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Nanosystems: Physics, Chemistry, Mathematics

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Our journal "Nanosystems: Physics, Chemistry, Mathematics" is devoted to fundamental problems of physics, chemistry and mathematics concerning all aspects of nanosystems science. It considers both theoretical and experimental problems of physics and chemistry of nanosystems, including methods of their design and creation, studies of their structure and properties, behavior under external influences, and the possibility of use. We accept papers directly or conceptually related to the key properties of nanosystems. Nanotechnology has required the creation of new methods of mathematical modeling and mathematical physics, as well as the development of existing methods for their extension to the study of new objects, many of which were previously simply absent. The corresponding mathematical problems will be covered in our journal. The scope of the journal includes all areas of nano-sciences. Papers devoted to basic problems of physics, chemistry and mathematics inspired by nanosystems investigations are welcomed. Both theoretical and experimental works concerning the properties and behavior of nanosystems, problems of their creation and application, mathematical methods of nanosystem studies are considered. The journal publishes scientific reviews (up to 30 journal pages), research papers (up to 15 pages) and letters (up to 5 pages). All manuscripts are peer-reviewed. Authors are informed about the referee opinions and the Editorial decisions.

Current issue

Vol 1, No 1 (2010)
View or download the full issue PDF (Russian)
108-147
Abstract

In this paper we propose a synthesis of various approaches mixing computational modeling, solving complex and sometimes ill-posed inverse problems and the development of efficient analytic perturbation procedures, which offer an analytic path to the solution of the mathematical design and optimization problems for constructing quantum networks with prescribed transport properties. We consider the simplest sort of 2𝐷 quantum networks — the junctions — and focus on the problems of the resonance scattering, caused by the spectral properties of the relevant Schrodinger operator on the vertex domain. Typically, ¨ 1-D features appear in the form of the single-mode scattering on the first spectral (energy) band in the resulting solvable model, but the analysis of multi-mode scattering is possible with our methodology. However, this comes at the price of assuming realistic (as opposed to quite general) matching between the scattering Ansatz in the wires and the solution of the Schrodinger equation on the vertex ¨ domain. Here this matching is based on a recently developed version of the Dirichlet-to-Neumann map. We are further able to observe the transformation of the discrete spectrum of the Schrodinger operator on the vertex domain ¨ into the resonance features of the relevant scattering problem. 

178-187
Abstract

We have developed a theory of the one-phonon intraband resonance scattering of electromagnetic radiation (IRSER) in anisotropic quantum dots subjected to an arbitrarily directed magnetic field. The differential cross section of scattering is obtained. The resonance structure of the cross section is studied. It is shown that the quantum dot subjected in a magnetic field can be used as the detector of phonon modes. The interesting multiplet structure of the resonance peaks is studied. 



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