Valtierra, Iván F.Klimov, Andrei B.Leuchs, GerdSánchez Soto, Luis Lorenzo2023-06-162023-06-162020-03-022469-992610.1103/PhysRevA.101.033803https://hdl.handle.net/20.500.14352/6110©2020 American Physical Society. This work is partially supported by Grant No. 254127 from CONACyT (Mexico). L.L.S.S. acknowledges the support of the Spanish MINECO (Grants No. FIS2015-67963-P and No. PGC2018-099183-B-I00).We present analytic expressions for the s-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents for quadratic Hamiltonians. The results are applied for the study of the quantum dissipative dynamics of the time-honored Kerr and Lipkin models, exploring the appearance of the semiclassical limit in stable, unstable, and tunneling regimes.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.101.033803https://journals.aps.orgopen access535Body approximation methodsQuantum-superposition statesSolvable modelPhase propertiesWigner functionsKerr mediumNondemolitionRepresentationCoherentValidityÓptica (Física)2209.19 Óptica Física