SMEARING OF OBSERVABLES AND SPECTRAL MEASURES ON QUANTUM STRUCTURES

Caishi Wang

In this paper, we study the mapping r ↦ δr(Q), where Q is an observable satisfying mild conditions and δr(Q) is the delta function of Q with r ∈ ℝ. We find that, under certain integrable conditions, the mapping r ↦ δr(Q) is just the Radon–Nikodym derivative of Q 's spectral measure with respect to Lebesgue measure and, moreover, Q can be represented as an integral of the mapping r ↦ rδr(Q) with respect to Lebesgue measure. An example is also given.

Anatolij Dvurečenskij

Anatolij Dvurečenskij, Mária Kuková

Anatolij Dvurečenskij

Joint distribution of observables in measures attaining infinite values is ivestigated in the framework of quantum logics.For a logio of a separable Hilbert space, dim H>3, it is proved that any -finite measure has a carrier, and this result is applied to the problem of the existence of a joint distribution.

S. I. Petrov, M.V. Klimenko, Шулика Алексей Владимирович

In this paper we come up with a new approach to retuning the spectral characteristics of quantum-cascade structure amplification. The process of retuning proceeds using the continuous-wave optical pumping and it is strongly dependent upon the phase space filling effect. As suggested by the results from the mathematical simulation of the quantum-cascade structure optical properties, this particular method allows the spectral amplification characteristics to be retuned within the limits of 1.1 meV with no substantial change in the plan gain magnitude. The results thus obtained is of certain interest for spectroscopic detection of explosive.