Mott transition of fermionic atoms in a three-dimensional optical trap

We study theoretically the Mott metal-insulator transition for a system of fermionic atoms confined in a three-dimensional optical lattice and a harmonic trap. We describe an inhomogeneous system of several thousand sites using an adaptation of dynamical mean field theory solved efficiently with the numerical renormalization group method. Above a critical value of the on-site interaction, a Mott-insulating phase appears in the system. We investigate signatures of the Mott phase in the density profile and in time-of-flight experiments.Comment: 4 pages and 5 figure

Kondo proximity effect: How does a metal penetrate into a Mott insulator?

We consider a heterostructure of a metal and a paramagnetic Mott insulator using an adaptation of dynamical mean field theory to describe inhomogeneous systems. The metal can penetrate into the insulator via the Kondo effect. We investigate the scaling properties of the metal-insulator interface close to the critical point of the Mott insulator. At criticality, the quasiparticle weight decays as 1/x^2 with distance x from the metal within our mean field theory. Our numerical results (using the numerical renormalization group as an impurity solver) show that the prefactor of this power law is extremely small.Comment: 4 pages, 3 figure

On Optimal Harvesting in Stochastic Environments: Optimal Policies in a Relaxed Model

This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in Alvarez (2000) using dynamic programming techniques and, due to the natural payoff structure of the price rate function (the price decreases as the population increases), no optimal harvesting policy exists. This paper establishes a relaxed formulation of the harvesting model in such a manner that existence of an optimal relaxed harvesting policy can not only be proven but also identified. The analysis embeds the harvesting problem in an infinite-dimensional linear program over a space of occupation measures in which the initial position enters as a parameter and then analyzes an auxiliary problem having fewer constraints. In this manner upper bounds are determined for the optimal value (with the given initial position); these bounds depend on the relation of the initial population size to a specific target size. The more interesting case occurs when the initial population exceeds this target size; a new argument is required to obtain a sharp upper bound. Though the initial population size only enters as a parameter, the value is determined in a closed-form functional expression of this parameter.Comment: Key Words: Singular stochastic control, linear programming, relaxed contro

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

The Euler-Maruyama approximation for the absorption time of the CEV diffusion

A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time can be constructed, using the Euler-Maruyama scheme

Metallic and Insulating Phases of Repulsively Interacting Fermions in a 3D Optical Lattice

The fermionic Hubbard model plays a fundamental role in the description of strongly correlated materials. Here we report on the realization of this Hamiltonian using a repulsively interacting spin mixture of ultracold $^{40}$K atoms in a 3D optical lattice. We have implemented a new method to directly measure the compressibility of the quantum gas in the trap using in-situ imaging and independent control of external confinement and lattice depth. Together with a comparison to ab-initio Dynamical Mean Field Theory calculations, we show how the system evolves for increasing confinement from a compressible dilute metal over a strongly-interacting Fermi liquid into a band insulating state. For strong interactions, we find evidence for an emergent incompressible Mott insulating phase.Comment: 21 pages, 5 figures and additional supporting materia

Structural Analysis of the German Self‐Report Questionnaire for Anxiety and Depression in People With Disorders of Intellectual Development (SAD‐IE)

