Central limit theorems for the real eigenvalues of large Gaussian random matrices

Let G be an N×N real matrix whose entries are independent identically distributed standard normal random variables Gij∼N(0,1). The eigenvalues of such matrices are known to form a two-component system consisting of purely real and complex conjugated points. The purpose of this paper is to show that by appropriately adapting the methods of [E. Kanzieper, M. Poplavskyi, C. Timm, R. Tribe and O. Zaboronski, Annals of Applied Probability 26(5) (2016) 2733–2753], we can prove a central limit theorem of the following form: if λ1,…,λNR are the real eigenvalues of G, then for any even polynomial function P(x) and even N=2n, we have the convergence in distribution to a normal random variable 1E(NR)−−−−−√⎛⎝∑j=1NRP(λj/2n−−√)−E∑j=1NRP(λj/2n−−√)⎞⎠→N(0,σ2(P)) as n→∞, where σ2(P)=2−2√2∫1−1P(x)2dx

Coulomb singularity effects in tunnelling spectroscopy of individual impurities

Non-equilibrium Coulomb effects in resonant tunnelling processes through deep impurity states are analyzed. It is shown that Coulomb vertex corrections to the tunnelling transfer amplitude lead to a power-law singularity in current- voltage characteristicsComment: 7 pages, 2 figure

Tuning of tunneling current noise spectra singularities by localized states charging

We report the results of theoretical investigations of tunneling current noise spectra in a wide range of applied bias voltage. Localized states of individual impurity atoms play an important role in tunneling current noise formation. It was found that switching "on" and "off" of Coulomb interaction of conduction electrons with two charged localized states results in power law singularity of low-frequency tunneling current noise spectrum ($1/f^{\alpha}$) and also results on high frequency component of tunneling current spectra (singular peaks appear).Comment: 7 pages, 4 figure

Finite Almost Simple Groups Whose Gruenberg–Kegel Graphs Coincide with Gruenberg–Kegel Graphs of Solvable Groups

It is shown that the Gruenberg–Kegel graph of a finite almost simple group is equal to the Gruenberg–Kegel graph of some finite solvable group iff it does not contain 3-cocliques. Furthermore, we obtain a description of finite almost simple groups whose Gruenberg–Kegel graphs contain no 3-cocliques. © 2018, Springer Science+Business Media, LLC, part of Springer Nature

Correlations between zeros of a random polynomial

We obtain exact analytical expressions for correlations between real zeros of the Kac random polynomial. We show that the zeros in the interval $(-1,1)$ are asymptotically independent of the zeros outside of this interval, and that the straightened zeros have the same limit translation invariant correlations. Then we calculate the correlations between the straightened zeros of the SO(2) random polynomial.Comment: 31 pages, 2 figures; a revised version of the J. Stat. Phys. pape

Eocene–early Oligocene climate and vegetation change in southern China: Evidence from the Maoming Basin

Although the Eocene-Oligocene climate transition marks a critical point in the development of the ‘icehouse’ global climate of the present little is known about this important change in the terrestrial realm at low latitudes. Our palynological study of the Shangcun Formation shows it to be early Oligocene in age: palyno-assemblages in the lower part of the formation indicate a cool interval dominated by conifer pollen in the earliest Oligocene followed by a warmer regime in the second half of the early Oligocene. To quantify middle Eocene to late early Oligocene climate conditions at low (~ 20°N) palaeolatitudes in southern Asia several thousand leaf fossil specimens from the Maoming Basin, southern China, were subjected to a multivariate (CLAMP) analysis of leaf form. For terrestrial palaeoclimate comparisons to be valid the palaeoaltitude at which the proxy data are obtained must be known. We find that leaves preserved in the Youganwo (middle Eocene), Huangniuling (late Eocene) and Shangcun (early Oligocene) formations were likely to have been deposited well above sea level at different palaeoelevations. In the Youganwo Formation fine-grained sediments were deposited at an altitude of ~ 1.5 km, after which the basin dropped to ~ 0.5 km by the time the upper Huangniuling sediments were deposited. The basin floor then rose again by 0.5 km reaching an altitude of approximately 1 km in which the Shangcun Formation fine-grained sediments were accumulated. Within the context of these elevation changes the prevailing climates experienced by the Youganwo, Lower Huangniuling, Upper Huangniuling and Shangcun fossil floras were humid subtropical with hot summers and warm winters, but witnessed a progressive increase in rainfall seasonality. By the early Oligocene rainfall seasonality was similar to that of the modern monsoonal climate of Guangdong Province, southern China. All floras show leaf physiognomic spectra most similar to those growing under the influence of the modern Indonesia-Australia Monsoon, but with no evidence of any adaptation to today's South or East Asia Monsoon regimes. The Upper Huangniuling Flora, rich in dipterocarp plant megafossils, grew in the warmest conditions with the highest cold month mean temperature and at the lowest altitude

