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

Simulation of adaptation board cable connection spacecraft "Electro-L" № 3 upper overclocking block 11s861-03 with carrier rocket "Proton-M"

With SolidWorks software built a three-dimensional model of the frame mounting and installation on-board the spacecraft communication cable "Electro-L» № 3, carried out simulation and analysis of structural strength. For all received three-dimensional models using AutoCAD design documentation package was developed

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

A high-performance 8 nV/root Hz 8-channel wearable and wireless system for real-time monitoring of bioelectrical signals

Background: It is widely accepted by the scientific community that bioelectrical signals, which can be used for the identification of neurophysiological biomarkers indicative of a diseased or pathological state, could direct patient treatment towards more effective therapeutic strategies. However, the design and realisation of an instrument that can precisely record weak bioelectrical signals in the presence of strong interference stemming from a noisy clinical environment is one of the most difficult challenges associated with the strategy of monitoring bioelectrical signals for diagnostic purposes. Moreover, since patients often have to cope with the problem of limited mobility being connected to bulky and mains-powered instruments, there is a growing demand for small-sized, high-performance and ambulatory biopotential acquisition systems in the Intensive Care Unit (ICU) and in High-dependency wards. Finally, to the best of our knowledge, there are no commercial, small, battery-powered, wearable and wireless recording-only instruments that claim the capability of recording electrocorticographic (ECoG) signals. Methods: To address this problem, we designed and developed a low-noise (8 nV/√Hz), eight-channel, battery-powered, wearable and wireless instrument (55 × 80 mm2). The performance of the realised instrument was assessed by conducting both ex vivo and in vivo experiments. Results: To provide ex vivo proof-of-function, a wide variety of high-quality bioelectrical signal recordings are reported, including electroencephalographic (EEG), electromyographic (EMG), electrocardiographic (ECG), acceleration signals, and muscle fasciculations. Low-noise in vivo recordings of weak local field potentials (LFPs), which were wirelessly acquired in real time using segmented deep brain stimulation (DBS) electrodes implanted in the thalamus of a non-human primate, are also presented. Conclusions: The combination of desirable features and capabilities of this instrument, namely its small size (~one business card), its enhanced recording capabilities, its increased processing capabilities, its manufacturability (since it was designed using discrete off-the-shelf components), the wide bandwidth it offers (0.5 – 500 Hz) and the plurality of bioelectrical signals it can precisely record, render it a versatile and reliable tool to be utilized in a wide range of applications and environments