Background Anxiety disorders and depression are among the most common mental disorders in people with disorders of intellectual development (DID). As many symptoms are not directly observable, diagnoses should not be based solely on third‐party assessment. The aim of the study was the development and structural analysis of a self‐report questionnaire (SAD‐IE) for anxiety and depression in people with DID. Methods Based on the specific diagnostic criteria of DM‐ID‐2, a trial version of the SAD‐IE with 49 items was constructed in plain language. After contacting N  = 233 institutions across all 16 German federal states, N  = 286 adults with DID and their proxies were included. The factorial structure of the SAD‐IE was analyzed using confirmatory factor analysis for ordinal data (CFA, WLSMV estimation). Results The CFA showed that a two‐factor model captured the latent structure of the SAD‐IE best (CFI = 0.956, TLI = 0.954, RMSEA = 0.040, SRMR = 0.069), with 39 of the original items having sufficient discriminatory power. The first factor, depression, was reliably represented by 22 items ( r (it,c) = 0.520–0.770; α  = 0.900, ω  = 0.901) and the second factor, anxiety, by 17 items ( r (it,c) = 0.504–0.796; α  = 0.895, ω  = 0.897). Conclusion The German SAD‐IE is a reliable self‐report questionnaire measuring the major symptoms of anxiety and depression in people with borderline, mild, or moderate DID. It provides the foundation for an urgently needed self‐assessment in addition to existing third‐party assessments, ensuring a more comprehensive diagnosis. Further evaluation in practice is recommended. Summary The SAD‐IE is a self‐report questionnaire in German that can be completed independently or with little assistance by people with borderline or mild to moderate DID. Instructions and items of the SAD‐IE are written in plain language, and pictures for augmentative and alternative communication (AAC) are provided. The SAD‐IE takes into account the deviations in anxiety and depression in people with DID compared to the general population. The SAD‐IE includes relevant items to diagnose anxiety and depression, as well as two additional items to measure general psychological distress. The SAD‐IE is designed as a screening tool but could also be used to monitor subjective changes in symptoms during follow‐up assessments or in research

Dynamical Mean-Field Theory

The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.Comment: Chapter in "Theoretical Methods for Strongly Correlated Systems", edited by A. Avella and F. Mancini, Springer (2011), 31 pages, 5 figure

Left ventricular speckle tracking-derived cardiac strain and cardiac twist mechanics in athletes: a systematic review and meta-analysis of controlled studies

Background: The athlete’s heart is associated with physiological remodeling as a consequence of repetitive cardiac loading. The effect of exercise training on left ventricular (LV) cardiac strain and twist mechanics are equivocal, and no meta-analysis has been conducted to date. Objective: The objective of this systematic review and meta-analysis was to review the literature pertaining to the effect of different forms of athletic training on cardiac strain and twist mechanics and determine the influence of traditional and contemporary sporting classifications on cardiac strain and twist mechanics. Methods: We searched PubMed/MEDLINE, Web of Science, and ScienceDirect for controlled studies of aged-matched male participants aged 18–45 years that used two-dimensional (2D) speckle tracking with a defined athlete sporting discipline and a control group not engaged in training programs. Data were extracted independently by two reviewers. Random-effects meta-analyses, subgroup analyses, and meta-regressions were conducted. Results: Our review included 13 studies with 945 participants (controls n = 355; athletes n = 590). Meta-analyses showed no athlete–control differences in LV strain or twist mechanics. However, moderator analyses showed greater LV twist in high-static low-dynamic athletes (d = –0.76, 95% confidence interval [CI] –1.32 to –0.20; p < 0.01) than in controls. Peak untwisting velocity (PUV) was greater in high-static low-dynamic athletes (d = –0.43, 95% CI –0.84 to –0.03; p < 0.05) but less than controls in high-static high-dynamic athletes (d = 0.79, 95% CI 0.002–1.58; p = 0.05). Elite endurance athletes had significantly less twist and apical rotation than controls (d = 0.68, 95% CI 0.19–1.16, p < 0.01; d = 0.64, 95% CI 0.27–1.00, p = 0.001, respectively) but no differences in basal rotation. Meta-regressions showed LV mass index was positively associated with global longitudinal (b = 0.01, 95% CI 0.002–0.02; p < 0.05), whereas systolic blood pressure was negatively associated with PUV (b = –0.06, 95% CI –0.13 to –0.001; p = 0.05). Conclusion: Echocardiographic 2D speckle tracking can identify subtle physiological differences in adaptations to cardiac strain and twist mechanics between athletes and healthy controls. Differences in speckle tracking echocardiography-derived parameters can be identified using suitable sporting categorizations