in left side are randomized. Together, these data indicate that fish-specific duplicated dmrt2b contributes to a divergent function in somitogenesis through Hedgehog pathway and maintains the common function for left-right asymmetry establishment

ccdc80-l1 Is Involved in Axon Pathfinding of Zebrafish Motoneurons

Axon pathfinding is a subfield of neural development by which neurons send out axons to reach the correct targets. In particular, motoneurons extend their axons toward skeletal muscles, leading to spontaneous motor activity. In this study, we identified the zebrafish Ccdc80 and Ccdc80-like1 (Ccdc80-l1) proteins in silico on the basis of their high aminoacidic sequence identity with the human CCDC80 (Coiled-Coil Domain Containing 80). We focused on ccdc80-l1 gene that is expressed in nervous and non-nervous tissues, in particular in territories correlated with axonal migration, such as adaxial cells and muscle pioneers. Loss of ccdc80-l1 in zebrafish embryos induced motility issues, although somitogenesis and myogenesis were not impaired. Our results strongly suggest that ccdc80-l1 is involved in axon guidance of primary and secondary motoneurons populations, but not in their proper formation. ccdc80-l1 has a differential role as regards the development of ventral and dorsal motoneurons, and this is consistent with the asymmetric distribution of the transcript. The axonal migration defects observed in ccdc80-l1 loss-of-function embryos are similar to the phenotype of several mutants with altered Hedgehog activity. Indeed, we reported that ccdc80-l1 expression is positively regulated by the Hedgehog pathway in adaxial cells and muscle pioneers. These findings strongly indicate ccdc80-l1 as a down-stream effector of the Hedgehog pathway

In the Absence of Sonic Hedgehog, p53 Induces Apoptosis and Inhibits Retinal Cell Proliferation, Cell-Cycle Exit and Differentiation in Zebrafish

Background: Sonic hedgehog (Shh) signaling regulates cell proliferation during vertebrate development via induction of cell-cycle regulator gene expression or activation of other signalling pathways, prevents cell death by an as yet unclear mechanism and is required for differentiation of retinal cell types. Thus, an unsolved question is how the same signalling molecule can regulate such distinct cell processes as proliferation, cell survival and differentiation. Methodology/Principal Findings: Analysis of the zebrafish shh 2/2 mutant revealed that in this context p53 mediates elevated apoptosis during nervous system and retina development and interferes with retinal proliferation and differentiation. While in shh 2/2 mutants there is activation of p53 target genes and p53-mediated apoptosis, an increase in Hedgehog (Hh) signalling by over-expression of dominant-negative Protein Kinase A strongly decreased p53 target gene expression and apoptosis levels in shh 2/2 mutants. Using a novel p53 reporter transgene, I confirm that p53 is active in tissues that require Shh for cell survival. Proliferation assays revealed that loss of p53 can rescue normal cell-cycle exit and the mitotic indices in the shh 2/2 mutant retina at 24, 36 and 48 hpf. Moreover, generation of amacrine cells and photoreceptors was strongly enhanced in the double p53 2/2 shh 2/2 mutant retina suggesting the effect of p53 on retinal differentiation. Conclusions: Loss of Shh signalling leads to the p53-dependent apoptosis in the developing nervous system and retina