An Exclusion Principle for Sum-Free Quantum Numbers

• URL: http://arxiv.org/abs/2009.14491v1
• Date: Wed, 30 Sep 2020 08:03:00 GMT
• Title: An Exclusion Principle for Sum-Free Quantum Numbers
• Authors: Miguel A. Martin-Delgado
• Abstract summary: The sum-free condition for Schur numbers can be read off as a form of exclusion principle for quantum particles. A particular instance of the correlated exclusion principle can be solved explicitly yielding a sequence of quantum numbers that exhibits a fractal structure. The corresponding algebra of creation and annihilation operators can be identified in terms of commutation and anticommutation relations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A hypothetical exclusion principle for quantum particles is introduced that generalizes the exclusion and inclusion principles for fermions and bosons, respectively: the correlated exclusion principle. The sum-free condition for Schur numbers can be read off as a form of exclusion principle for quantum particles. Consequences of this interpretation are analysed within the framework of quantum many-body systems. A particular instance of the correlated exclusion principle can be solved explicitly yielding a sequence of quantum numbers that exhibits a fractal structure and is a relative of the Thue-Thurston sequence. The corresponding algebra of creation and annihilation operators can be identified in terms of commutation and anticommutation relations of a restricted version of the hard-core boson algebra.

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