Scanning tunneling microscopy and spectroscopy at low temperatures of the (110) surface of Te doped GaAs single crystals

We have performed voltage dependent imaging and spatially resolved spectroscopy on the (110) surface of Te doped GaAs single crystals with a low temperature scanning tunneling microscope (STM). A large fraction of the observed defects are identified as Te dopant atoms which can be observed down to the fifth subsurface layer. For negative sample voltages, the dopant atoms are surrounded by Friedel charge density oscillations. Spatially resolved spectroscopy above the dopant atoms and above defect free areas of the GaAs (110) surface reveals the presence of conductance peaks inside the semiconductor band gap. The appearance of the peaks can be linked to charges residing on states which are localized within the tunnel junction area. We show that these localized states can be present on the doped GaAs surface as well as at the STM tip apex.Comment: 8 pages, 8 figures, accepted for publication in PR

Coulomb correlations effects on localized charge relaxation in the coupled quantum dots

We analyzed localized charge time evolution in the system of two interacting quantum dots (QD) (artificial molecule) coupled with the continuous spectrum states. We demonstrated that Coulomb interaction modifies relaxation rates and is responsible for non-monotonic time evolution of the localized charge. We suggested new mechanism of this non-monotonic charge time evolution connected with charge redistribution between different relaxation channels in each QD.Comment: 10 pages, 10 figure

Hemodynamics at different levels of salt intake in patients with hypertrophic cardiomyopathy of different age groups

Aim. To assess the relationship between the level of salt (NaCl) consumption and clinical and hemodynamic parameters in patients with hypertrophic cardiomyopathy (HCM) of different age groups.Material and methods. We examined 57 patients with HCM (mean age, 59,2±16,2 years). The patients were divided into groups according to the World Health Organization (WHO): I — young age (≤44 years old) — 12,4% of patients; II — middle (45-59 years old) — 37,2%; III — elderly (60–74 years old) — 36%; IV — senile (≥75 years old old) — 14,4%. The clinical status of patients was assessed, during which special attention was paid to syncope not related to cardiac arrhythmias. NaCl intake was assessed by the 24-hour urine sodium (Na+) level.Results. In the general cohort, in Na+ level <50 mmol/day, the lowest left ventricular stroke volume (LVSV) index was observed, which were associated with syncope (r=-0,9, p=0,03). With the urinary sodium level of 50-70 mmol/day, an increase in LVSV index was observed and the absence of syncope. At Na+ level more than 70 mmol/day, no increase in LVSV index was observed. In this regard, a predictive model was created, as a result of which it was found that with an increase in Na+ consumption by 1 mmol/day, an increase in LVSV index by 0,3 ml/m2 should be expected. There were no significant differences in the effect of NaCl intake on the studied parameters in patients with HCM of different ages. At the same time, low NaCl intake in elderly patients was associated with syncope.Conclusion. Minimal values of Na+ intake (<50 mmol/day or NaCl 3 g/day) were found, which are unfavorable for patients with HCM due to the risk syncope. The 24-hour urine sodium level to maintain a hemodynamically safe level of LVSV index in patients with HCM should be more than 70 mmol/day (NaCl 4,1 g/day). Monitoring of Na+ consumption level is especially important in elderly people with HCM