The spectrum of eigenenergies of a quantum integrable system whose hamiltonian depends on a single parameter shows degeneracies (crossings) when the parameter varies. We derive a semiclassical expression for the density of crossings in the plane energy-parameter, that is the number of crossings per unit of energy and unit of parameter, in terms of classical periodic orbits. We compare the resul...

We generalize to non-flat geometries the formalism of Simon et al. (2005) to reconstruct the dark energy potential. This formalismmakes use of quantities similar to the Horizon-flow parameters in inflation, can, in principle, be made non-parametric and is general enough to be applied outside the simple, single scalar field quintessence. Since presently available and forthcoming data do not allo...

Talmi's method of calculating coefficients of fractional parentage to states forbidden by the Pauli principle. Abstract In a previous work we studied the effects of setting all two body T=0 matrix elements to zero in shell model calculations for 43 Ti (43 Sc) and 44 Ti. The results for 44 Ti were surprisingly good despite the severity of this approximation. We found degeneracies in this approxi...

The standard genetic code multiplet structure as well as the correct degeneracies, class by class, are all extracted from the (unique) number 23!, the order of the permutation group of 23 objects.

We give an exact spectral equivalence between the quantum group invariant XXZ chain with arbitrary left boundary term and the same XXZ chain with purely diagonal boundary terms. This equivalence, and a further one with a link pattern Hamiltonian, can be understood as arising from different representations of the one-boundary Temperley–Lieb algebra. For a system of size L these representations a...

Recent developments in the physics of ultracold gases provide wide possibilities for reducing the dimensionality of space for magnetically or optically trapped atoms. The goal of these lectures is to show that regimes of quantum degeneracy in two-dimensional (2D) and one-dimensional (1D) trapped gases are drastically different from those in three dimensions and to stimulate an interest in low-d...

The starred for-adverbial in (1a) reflects standard judgments: in the presence of a DP direct object like a cake—which following terminology by Borer (2005) is referred to here as a Q(uantity)-DP— with an incremental theme verb like eat, the VP is telic. In contrast, in (1b), with a mass noun direct object like cake—referred to here as a non-Q-DP—the VP is atelic. Although these are the pattern...

We prove sharp L estimates for oscillatory integral and Fourier integral operators for which the associated canonical relation C ⊂ T ∗ΩL × T ∗ΩR projects to T ∗ΩL and to T ∗ΩR with corank one singularities of type ≤ 2. This includes two-sided cusp singularities. Applications are given to operators with one-sided swallowtail singularities such as restricted X-ray transforms for well-curved line ...