Magnetic field effects in few-level quantum dots: theory, and application to experiment

We examine several effects of an applied magnetic field on Anderson-type models for both single- and two-level quantum dots, and make direct comparison between numerical renormalization group (NRG) calculations and recent conductance measurements. On the theoretical side the focus is on magnetization, single-particle dynamics and zero-bias conductance, with emphasis on the universality arising in strongly correlated regimes; including a method to obtain the scaling behavior of field-induced Kondo resonance shifts over a very wide field range. NRG is also used to interpret recent experiments on spin-1/2 and spin-1 quantum dots in a magnetic field, which we argue do not wholly probe universal regimes of behavior; and the calculations are shown to yield good qualitative agreement with essentially all features seen in experiment. The results capture in particular the observed field-dependence of the Kondo conductance peak in a spin-1/2 dot, with quantitative deviations from experiment occurring at fields in excess of $\sim$ 5 T, indicating the eventual inadequacy of using the equilibrium single-particle spectrum to calculate the conductance at finite bias.Comment: 15 pages, 12 figures. Version as published in PR

Correlated electron physics in multilevel quantum dots: phase transitions, transport, and experiment

We study correlated two-level quantum dots, coupled in effective 1-channel fashion to metallic leads; with electron interactions including on-level and inter-level Coulomb repulsions, as well as the inter-orbital Hund's rule exchange favoring the spin-1 state in the relevant sector of the free dot. For arbitrary dot occupancy, the underlying phases, quantum phase transitions (QPTs), thermodynamics, single-particle dynamics and electronic transport properties are considered; and direct comparison is made to conductance experiments on lateral quantum dots. Two distinct phases arise generically, one characterised by a normal Fermi liquid fixed point (FP), the other by an underscreened (USC) spin-1 FP. Associated QPTs, which occur in general in a mixed valent regime of non-integral dot charge, are found to consist of continuous lines of Kosterlitz-Thouless transitions, separated by first order level-crossing transitions at high symmetry points. A `Friedel-Luttinger sum rule' is derived and, together with a deduced generalization of Luttinger's theorem to the USC phase (a singular Fermi liquid), is used to obtain a general result for the T=0 zero-bias conductance, expressed solely in terms of the dot occupancy and applicable to both phases. Relatedly, dynamical signatures of the QPT show two broad classes of behavior, corresponding to the collapse of either a Kondo resonance, or antiresonance, as the transition is approached from the Fermi liquid phase; the latter behavior being apparent in experimental differential conductance maps. The problem is studied using the numerical renormalization group method, combined with analytical arguments.Comment: 22 pages, 18 figures, submitted for publicatio

Renormalization group study of capacitively coupled double quantum dots

The numerical renormalization group is employed to study a double quantum (DQD) dot system consisting of two equivalent single-level dots, each coupled to its own lead and with a mutual capacitive coupling embodied in an interdot interaction U', in addition to the intradot Coulomb interaction U. We focus on the regime with two electrons on the DQD, and the evolution of the system on increasing U'/U. The spin-Kondo effect arising for U'=0 (SU(2) x SU(2)) is found to persist robustly with increasing U'/U, before a rapid but continuous crossover to (a) the SU(4) point U'=U where charge and spin degrees of freedom are entangled and the Kondo scale strongly enhanced; and then (b) a charge-Kondo state, in which a charge-pseudospin is quenched on coupling to the leads/conduction channels. A quantum phase transition of Kosterlitz-Thouless type then occurs from this Fermi liquid, strong coupling (SC) phase, to a broken symmetry, non-Fermi liquid charge ordered (CO) phase at a critical U'_c. Our emphasis in this paper is on the structure, stability and flows between the underlying RG fixed points, on the overall phase diagram in the (U,U')-plane and evolution of the characteristic low-energy Kondo scale inherent to the SC phase; and on static physical properties such as spin- and charge-susceptibilities (staggered and uniform), including universality and scaling behaviour in the strongly correlated regime. Some exact results for associated Wilson ratios are also obtained.Comment: 27 pages, 12 figure

Fiber Type Profile and its Relation to Wilks Coefficient in Both Male and Female Powerlifters

