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Cyclotomy and Ramanujan sums in quantum phase locking

dc.contributor.authorMichel Planat
dc.contributor.authorRosu Barbus, Haret-Codratian
dc.identifier.citationMichel Planat, Haret C. Rosu, Cyclotomy and Ramanujan sums in quantum phase locking, In Physics Letters A, Volume 315, Issues 1-2, 2003, Pages 1-5
dc.description.abstract"Phase-locking governs the phase noise in classical clocks through effects described in precise mathematical terms. We seek here a quantum counterpart of these effects by working in a finite Hilbert space. We use a coprimality condition to define phase-locked quantum states and the corresponding Pegg-Barnett type phase operator. Cyclotomic symmetries in matrix elements are revealed and related to Ramanujan sums in the theory of prime numbers. The employed mathematical procedures also emphasize the isomorphism between algebraic number theory and the theory of quantum entanglement."
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional
dc.subjectRamanujan sums
dc.subjectPhase locking
dc.titleCyclotomy and Ramanujan sums in quantum phase locking
dc.rights.accessAcceso Abierto

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