2011 Issue №4

The task is to define a function EH(λ), such that if { n  } are the points of the continuous spectrum of operator H and n λ  λ , then EH(λ) is defined and is non-zero.

A class of spatially localized solutions of Davey — Stewartson II equation is examined; it is shown that such solutions tend to lose the locality properties with time scale corresponding to a characteristic space scale of initial localization. The locality loss manifests itself with emergence of resonance spikes, whose total number is determined by the asymptotic behavior of support function on infinity. In particular, the exponentially localized perturbations split into an infinite number of the resonances.

In this paper we study the back-action of the quantum point contacton the state of a double quantum dot during the measurement process. To describe this action we introduce an auxiliary subsystem, which is in the entangled states with the original system. This model allowed us to estimate establishment of the steady state of the combined system «double quantum dot — quantum point contact», and identify it as a measurement time and estimate the errors of the qubit states detection.

On the basis of a method of the image of special points the hydrodynamic model of work of a water chink at sea coast in the presence of semicircular inclusion is received. For various cases working conditions of a chink without pollution are investigated.