Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions for each type of controllability are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies. Degrees of controllability for quantum systems and application to...

It now appears phenomenologically that the third family may be essentially different from the first two. Particularly the high value of the top quark mass suggests a special role. In the standard model all three families are treated similarly [becoming exactly the same at asymptotically high energies] so I need to extend the model to accommodate the goal of a really different third family. In t...

We propose a new approach to calculate perturbatively the effects of a particular deformed Heisenberg algebra on energy spectrum. We use this method to calculate the harmonic oscillator spectrum and find that corrections are in agreement with a previous calculation. Then, we apply this approach to obtain the hydrogen atom spectrum and we find that splittings of degenerate energy levels appear. ...

We discuss the deletion of a single vertex in a Delaunay tetrahedralization (DT). While some theoretical solutions exist for this problem, the many degeneracies in three dimensions make them impossible to be implemented without the use of extra mechanisms. In this paper, we present an algorithm that uses a sequence of bistellar flips to delete a vertex in a DT, and we present two different mech...

We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with reflection) predict only two fold degeneracies. However , we have found that degeneracies of higher order also exist and, as the system size increases, higher and higher orders appear. These degeneracies ...

In the geometric realization of a cubical complex without degeneracies, a 2-set, dipaths and dihomotopies may not be combinatorial, i.e., not geometric realizations of combinatorial dipaths and equivalences. When we want to use geometric/topological tools to classify dipaths on the 1-skeleton, combinatorial dipaths, up to dihomotopy, and in particular up to combinatorial dihomotopy, we need tha...

Strong evidence indicates that the spectrum of planar anomalous dimensions of N = 4 super Yang-Mills theory is given asymptotically by Bethe equations. A curious observation is that the Bethe equations for the psu(1, 1|2) subsector lead to very large degeneracies of 2 multiplets, which apparently do not follow from conventional integrable structures. In this article, we explain such degeneracie...

We compute the boundary entropies for the allowed boundary conditions of the SU (2)-invariant principal chiral model at level k = 1. We used the reflection factors determined in previous work. As a by-product we obtain some miscellaneous results such as the ground-state energy for mixed boundary conditions as well as the degeneracies of the Kondo model in the underscreened and exactly screened ...

We update a recent work devoted to resolve the degeneracies that appear in the simultaneous extraction of θ13 and δ at future Neutrino Factories (NF, that exploit the golden channels, i.e. νe → νμ (ν̄e → ν̄μ)) and Superbeam experiments (SB, that measure the νμ → νe (ν̄μ → ν̄e) transitions). We consider the neutrino fluxes obtained with a new optics design for the CERNSPL SB and assume the solar par...

Topological sweep can contribute to efficient implementations of various algorithms for data analysis. Real data, however, has degeneracies. The modification of the topological sweep algorithm presented here handles degenerate cases such as parallel or multiply concurrent lines without requiring numerical perturbations to achieve general position. Our method maintains the O(n) and O(n) time and...