While powerlifters tend to display higher fast-twitch fiber content, it is unknown if this content predicts competitive performance via Wilks coefficient. Purpose: to 1) compare the myosin heavy chain (MHC) fiber type (FT) profiles between powerlifters and sedentary controls of both sexes, and 2) determine if fast-twitch fiber content predicts Wilks coefficient. Methods: Twelve actively competing powerlifters (PL; n=6M/6F; age=21±1.0y; 3.0±1.8y competing; 7.3±6.6 meets attended) and ten sedentary controls (CON; n=5M/5F; age=19.4±2.0y) underwent vastus lateralis muscle biopsies, with samples analyzed for MHC isoform content via mixed homogenate SDS-PAGE. Individual MHC isoform differences between group and sex were analyzed using a 3x2x2 (FT [MHC I, IIa, & IIx] x group [PL & CON] x sex [male & female]) ANOVA and MHC IIa content was compared to Wilks coefficient using Pearson correlation coefficient at pResults: Male PL MHC isoform distribution was 50±6% I, 45±6% IIa, and 5±11% IIx, vs 46±6% I, 53±6 IIa, and 0% IIx in PL females. Conversely, male CON MHC distribution was 33±5% I, 38±7% IIa, and 30±8% IIx, vs 35±9% I, 44±8% IIa, and 21±17% IIx in CON females. Analysis revealed a significant FT main effect (pConclusions:These results illustrate powerlifters have higher MHC I and IIa proportions, as well as lower MHC IIx content compared to sedentary controls. While overall limited by sample size, MHC IIa content does not appear to be a significant predictor of powerlifting Wilks coefficient, suggesting this characteristic alone does not define powerlifter skill variations

Prevalence of adulteration in dietary supplements and recommendations for safe supplement practices in sport

The prevalence of dietary supplement use among athletes continues to rise with 60–80% of athletes often reporting current or previous use of dietary supplements. While select dietary ingredients have been shown to improve acute performance and enhance training adaptations over time, it is important to still consider the risk vs. reward for athletes before opting to consume a dietary supplement. Previous work has indicated that certain dietary supplements may pose risks for inadvertent doping, may be susceptible to mislabelling, could be banned by certain governing bodies of sport, or pose health risks for certain populations. The purpose of the current narrative review is to summarize the prevalence of adulteration in dietary sport supplement products, outline the risks of inadvertent doping for athletes, and highlight best practices regarding safe supplementation strategies. Analytical studies have found anywhere from 14 to 50% of samples analyzed from dietary supplement products have tested positive for anabolic agents or other prohibited substances. It is important for the consumer to adhere to safe supplementation strategies, which include following serving size recommendations, cross-referencing ingredient profiles with the list of prohibited substances, choosing quality products that have been verified by a third-party certification program, and being cognizant of consuming multiple dietary supplement products with overlapping ingredient profiles. Once these practices have been considered, it is reasonable for an athlete to utilize dietary supplements as a strategy to optimize performance and health, with a low risk of failing a drug test (adverse analytical finding) and experiencing adverse events

Robust Henderson III estimators of variance components in the nested error model

Common methods for estimating variance components in Linear Mixed Models include Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML). These methods are based on the strong assumption of multivariate normal distribution and it is well know that they are very sensitive to outlying observations with respect to any of the random components. Several robust altematives of these methods have been proposed (e.g. Fellner 1986, Richardson and Welsh 1995). In this work we present several robust alternatives based on the Henderson method III which do not rely on the normality assumption and provide explicit solutions for the variance components estimators. These estimators can later be used to derive robust estimators of regression coefficients. Finally, we describe an application of this procedure to small area estimation, in which the main target is the estimation of the means of areas or domains when the within-area sample sizes are small

Universal conductance enhancement and reduction of the two-orbital Kondo effect

We investigate theoretically the linear and nonlinear conductance through a nanostructure with two-fold degenerate single levels, corresponding to the transport through nanostructures such as a carbon nanotube, or double dot systems with capacitive interaction. It is shown that the presence of the interaction asymmetry between orbits/dots affects significantly the profile of the linear conductance at finite temperature, and, of the nonlinear conductance, particularly around half-filling, where the two-particle Kondo effect occurs. Within the range of experimentally feasible parameters, the SU(4) universal behavior is suggested, and comparison with relevant experiments is made.Comment: 10 pages, 16 figure