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Towards a Theory of Degenerated Solectrons in Doped Lattices: Problems and Perspectives

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Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

The theory of solectrons is restricted so far to one, or two charges embedded into a chain or a layer of atoms. We discuss here the open problems arising by adding excess charges into a chain or a layer when generalizing the existing theory of individual solectrons to many-body thermal systems. Several methods to include degeneration effects and interactions of the solectrons are discussed in order to extend the theory to finite densities and to discuss density—as well as temperature effects. In the present model the charges are embedded into one- or two-dimensional systems of atoms which are treated by classical embedded Langevin equations. By nonlinear interactions between atoms and charges moving quasi-particles as solectrons or solectron pairs are formed which are treated in stochastic tight-binding approximation based on Pauli-type kinetic equations. We discuss results for degenerated solectron systems with zero spin including spatial distributions, and energy distributions. We notice interesting structures of the energy distribution including the Fermi edge and the possible existence of gaps in the spectrum. Finally we discuss the perspectives of many-body systems and give an estimate of the phase plane temperature against density of doping charges—discussing possibilities to create degenerate solectron systems in heavily doped lattices.

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Acknowledgements

The authors acknowledge fruitful discussions with A.S. Alexandrov, E. Brändas, L. Brizhik, L. Cisneros-Ake, L. Cruzeiro, F. de Moura, C. Eilbeck, J. Feder, D. Hennig, J.J. Kozak, S. Larsson, R. Lima, D.M. Newns, G. Röpke, F.M. Russell, G.A. Vinogradov and E.G. Wilson. This research was supported by the Spanish Ministerio de Economía y Competitividad, under Grant MAT2011-26221.

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Authors and Affiliations

  1. Department of Physics, Saratov State University, Astrakhanskaya 83, Saratov, 410012, Russia

    A. P. Chetverikov

  2. Institut für Physik, Humboldt-Universität Berlin, Newtonstrasse 15, Berlin, 12489, Germany

    W. Ebeling

  3. Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, Madrid, 28040, Spain

    M. G. Velarde

Authors
  1. A. P. Chetverikov
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  2. W. Ebeling
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  3. M. G. Velarde
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Corresponding author

Correspondence to A. P. Chetverikov .

Editor information

Editors and Affiliations

  1. , Dpt. Quimica-Fisica-I, UCM, Madrid, 28040, Spain

    Ramon G. Rubio

  2. Instituto Pluridisciplinar, UCM, Paseo Juan XXIII 1, Madrid, 28040, Spain

    Yuri S. Ryazantsev

  3. , Dpt. of Chemical Engineering, Loughborough University, Loughborough, LE11 3TU, United Kingdom

    Victor M Starov

  4. , Physics Dpt., East China Normal University, Zhongshan Northern Road 3663, Shanghai, 200062, China, People's Republic

    Guo-Xiang Huang

  5. , Faculty of Physics, Saratov State University, Astrakhanskaya Str. 83, Saratov, 410012, Russia

    Alexander P Chetverikov

  6. , Dpt. di Ingegneria Elettrica Elettronica, Università di Catania, V. le A. Doria 6, Catania, 95125, Italy

    Paolo Arena

  7. , Dept. of Mathematics, Technion, Haifa, 32000, Israel

    Alex A. Nepomnyashchy

  8. , Instituto Cajal, CSIC, Av. Dr. Arce 37, Madrid, 28002, Spain

    Alberto Ferrus

  9. Shirshov Institute of Oceanology, Nakhimovsky prospekt 36, Moscow, 117851, Russia

    Eugene G. Morozov

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Chetverikov, A.P., Ebeling, W., Velarde, M.G. (2013). Towards a Theory of Degenerated Solectrons in Doped Lattices: Problems and Perspectives. In: Rubio, R., et al. Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34070-3_36

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  • DOI: https://doi.org/10.1007/978-3-642-34070-3_36

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