1,720 research outputs found
On (Sub)stochastic and Transient Weightings of Infinite Strong Digraphs
In the present paper, for a given (possibly, infinite) strongly connected
digraph we consider the class of all truthly
substochastic weightings of (here, the word "truthly" means that
there exists a vertex whose out-weight is strictly less than ). For a finite
subdigraph of weighted by
let be the length of its longest directed cycle and
be the Perron root (spectral radius) of its weighted
adjacency matrix. We prove that the infimum of
taken over all
is positive for every if and only if
admits a finite cycle transversal. The result obtained provides
general theorems on the set of transient weightings of
In particular, we present a theorem of alternatives for finite
approximations to elements of and simply reprove V. Cyr's
criterion for to be empty
Metallic and insulating behaviour of the two-dimensional electron gas on a vicinal surface of Si MOSFETs
The resistance R of the 2DEG on the vicinal Si surface shows an unusual
behaviour, which is very different from that in the (100) Si MOSFET where an
unconventional metal to insulator transition has been reported. The crossover
from the insulator with dR/dT0 occurs at a low
resistance of R_{\Box}^c \sim 0.04h/e^2. At the low-temperature transition,
which we attribute to the existence of a narrow impurity band at the interface,
a distinct hysteresis in the resistance is detected. At higher temperatures,
another change in the sign of dR/dT is seen and related to the crossover from
the degenerate to non-degenerate 2DEG.Comment: 4 pages, 4 figure
Inhomogeneous broadening of the exciton band in optical absorption spectra of InP/ZnS nanocrystals
In this work, we have simulated the processes of broadening the first exciton band in optical absorption spectra (OA) for InP/ZnS ensembles of colloidal quantum dots (QDs). A phenomenological model has been proposed that takes into account the effects of the exciton–phonon interaction, and allows one to analyze the influence of the static and dynamic types of atomic disorder on the temperature changes in the spectral characteristics in question. To vary the degree of static disorder in the model system, we have used a parameter δ, which characterizes the QD dispersion in size over the ensemble. We have also calculated the temperature shifts of the maxima and changes in the half-width for the exciton peaks in single nanocrystals (δ = 0), as well as for the integrated OA bands in the QD ensembles with different values of δ = 0.6–17%. The simulation results and the OA spectra data measured for InP/ZnS nanocrystals of 2.1 nm (δ = 11.1%) and 2.3 nm (δ = 17.3%), are in good mutual agreement in the temperature range of 6.5 K–RT. It has been shown that the contribution of static disorder to the observed inhomogeneous broadening of the OA bands for the QDs at room temperature exceeds 90%. The computational experiments performed indicate that the temperature shift of the maximum for the integrated OA band coincides with that for the exciton peak in a single nanocrystal. In this case, a reliable estimate of the parameters of the fundamental exciton–phonon interaction can be made. Simultaneously, the values of the specified parameters, calculated from the temperature broadening of the OA spectra, can be significantly different from the true ones due to the effects of static atomic disorder in real QD ensembles. © 2019 by the authors. Licensee MDPI, Basel, Switzerland.Funding: This research was supported by RFBR according to the research project № 18-32-00664 and Act 211 Government of the Russian Federation, contract no. 02.A03.21.0006. I.W. thanks the Minobrnauki initiative research project № 16.5186.2017/8.9 for support
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