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    Renormalization of total sets of states into generalized bases with a resolution of the identity

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    Vourdas_Journal_of_Physics_A.pdf (434.5Kb)
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    Publication date
    2017-07
    Author
    Vourdas, Apostolos
    Keyword
    Renormalization; Total set of states; Hilbert spaces; Generalized bases; Redundancy
    Rights
    © 2017 IOP Publishing Ltd. Reproduced in accordance with the publisher's self-archiving policy.
    Peer-Reviewed
    Yes
    
    Metadata
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    Abstract
    A total set of states for which we have no resolution of the identity (a `pre-basis'), is considered in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices which resolve the identity, and makes them a `generalized basis', which is practically useful. The dresssing mechanism is inspired by Shapley's methodology in cooperative game theory, and it uses Mobius transforms. There is non-independence and redundancy in these generalized bases, which is quantifi ed with a Shannon type of entropy. Due to this redundancy, calculations based on generalized bases, are sensitive to physical changes and robust in the presence of noise. For example, the representation of an arbitrary vector in such generalized bases, is robust when noise is inserted in the coeffcients. Also in a physical system with ground state which changes abruptly at some value of the coupling constant, the proposed methodology detects such changes, even when noise is added to the parameters in the Hamiltonian of the system.
    URI
    http://hdl.handle.net/10454/12580
    Version
    Accepted Manuscript
    Citation
    Vourdas A (2017) Renormalization of total sets of states into generalized bases with a resolution of the identity. Journal of Physics A: Mathematical and Theoretical. 50(32): 325207.
    Link to publisher’s version
    https://doi.org/10.1088/1751-8121/aa7b6a
    Type
    Article
    Collections
    Engineering and Digital Technology Publications

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