We present a simple measure of the conductance fluctuations in open ballistic chaotic quantum dots, extending the number of maxima method originally proposed for the statistical analysis of compound nuclear reactions. The average number of extreme points (maxima and minima) in the dimensionless conductance T as a function of an arbitrary external parameter Z is directly related to the autocorre...

with A= θ/4, B = (r − 1)θ/2N and C = rθ/2N . Note that k represents the number of steps in time, each of duration δt= σt/ √ N , from the position of the maxima. We want the approximation to be valid for a finite range around the maxima in the limit N→∞, and so we need k, and thus r, to vary over the range from 1 to order √ N . It follows that we can use the approximations cos(B)≈ 1, cos(C)≈ 1, ...

Substantiation of the averaging method for differential equations with maxima is presented. Two theorems on substantiates for differential equations with maxima are established.

Double doped (Nd + K) ferroelectric lead germanate single crystals were grown by controlled cooling of melt. Greenish tinge crystals of 5 x 4 x 3 mm were found embedded in the solid. Pure lead germanate was grown by cz technique for comparative analysis. Dielectric constant and loss tangent of pure crystals showed a sharp dielectric peak at 179°C while dielectric constant of doped crystals show...