The problem of explicit generation of unitary operators for atomic systems with degenerate energy levels is considered. The Lie algebra structure is used to derive constructive control schemes for the creation of arbitrary superposition states and selective population interchanges for a transition between two three-fold degenerate energy levels.

I briefly review the source of the so-called intrinsic ambiguity and show how the combination of “golden” and “silver” channel at the Neutrino Factory can solve the problem, in the absence of other sources of degeneracies. I then relaxed the hypothesis θ23 = 45◦ and show how the different dependence of the two channels on θ23 can help in solving the intrinsic and θ23-octant ambiguity at the sam...

The category of finite cardinals (or, equivalently, of finite sets) is the symmetric analogue of the category of finite ordinals, and the ground category of a relevant category of presheaves, the augmented symmetric simplicial sets. We prove here that this ground category has characterisations similar to the classical ones for the category of finite ordinals, by the existence of a universal sym...

An algebraic classification of second order symmetric tensors in 5-dimensional Kaluza-Klein-type Lorentzian spaces is presented by using Jordan matrices. We show that the possible Segre types are [1, 1111], [2111], [311], [z z̄ 111], and the degeneracies thereof. A set of canonical forms for each Segre type is found. The possible continuous groups of symmetry for each canonical form are also stu...

The body of work on multi-body factorization separates between objects whose motions are independent. In this work we show that in many cases objects moving with different 3D motions will be captured as a single object using these approaches. We analyze what causes these degeneracies between objects and suggest an approach for overcoming some of them. We further show that in the case of multipl...