653 research outputs found
Multipliers of embedded discs
We consider a number of examples of multiplier algebras on Hilbert spaces
associated to discs embedded into a complex ball in order to examine the
isomorphism problem for multiplier algebras on complete Nevanlinna-Pick
reproducing kernel Hilbert spaces. In particular, we exhibit uncountably many
discs in the ball of which are multiplier biholomorphic but have
non-isomorphic multiplier algebras. We also show that there are closed discs in
the ball of which are varieties, and examine their multiplier
algebras. In finite balls, we provide a counterpoint to a result of Alpay,
Putinar and Vinnikov by providing a proper rational biholomorphism of the disc
onto a variety in such that the multiplier algebra is not all
of . We also show that the transversality property, which is one
of their hypotheses, is a consequence of the smoothness that they require.Comment: 34 pages; the earlier version relied on a result of Davidson and
Pitts that the fibre of the maximal ideal space of the multiplier algebra
over a point in the open ball consists only of point evaluation. This result
fails for , and has necessitated some changes; to appear in
Complex Analysis and Operator Theor
Relation Between a Three Parameter Formula for Isotope Shifts and Staggering Parameters
It is noted that the staggering parameters used to describe even-odd effects
for isotope shifts can in some cases exhibit very rapidly varying behavior as a
function of neutron number. On the other hand a three parameter formula (3P)
with fixed coefficients can explain the same behaviour
Composite Fermions and quantum Hall systems: Role of the Coulomb pseudopotential
The mean field composite Fermion (CF) picture successfully predicts angular
momenta of multiplets forming the lowest energy band in fractional quantum Hall
(FQH) systems. This success cannot be attributed to a cancellation between
Coulomb and Chern-Simons interactions beyond the mean field, because these
interactions have totally different energy scales. Rather, it results from the
behavior of the Coulomb pseudopotential V(L) (pair energy as a function of pair
angular momentum) in the lowest Landau level (LL). The class of short range
repulsive pseudopotentials is defined that lead to short range Laughlin like
correlations in many body systems and to which the CF model can be applied.
These Laughlin correlations are described quantitatively using the formalism of
fractional parentage. The discussion is illustrated with an analysis of the
energy spectra obtained in numerical diagonalization of up to eleven electrons
in the lowest and excited LL's. The qualitative difference in the behavior of
V(L) is shown to sometimes invalidate the mean field CF picture when applied to
higher LL's. For example, the nu=7/3 state is not a Laughlin nu=1/3 state in
the first excited LL. The analysis of the involved pseudopotentials also
explains the success or failure of the CF picture when applied to other systems
of charged Fermions with Coulomb repulsion, such as the Laughlin quasiparticles
in the FQH hierarchy or charged excitons in an electron-hole plasma.Comment: 27 pages, 23 figures, revised version (significant changes in text
and figures), submitted to Phil. Mag.
Number of Spin States of Identical Particles
In this paper we study the enumeration of number (denoted as ) of spin
states for fermions in a single- shell and bosons with spin . We show
that can be enumerated by the reduction from SU to SO(3). New
regularities of are discerned.Comment: 3 pages, no figures. to be publishe
The isomorphism problem for some universal operator algebras
This paper addresses the isomorphism problem for the universal
(nonself-adjoint) operator algebras generated by a row contraction subject to
homogeneous polynomial relations. We find that two such algebras are
isometrically isomorphic if and only if the defining polynomial relations are
the same up to a unitary change of variables, and that this happens if and only
if the associated subproduct systems are isomorphic. The proof makes use of the
complex analytic structure of the character space, together with some recent
results on subproduct systems. Restricting attention to commutative operator
algebras defined by radical relations yields strong resemblances with classical
algebraic geometry. These commutative operator algebras turn out to be algebras
of analytic functions on algebraic varieties. We prove a projective
Nullstellensatz connecting closed ideals and their zero sets. Under some
technical assumptions, we find that two such algebras are isomorphic as
algebras if and only if they are similar, and we obtain a clear geometrical
picture of when this happens. This result is obtained with tools from algebraic
geometry, reproducing kernel Hilbert spaces, and some new complex-geometric
rigidity results of independent interest. The C*-envelopes of these algebras
are also determined. The Banach-algebraic and the algebraic classification
results are shown to hold for the weak-operator closures of these algebras as
well.Comment: 46 pages. Final version, to appear in Advances in Mathematic
Seniority conservation and seniority violation in the g_{9/2} shell
The g_{9/2} shell of identical particles is the first one for which one can
have seniority-mixing effects. We consider three interactions: a delta
interaction that conserves seniority, a quadrupole-quadrupole (QQ) interaction
that does not, and a third one consisting of two-body matrix elements taken
from experiment (98Cd) that also leads to some seniority mixing. We deal with
proton holes relative to a Z=50,N=50 core. One surprising result is that, for a
four-particle system with total angular momentum I=4, there is one state with
seniority v=4 that is an eigenstate of any two-body interaction--seniority
conserving or not. The other two states are mixtures of v=2 and v=4 for the
seniority-mixing interactions. The same thing holds true for I=6. Another point
of interest is that the splittings E(I_{max})-E(I_{min}) are the same for three
and five particles with a seniority conserving interaction (a well known
result), but are equal and opposite for a QQ interaction. We also fit the
spectra with a combination of the delta and QQ interactions. The Z=40,N=40 core
plus g_{9/2} neutrons (Zr isotopes) is also considered, although it is
recognized that the core is deformed.Comment: 19 pages, 9 figures; RevTeX4. We have corrected the SDI values in
Table1 and Fig.1; in Sect.VII we have included an explanation of Fig.3
through triaxiality; we have added comments of Figs.10-12 in Sect.IX; we have
removed Figs.7-
Potential Models and Lattice Gauge Current-Current Correlators
We compare current-current correlators in lattice gauge calculations with
correlators in different potential models, for a pseudoscalar charmonium in the
quark-gluon plasma. An important ingredient in the evaluation of the
current-current correlator in the potential model is the basic principle that
out of the set of continuum states, only resonance states and Gamow states with
lifetimes of sufficient magnitudes can propagate as composite objects and can
contribute to the current-current correlator. When the contributions from the
bound states and continuum states are properly treated, the potential model
current-current correlators obtained with the potential proposed in Ref. [11]
are consistent with the lattice gauge correlators. The proposed potential model
thus gains support to be a useful tool to complement lattice gauge calculations
for the study of states at high temperatures.Comment: 18 pages, 4 figures, to be published in Physcial Review
Cluster sum rules for three-body systems with angular-momentum dependent interactions
We derive general expressions for non-energy weighted and energy-weighted
cluster sum rules for systems of three charged particles. The interferences
between pairs of particles are found to play a substantial role. The
energy-weighted sum rule is usually determined by the kinetic energy operator,
but we demonstrate that it has similar additional contributions from the
angular momentum and parity dependence of two- and three-body potentials
frequently used in three-body calculations. The importance of the different
contributions is illustrated with the dipole excitations in He. The results
are compared with the available experimental data.Comment: 11 pages, 3 figures, 2 table
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