RESUMEN
We investigate the effects of disorder and shielding on quantum transports in a two dimensional system with all-to-all long range hopping. In the weak disorder, cooperative shielding manifests itself as perfect conducting channels identical to those of the short range model, as if the long range hopping does not exist. With increasing disorder, the average and fluctuation of conductance are larger than those in the short range model, since the shielding is effectively broken and therefore long range hopping starts to take effect. Over several orders of disorder strength (until [Formula: see text] times of nearest hopping), although the wavefunctions are not fully extended, they are also robustly prevented from being completely localized into a single site. Each wavefunction has several localization centers around the whole sample, thus leading to a fractal dimension remarkably smaller than 2 and also remarkably larger than 0, exhibiting a hybrid feature of localization and delocalization. The size scaling shows that for sufficiently large size and disorder strength, the conductance tends to saturate to a fixed value with the scaling function [Formula: see text], which is also a marginal phase between the typical metal ([Formula: see text]) and insulating phase ([Formula: see text]). The all-to-all coupling expels one isolated but extended state far out of the band, whose transport is extremely robust against disorder due to absence of backscattering. The bond current picture of this isolated state shows a quantum version of short circuit through long hopping.
RESUMEN
A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g. clear mobility edges (Wanget al2020Phys. Rev. Lett.125196604). We generalize this mosaic quasiperiodic model to a two-dimensional version, and numerically investigate its localization properties: the phase diagram from the fractal dimension of the wavefunction, the statistical and scaling properties of the conductance. Compared with disordered systems, our model shares many common features but also exhibits some different characteristics in the same dimensionality and the same universality class. For example, the sharp peak atgâ¼0of the critical distribution and the largeglimit of the universal scaling functionßresemble those behaviors of three-dimensional disordered systems.
RESUMEN
The demand for analysis of carotenoids (CAR) and fat-soluble vitamins (FSV) is continuously expanding, but currently used sample preparation methods either require complicated extraction procedure or large sample volume, let alone the reliability of the results. This study aimed to develop a fast, high-efficient, and high-throughput method based on supported liquid extraction (SLE) for the simultaneous extraction of FSV and CAR from human serum before using high-performance liquid chromatography-diode array detector (HPLC-DAD) analysis. The optimization of SLE parameters was achieved through response surface methodology (RSM) based on the Box-Behnken design (BBD) and included serum-water-extraction solvent ratio and eluent volume. Under optimal conditions, the proposed method gives acceptable limits of detection (LOD) (0.005-0.3⯵g/mL), good recovery (89.6-110.9%) as well as relative standard deviation (RSD) of less than 10.1% by consuming lower serum sample (100⯵L) and less sample preparation time (2â¯min per sample). Compared with liquid-phase extraction (LLE), the SLE delivers rapid extraction with higher recovery, better reproducibility, and lower matrix effect for CAR and FSV analysis. The method has been successfully applied to quantify CAR and FSV levels in serum of healthy individuals and age-related macular degeneration (AMD) patients, demonstrating the feasibility of the proposed method for epidemiology and routine applications.