We calculate the radiative corrections to the Dalitz plot of K_{l3}^pm decays to order (alpha/pi)(q/M_1), where q is the momentum transfer and M_1 is the mass of the kaon. We restrict the analysis to the so-called four-body region, which arises when
no discrimination of real photons is made either kinematically or experimentally. We present our results in two ways: the first one with the triple integration over the photon kinematical variables ready to be performed numerically and the second one in a fully analytical form. Our results can be useful in experimental analyses of the Dalitz plot, by evaluating the model-independent coefficients of the quadratic products of the form factors; we provide some numbers as a case example. We find a small, albeit non-negligible, contribution from the four-body region to the radiative correction to the total decay rate of K_{l3}^pm decays.
We have developed an approach allowing us to resolve the problem of non-conventional Anderson localization emerging in bilayered periodic-on-average structures with alternating layers of right-handed and left-handed materials. Recently, it was numeri
cally discovered that in such structures with weak fluctuations of refraction indices, the localization length $L_{loc}$ can be enormously large for small wave frequencies $omega$. Within the fourth order of perturbation theory in disorder, $sigma^2 ll 1$, we derive the expression for $L_{loc}$ valid for any $omega$. In the limit $omega rightarrow 0$ one gets a quite specific dependence, $L^{-1}_{loc} propto sigma ^4 omega^8$. Our approach allows one to establish the conditions under which this effect can be observed.
We report on reflective electro-optic sampling measurements of TeraHertz emission from nanometer-gate-length InGaAs-based high electron mobility transistors. The room temperature coherent gate-voltage tunable emission is demonstrated. We establish th
at the physical mechanism of the coherent TeraHertz emission is related to the plasma waves driven by simultaneous current and optical excitation. A significant shift of the plasma frequency and the narrowing of the emission with increasing channels current are observed and explained as due to the increase of the carriers density and drift velocity.
Experimental results of direct measurement of resonant monochromatic terahertz emission optically excited in InGaAs transistor channels are presented. The emission is attributed to two-dimensional plasma waves excited by photogeneration of electron-h
ole pairs in the channel at the frequency $f_0$ of the beating of two cw-laser sources. The presence of resonances for the radiation emission in the range of $f_0pm 10$ GHz (with $f_0$ from 0.3 up to 0.5 THz) detected by a Si-bolometer is found. Numerical results support that such a high quality of the emission resonances can be explained by the approach of an instability in the transistor channel.
We prove that functions defined on a lattice in a finite dimensional torus with bounded finite differences can be smoothly extended to the whole torus, and relate the bounds on the extensions derivatives with bounds on the original functions finite differences.
We derive some formulas that rule the behaviour of finite differences under composition of functions with vector values and arguments.
We study the effect of varying wiring in excitable random networks in which connection weights change with activity to mold local resistance or facilitation due to fatigue. Dynamic attractors, corresponding to patterns of activity, are then easily de
stabilized according to three main modes, including one in which the activity shows chaotic hopping among the patterns. We describe phase transitions to this regime, and show a monotonous dependence of critical parameters on the heterogeneity of the wiring distribution. Such correlation between topology and functionality implies, in particular, that tasks which require unstable behavior --such as pattern recognition, family discrimination and categorization-- can be most efficiently performed on highly heterogeneous networks. It also follows a possible explanation for the abundance in nature of scale--free network topologies.
