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

摘要

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 de-rived. An original formula is proved and demonstrated to incorporate general Jordan block configurations characterized by Segre characteristics larger than one. It is ver-ified that these triangular forms can portray realistic evolutions via maps established both within fundamental quantum mechanics as well as within a generalized ther-modynamic 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.