International Journal of Modern Physics B

Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest value among a set of random variables) may also play a role in the statistics of global quantities, in a direct or indirect way. This review discusses different connections that may appear between problems of sums and of extreme values of random variables, and emphasizes physical situations in which such connections are relevant. Along this line of thought, standard convergence theorems for sums and extreme values of independent and identically distributed random variables are recalled, and some rigorous results as well as more heuristic reasonings are presented for correlated or non-identically distributed random variables. More specifically, the role of extreme values within sums of broadly distributed variables is addressed, and a general mapping between extreme values and sums is presented, allowing us to identify a class of correlated random variables whose sum follows (generalized) extreme value distributions. Possible applications of this specific class of random variables are illustrated on the example of two simple physical models. A few extensions to other related classes of random variables sharing similar qualitative properties are also briefly discussed, in connection with the so-called BHP distribution.

The coupled cluster method (CCM) is a powerful and widely applied technique of modern-day quantum many-body theory. It has been used with great success in order to understand the properties of quantum magnets at zero temperature. This is largely due to the application of computational techniques that allow the method to be applied to high orders of approximation using a localized scheme known as the LSUBm scheme. A hitherto unreported aspect of this scheme is that results for LSUBm expectation values behave in distinctly different ways with odd and even values of m. Here, we consider the behavior of ground-state expectation values of odd and even orders of the CCM LSUBm approximation for unfrustrated spin-half Heisenberg antiferromagnets on the square and honeycomb lattice and the frustrated spin-half Heisenberg antiferromagnet on the triangular lattice. We demonstrate that results for odd and even orders of approximation show qualitatively different behavior for both the ground-state energy and the sublattice magnetization. Indeed, the odd series consistently forms an upper branch of results, and the even series a lower branch with respect to both ground-state energy and sublattice magnetization, for all of the models considered here.

Klimontovich's S theorem serves as a measure of order relative to a reference state for open systems, thereby providing the correct ordering of entropy values with respect to their distance from the equilibrium state. It can also be considered as a generalization of Gibbs' theorem if one of the distributions is associated with the equilibrium state. Here, a nonadditive generalization of S theorem is obtained by the employment of Tsallis entropy. This generalized form is then illustrated by applying it to the Van der Pol oscillator. Interestingly, this generalization procedure favors the use of ordinary probability distribution instead of escort distribution.

In this paper, Atomic Force Microscope (AFM) was used to observe the microscopic figure of aged insulation paper in order to analyze the microscopic ageing mechanism of power transformer insulation paper under electrical and thermal stresses. The results indicate that there are obvious concaves and convexes on the surface of aged insulation paper, and the paper samples are punctured because of chain scission and the flow of discharge current, which destroyed the compact cellulose chains structures and the diameter of punctures is about 0.5 nm. In addition, this paper analyzed the influence to the physical chemistry characteristics of insulation paper caused by partial discharge and paper ageing.

The quantum transport in the Superconductor–Semiconductor (S–Sm) mesoscopic interface is investigated in the presence of an external electromagnetic field by suggesting a Maxwell potential at the interface. We analyze the current spectrum as a function of the frequency and the distance between the superconductor electrodes. The current displays oscillations with an amplitude that shows a strong dependence on the photon frequency, the field intensity dependence of the current can give direct information of the lead–semiconductor interface energy spectra.

M-type SrFe_12-xAl_xO₁₉(0 < x < 2.5) nanoparticles have been synthesized by citrate–nitrite sol–gel technique. The experimental results have shown that Al³⁺ ions substitute Fe³⁺ ions in the sublattice, and the samples remain in the hexagonal magnetoplumbite phase. The saturation magnetization M_s and remanence M_r of M-type SrFe_12-xAl_xO₁₉(0 < x < 2.5) nanoparticles linearly decrease when x increases. x = 0, M_s = 63.5 emu/g and M_s = 23.8 emu/g at x = 2.5 when the magnets are sintered at 1100°C. Meanwhile, the coercivity H_c of the samples fluctuate as doped with Al, and reach maximum H_c = 10.59 kOe when x = 1.5. The intergranular exchange–coupling interactions between the nanoparticles, which are proved by the measurement of Henkel plots (δM), and the interactions become more intensive as the Al substitution x increases.

We evaluate the universal turbulent Prandtl numbers in the energy and enstrophy régimes of the Kraichnan-Batchelor spectra of two-dimensional turbulence using a self-consistent mode-coupling formulation coming from a renormalized perturbation expansion coupled with dynamic scaling ideas. The turbulent Prandtl number is found to be exactly unity in the (logarithmic) enstrophy régime, where the theory is infrared marginal. In the energy régime, the theory being finite, we extract singularities coming from both ultraviolet and infrared ends by means of Laurent expansions about these poles. This yields the turbulent Prandtl number σ ≈ 0.9 in the energy régime.

Nanocrystalline Mn_0.6Zn_0.4Fe₂O₄ particles are synthesized by a phase transformation method. The crystal structure of these particles is that of spinel MnZn ferrite. The average particle size is about 50 nm and the grain size is about 11 nm. Magnetic measurements show that the saturation magnetization at 120 K is ~80% larger than that at 300 K, and imply that the majority of the nanoparticles are superparamagnetic from 65 to 300 K.

When the usual operator of the Fröhlich's coupling between electrons and longitudinal optical phonons of semiconductor single quantum dot is used to calculate electronic energy relaxation, a permanent phonon generation in quantum dot is obtained, leading to an artificial effect of permanent heating up of the lattice. The mechanism of the phonon heating is identified here with the influence of the transverse part of the interaction operator. This part is responsible first of all for a tendency to build the polaronic well of an electron in a quantum dot. The effect of overheating is shown to be possibly eliminated to a considerable extent upon removing the transverse part of the interaction with the help of the Lang–Firsov canonical transformation and upon modifying accordingly the longitudinal part of the coupling. The resulting electronic relaxation and optical phonon generation is demonstrated numerically in a relatively simple approximation to electron and phonon self-energy, in which the model of quantum dot is reduced to an electron coupled to a single-LO-phonon mode. It is interesting to see that the removal of the phonon overheating based on the application of the Lang–Firsov canonical transformation has a rather small influence on electronic characteristics calculated with electronic transport equations. In this sense, the long-time limit properties of the electronic subsystem, like the electronic up-conversion and incomplete depopulation effect, calculated earlier, remain nearly untouched.

The nature of the stable points of the general two-dimensional quadratic map is considered analytically, and the boundary equation of the first bifurcation of the map in the parameter space is given out. The general feature of the nonlinear dynamic activities of the map is analyzed by the method of numerical computation. By utilizing the Lyapunov exponent as a criterion, this paper constructs the strange attractors of the general two-dimensional quadratic map, and calculates the fractal dimension of the strange attractors according to the Lyapunov exponents. At the same time, the researches on the fractal images of the general two-dimensional quadratic map make it clear that when the control parameters are different, the fractal images are different from each other, and these fractal images exhibit the fractal property of self-similarity.

The paper discusses the problem of a two-dimensional static deformation as the result of normal line-load acting inside an irregular initially stressed isotropic half-space. The eigenvalue approach method has been used. The irregularity is expressed by a rectangle shape. Further, the results for the displacements and stresses have been derived in the closed form. The effect of initial stress and irregularity are shown graphically. It was found that the initial stresses as well as irregularity have a notable effect on this deformation.