A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade

We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy $E_T$ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi liquid parameters. When $g$, the dimensionless conductance of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $g\to\infty$ (as in a large-N theory). The infinite $g$ theory shows a transition to a strong-coupling phase characterized by the same order parameter as in the Pomeranchuk transition in clean systems (a spontaneous interaction-induced Fermi surface distortion), but smeared and pinned by disorder. At finite $g$, the two phases and critical point evolve into three regimes in the $u_m-1/g$ plane -- weak- and strong-coupling regimes separated by crossover lines from a quantum-critical regime controlled by the quantum critical point. In the strong-coupling and quantum-critical regions, the quasiparticle acquires a width of the same order as the level spacing $\Delta$ within a few $\Delta$'s of the Fermi energy due to coupling to collective excitations. In the strong coupling regime if $m$ is odd, the dot will (if isolated) cross over from the orthogonal to unitary ensemble for an exponentially small external flux, or will (if strongly coupled to leads) break time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we are treating charge-channel instabilities in spinful systems, leaving spin-channel instabilities for future work. No substantive results are change

The renormalization group for interacting fermions: from Fermi liquids to quantum dots

The renormalization group approach as developed by the author for Fermi liquids is applied to clean Fermi liquids and ballistic quantum dots. In the former case Landau theory is shown to be a fixed point and in the latter the Universal Hamiltonian is shown to be a fixed point for weak coupling. The strong coupling phase is analyzed using large N and Random Matrix methods.Comment: Lectures given at the Fifteenth Chris Engelbrecht Summer School South Africa, January 2004. 6 eps figs and springer style file (svmult

Length-of-Stay in the Emergency Department and In-Hospital Mortality: A Systematic Review and Meta-Analysis

The effect of emergency department (ED) length of stay (EDLOS) on in-hospital mortality (IHM) remains unclear. The aim of this systematic review and meta-analysis was to determine the association between EDLOS and IHM. We searched the PubMed, Medline, Embase, Web of Science, Cochrane Controlled Register of Trials, CINAHL, PsycInfo, and Scopus databases from their inception until 14–15 January 2022. We included studies reporting the association between EDLOS and IHM. A total of 11,337 references were identified, and 52 studies (total of 1,718,518 ED patients) were included in the systematic review and 33 in the meta-analysis. A statistically significant association between EDLOS and IHM was observed for EDLOS over 24 h in patients admitted to an intensive care unit (ICU) (OR = 1.396, 95% confidence interval [CI]: 1.147 to 1.701; p 2 = 0%) and for low EDLOS in non-ICU-admitted patients (OR = 0.583, 95% CI: 0.453 to 0.745; p 2 = 0%). No associations were detected for the other cut-offs. Our findings suggest that there is an association between IHM low EDLOS and EDLOS exceeding 24 h and IHM. Long stays in the ED should not be allowed and special attention should be given to patients admitted after a short stay in the ED