2,114 research outputs found

    More on the Isomorphism SU(2)⊗SU(2)≅SO(4)SU(2)\otimes SU(2)\cong SO(4)

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    In this paper we revisit the isomorphism SU(2)⊗SU(2)≅SO(4)SU(2)\otimes SU(2)\cong SO(4) to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix QQ by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold SU(2n)/SO(2n)SU(2n)/SO(2n) which characterizes entanglements in the case of n=2n=2 is studied, and a clear-cut calculation of the universal Yang-Mills action in (hep-th/0602204) is given for the abelian case.Comment: Latex ; 19 pages ; 5 figures ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics (vol.4, no.3

    Orbital Evolution of Moons in Weakly Accreting Circumplanetary Disks

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    We investigate the formation of hot and massive circumplanetary disks (CPDs) and the orbital evolution of satellites formed in these disks. Because of the comparatively small size-scale of the sub-disk, quick magnetic diffusion prevents the magnetorotational instability (MRI) from being well-developed at ionization levels that would allow MRI in the parent protoplanetary disk. In the absence of significant angular momentum transport, continuous mass supply from the parental protoplanetary disk leads to the formation of a massive CPD. We have developed an evolutionary model for this scenario and have estimated the orbital evolution of satellites within the disk. We find, in a certain temperature range, that inward migration of a satellite can be stopped by a change in the structure due to the opacity transitions. Moreover, by capturing second and third migrating satellites in mean motion resonances, a compact system in Laplace resonance can be formed in our disk models.Comment: 10 pages, 9 figure
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