3,555 research outputs found
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
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
Radioactive beams and inverse kinematics: probing the quantal texture of the nuclear vacuum
The properties of the quantum electrodynamic (QED) vacuum in general, and of
the nuclear vacuum (ground) state in particular are determined by virtual
processes implying the excitation of a photon and of an electron--positron pair
in the first case and of, for example, the excitation of a collective
quadrupole surface vibration and a particle--hole pair in the nuclear case.
Signals of these processes can be detected in the laboratory in terms of what
can be considered a nuclear analogue of Hawking radiation. An analogy which
extends to other physical processes involving QED vacuum fluctuations like the
Lamb shift, pair creation by rays, van der Waals forces and the
Casimir effect, to the extent that one concentrates on the eventual outcome
resulting by forcing a virtual process to become real, and not on the role of
the black hole role in defining the event horizon. In the nuclear case, the
role of this event is taken over at a microscopic, fully quantum mechanical
level, by nuclear probes (reactions) acting on a virtual particle of the zero
point fluctuation (ZPF) of the nuclear vacuum in a similar irreversible,
no--return, fashion as the event horizon does, letting the other particle,
entangled with the first one, escape to infinity, and eventually be detected.
With this proviso in mind one can posit that the reactions
H(Be,Be;3.37 ))H and
H(Li,Li(; 2.69 ))H together with the
associated decay processes indicate a possible nuclear analogy of
Hawking radiation
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
LiLi(1) is discussed, and absolute cross sections
predicted.Comment: Typo corrected with respect to previous versio
The 9Li(d,p) reaction, a specific probe of 10Li, paradigm of parity--inverted nuclei around N=6 closed shell
We show, within the framework of renormalized nuclear field theory and of the
induced reaction surrogate formalism, that the highly debated Li
structure, observed in a recent Li(d,p)Li one--neutron transfer
experiment is consistent with or better, requires the presence of a virtual
state of similar single--particle strength than that of the
resonance at 0.45 0.03 MeV. Based on continuum spectroscopy self-energy
techniques, we find that the physical mechanism responsible for parity
inversion in Li is the same as that at the basis of the similar
phenomenon observed in Be and to that needed in Li to have an
important --wave ground state component. Furthermore, it is also consistent
with the (normal) sequence of the and levels in the
isotones B and C.Comment: Revised text and figures. The paper includes supplemental materia
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