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Complex Symmetry, Jordan Blocks and Microscopic Self-organization

An Examination of the Limits of Quantum Theory Based on Nonself-adjoint Extensions with Illustrations from Chemistry and Physics

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SelfOrganization of Molecular Systems

The basis and motivation for extending quantum mechanics beyond its traditional domain are recognized and examined. The mathematical details are briefly discussed and a convenient compact complex symmetric representation derived. An original formula is proved and demonstrated to incorporate general Jordan block configurations characterized by Segrè characteristics larger than one. It is verified that these triangular forms can portray realistic evolutions via maps established both within fundamental quantum mechanics as well as within a generalized thermodynamic formulation displaying features that are reminiscent of self-organization on a microscopic level. Various applications of these so-called coherent dissipative structures in physics and chemistry are pointed out, and discussed with possible inferences also made to the biological domain.

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Authors and Affiliations

  1. Department of Physical and Analytical Chemistry, Quantum Chemistry, Uppsala University, Uppsala, SE-751 20, Sweden

    Erkki J. Brändas

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  1. Erkki J. Brändas
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Editors and Affiliations

  1. Department of Chemistry, University of Calabria, Arcavacata di Rende, (CS), Italy

    Nino Russo

  2. Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    Victor Ya. Antonchenko  & Eugene S. Kryachko  & 

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Brändas, E.J. (2009). Complex Symmetry, Jordan Blocks and Microscopic Self-organization. In: Russo, N., Antonchenko, V.Y., Kryachko, E.S. (eds) SelfOrganization of Molecular Systems. NATO Science for Peace and Security Series A: Chemistry and Biology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2590-6_4

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