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

Droughts over southern Africa in a doubled-CO2 climate

The southern African region is susceptible to climatic extremes and particularly to extended dry periods. Possible changes in the probability of dry years under doubled‐CO2 conditions are examined using output from the CSIRO nine‐level general circulation model. Changes in annual mean rainfall are not expected to be significant. However, the model simulates an increase in the probability of dry years in the tropics, to the south‐west of the subcontinent, as well as over the western and eastern parts of South Africa and southern Mozambique, where large percentage increases in the most intense dry spells are indicated. A decrease in the frequency of dry years is simulated over much of the interior of the subcontinent south of 10°S. In regions where the frequency of dry years decreases, the most severe events occur less often. The CSIRO nine‐level model indicates a shift in the frequency distribution of daily rainfall events under doubled‐CO2 conditions. A small change in the frequency distribution of daily rainfall events may have further implications for the frequency of mid‐summer droughts during the peak summer rainfall period of December–February. Increases in the frequency of mid‐summer droughts are simulated over the eastern part of the subcontinent south of 20°S

Choice of distance matrices in cluster analysis: defining regions

Cluster analysis is a technique frequently used in climatology for grouping cases to define classes (synoptic types or climate regimes, for example), or for grouping stations or grid points to define regions. Cluster analysis is based on some form of distance matrix, and the most commonly used metric in the climatological field has been Euclidean distances. Arguments for the use of Euclidean distances are in some ways similar to arguments for using a covariance matrix in principal components analysis: the use of the metric is valid if all data are measured on the same scale. When using Euclidean distances for cluster analysis, however, the additional assumption is made that all the variables are uncorrelated, and this assumption is frequently ignored. Two possible methods of dealing with the correlation between the variables are considered: performing a principal components analysis before calculating Euclidean distances, and calculating Mahalanobis distances using the raw data. Under certain conditions calculating Mahalanobis distances is equivalent to calculating Euclidean distances from the principal components. It is suggested that when cluster analysis is used for defining regions, Mahalanobis distances are inappropriate, and that Euclidean distances should be calculated using the unstandardized principal component scores based on only the major principal components

Pregnancy- and lactation related folate deficiency in South Africa - a case for folate food fortification

Objective. Characterisation of patients presenting with megaloblastic anaemia according to clinical, sociological, haematological and aetiological aspects of their disease, and use of these findings to increase awareness among clinicians and to make recommendations regarding changes in national health policy.Methods. This study included 104 patients presenting with megaloblastic anaemia to a large referral.hospital over a 1year period. Data were collected and analysed in terms of age, gender, parity, gravidity, duration of lactation, socioeconomic status, geographical origins, diet, previous haematinic treatment, clinical presentation and haematological measurements.Results. The most common cause of megaloblastic anaemia was pernicious anaemia or probable pernicious anaemia (50%), followed by pregnancy- and lactation-related folate deficiency (32%); of these patients, the majority (28) presented postpartum while lactating; 5 patients were in the immediate puerperal period of 6 weeks, and a further 16 were seen during the first year and 7 during the second year following' delivery. Only 4 patients were pregnant, and it is noteworthy that 2 of these were still lactating at 34 weeks' gestation.Conclusion. Pregnancy- and lactation-related folate deficiency up to 2 years after delivery remains a common cause of megaloblastic anaemia in South Africa. Certain communities in rural South Africa have recently been shown to have high incidences of both neural tube defects and folate deficiency. The fortification of a staple food (e.g. maize or flour) with folic acid is feasible, inexpensive, safe and likely to be beneficial. This practice should reduce the prevalences of megaloblastic anaemia in fertile women, neural tube defects, other congenital abnormalities, intra-uterine growthretardation, prematurity and possibly cardiovascular disease. There is urgent need for a national policy in this regard

"The dots just don't join up": understanding the support needs of families of children on the autism spectrum

Much research has documented the elevated levels of stress experienced by families of autistic children. Yet remarkably little research has examined the types of support that these families perceive to be beneficial to their lives. This study, co-produced by researchers and school-based professionals, sought to establish these families’ support needs from their own perspectives. In total, 139 parents of autistic children with additional intellectual disabilities and limited spoken communication, all attending an inner-city London school, participated in an initial survey examining parental wellbeing, self-efficacy and the extent to which they felt supported. Semi-structured interviews were conducted with a subgroup of parents (n = 17), some of whom reported in the survey that they felt unsupported, in order to gain their in-depth perspectives. The results from both the survey and the interviews suggested that existing support (particularly from formal support services) was not meeting parents’ needs, which ultimately made them feel isolated and alienated. Parents who were interviewed called for service provision that adopted a relational, family-centred approach – one that understands the specific needs of the whole family, builds a close working relationship with them and ensures that they are supported at times when the parents and families feel they need it most

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