Renormalization of total sets of states into generalized bases with a resolution of the identity
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2017-07Author
Vourdas, ApostolosRights
© 2017 IOP Publishing Ltd. Reproduced in accordance with the publisher's self-archiving policy.Peer-Reviewed
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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.Version
Accepted ManuscriptCitation
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 Version of Record
https://doi.org/10.1088/1751-8121/aa7b6aType
Articleae974a485f413a2113503eed53cd6c53
https://doi.org/10.1088/1751-8121/aa7b6a