Commutative C∗C^*-algebras generated by Toeplitz operators on the super unit ball

We extend known results about commutative $C^*$-algebras generated Toeplitz operators over the unit ball to the supermanifold setup. This is obtained by constructing commutative $C^*$-algebras of super Toeplitz operators over the super ball $\mathbb{B}^{p|q}$ and the super Siegel domain $\mathbb{U}^{p|q}$ that naturally generalize the previous results for the unit ball and the Siegel domain. In particular, we obtain one such commutative $C^*$-algebra for each even maximal Abelian subgroup of automorphisms of the super ball.Comment: To appear in Advances in Applied Clifford Algebra

The Restriction Principle and Commuting Families of Toeplitz Operators on the Unit Ball

On the unit ball B^n we consider the weighted Bergman spaces H_\lambda and their Toeplitz operators with bounded symbols. It is known from our previous work that if a closed subgroup H of \widetilde{\SU(n,1)} has a multiplicity-free restriction for the holomorphic discrete series of \widetilde{\SU(n,1)}, then the family of Toeplitz operators with H-invariant symbols pairwise commute. In this work we consider the case of maximal abelian subgroups of \widetilde{\SU(n,1)} and provide a detailed proof of the pairwise commutativity of the corresponding Toeplitz operators. To achieve this we explicitly develop the restriction principle for each (conjugacy class of) maximal abelian subgroup and obtain the corresponding Segal-Bargmann transform. In particular, we obtain a multiplicity one result for the restriction of the holomorphic discrete series to all maximal abelian subgroups. We also observe that the Segal-Bargman transform is (up to a unitary transformation) a convolution operator against a function that we write down explicitly for each case. This can be used to obtain the explicit simultaneous diagonalization of Toeplitz operators whose symbols are invariant by one of these maximal abelian subgroups

Characterization of vorticity in pygmy resonances and soft-dipole modes with two-nucleon transfer reactions

The properties of the two-quasiparticle-like soft E1-modes and PDR have been and are systematically studied with the help of inelastic and electromagnetic experiments which essentially probe the particle-hole components of these vibrations. It is shown that further insight in their characterisation can be achieved with the help of two-nucleon transferreactions, in particular concerning the particle-particle components of the modes, in terms of absolute differential cross sections which take properly into account successive and simultaneous transfer mechanisms corrected for non-orthogonality, able to reproduce the experimental findings at the 10% level. The process $^9$Li$(t,p)^{11}$Li(1$^-$) is discussed, and absolute cross sections predicted.Comment: Typo corrected with respect to previous versio

K-Rb Fermi-Bose mixtures: vortical states and sag

We study a confined mixture of bosons and fermions in the quantal degeneracy regime with attractive boson-fermion interaction. We discuss the effect that the presence of vortical states and the displacement of the trapping potentials may have on mixtures near collapse, and investigate the phase stability diagram of the K-Rb mixture in the mean field approximation supposing in one case that the trapping potentials felt by bosons and fermions are shifted from each other, as it happens in the presence of a gravitational sag, and in another case, assuming that the Bose condensate sustains a vortex state. In both cases, we have obtained an analytical expression for the fermion effective potential when the Bose condensate is in the Thomas-Fermi regime, that can be used to determine the maxima of the fermionic density. We have numerically checked that the values one obtains for the location of these maxima using the analytical formulas remain valid up to the critical boson and fermion numbers, above which the mixture collapses.Comment: Submitted to Phys. Rev. A (on May 2004), 15 pages with 3 figure

Cooper pair transfer in nuclei

The second order DWBA implementation of two-particle transfer direct reactions which includes simultaneous and successive transfer, properly corrected by non-orthogonality effects is tested with the help of controlled nuclear structure and reaction inputs against data spanning the whole mass table, and showed to constitute a quantitative probe of nuclear pairing correlations

Testing two-nucleon transfer reaction mechanism with elementary modes of excitation in exotic nuclei

Nuclear Field Theory of structure and reactions is confronted with observations made on neutron halo dripline nuclei, resulting in the prediction of a novel (symbiotic) mode of nuclear excitation, and on the observation of the virtual effect of the halo phenomenon in the apparently non-halo nucleus $^7$Li. This effect is forced to become real by intervening the virtual process with an external (t,p) field which, combined with accurate predictive abilities concerning the absolute differential cross section, reveals an increase of a factor 2 in the cross section due to the presence of halo ground state correlations, and is essential to reproduce the value of the observed $d \sigma(^7$Li(t,p)$^9$Li)/d$\Omega$.Comment: Submitted to CERN proceedings for the 14th International Conference on Nuclear Reaction mechanisms, Varenna, June 15 - 19, 201