Show simple item record

dc.contributor.authorVourdas, Apostolos*
dc.date.accessioned2017-07-18T11:35:21Z
dc.date.available2017-07-18T11:35:21Z
dc.date.issued2017-07
dc.identifier.citationVourdas 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.en_US
dc.identifier.urihttp://hdl.handle.net/10454/12580
dc.descriptionYesen_US
dc.description.abstractA 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.en_US
dc.language.isoenen_US
dc.relation.isreferencedbyhttps://doi.org/10.1088/1751-8121/aa7b6aen_US
dc.rights© 2017 IOP Publishing Ltd. Reproduced in accordance with the publisher's self-archiving policy.en_US
dc.subjectRenormalization; Total set of states; Hilbert spaces; Generalized bases; Redundancyen_US
dc.titleRenormalization of total sets of states into generalized bases with a resolution of the identityen_US
dc.status.refereedYesen_US
dc.date.Accepted2017-06-23
dc.date.application2017-06-23
dc.typeArticleen_US
dc.type.versionAccepted Manuscripten_US
refterms.dateFOA2018-06-24T00:00:00Z


Item file(s)

Thumbnail
Name:
Vourdas_Journal_of_Physics_A.pdf
Size:
434.5Kb
Format:
PDF

This item appears in the following Collection(s)

Show simple item record