Inhomogeneous and nonstationary Hall states of the CDW with quantized normal carriers

We suggest a theory for a deformable and sliding charge density wave (CDW) in the Hall bar geometry for the quantum limit when the carriers in remnant small pockets are concentrated at lowest Landau levels (LL) forming a fractionally ($\nu<1$) filled quantum Hall state. The gigantic polarizability of the CDW allows for a strong redistribution of electronic densities up to a complete charge segregation when all carriers occupy, with the maximum filling, a fraction $\nu$ of the chain length - thus forming the integer quantum Hall state, while leaving the fraction $(1-\nu)$ of the chain length unoccupied. The electric field in charged regions easily exceeds the pinning threshold of the CDW, then the depinning propagates into the nominally pinned central region via sharp domain walls. Resulting picture is that of compensated collective and normal pulsing counter-currents driven by the Hall voltage. This scenario is illustrated by numerical modeling for nonstationary distributions of the current and the electric field. This picture can interpret experiments in mesa-junctions showing depinning by the Hall voltage and the generation of voltage-controlled high frequency oscillations (Yu.I. Latyshev, P. Monceau, A.A. Sinchenko, et al, presented at ECRYS-2011, unpublished).Comment: After International School - Workshop on Electronic Crystals: ECRYS-201

On Linearity of Nonclassical Differentiation

We introduce a real vector space composed of set-valued maps on an open set X and note it by S. It is a complete metric space and a complete lattice. The set of continuous functions on X is dense in S as in a metric space and as in a lattice. Thus the constructed space plays the same role for the space of continuous functions with uniform convergence as the field of reals plays for the field of rationals. The classical gradient may be extended in the space S as a close operator. If a function f belongs to its domain then f is locally lipschitzian and the values of our gradient coincide with the values of Clarke's gradient. However, unlike Clarke's gradient, our gradient is a linear operator.Comment: Sorry, this article is being rewritten. Please email the author to be informed about its availabilit

On Limiting Likelihood Ratio Processes of some Change-Point Type Statistical Models

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an exponential functional of a two-sided Poisson process driven by some parameter, while the second one is an exponential functional of a two-sided Brownian motion. We establish that for sufficiently small values of the parameter, the Poisson type likelihood ratio can be approximated by the Brownian type one. As a consequence, several statistically interesting quantities (such as limiting variances of different estimators) related to the first likelihood ratio can also be approximated by those related to the second one. Finally, we discuss the asymptotics of the large values of the parameter and illustrate the results by numerical simulations