129 research outputs found
Exactly-solvable models of proton and neutron interacting bosons
We describe a class of exactly-solvable models of interacting bosons based on
the algebra SO(3,2). Each copy of the algebra represents a system of neutron
and proton bosons in a given bosonic level interacting via a pairing
interaction. The model that includes s and d bosons is a specific realization
of the IBM2, restricted to the transition regime between vibrational and
gamma-soft nuclei. By including additional copies of the algebra, we can
generate proton-neutron boson models involving other boson degrees of freedom,
while still maintaining exact solvability. In each of these models, we can
study not only the states of maximal symmetry, but also those of mixed
symmetry, albeit still in the vibrational to gamma-soft transition regime.
Furthermore, in each of these models we can study some features of F-spin
symmetry breaking. We report systematic calculations as a function of the
pairing strength for models based on s, d, and g bosons and on s, d, and f
bosons. The formalism of exactly-solvable models based on the SO(3,2) algebra
is not limited to systems of proton and neutron bosons, however, but can also
be applied to other scenarios that involve two species of interacting bosons.Comment: 8 pages, 3 figures. Submitted to Phys.Rev.
Dobinski-type relations and the Log-normal distribution
We consider sequences of generalized Bell numbers B(n), n=0,1,... for which
there exist Dobinski-type summation formulas; that is, where B(n) is
represented as an infinite sum over k of terms P(k)^n/D(k). These include the
standard Bell numbers and their generalizations appearing in the normal
ordering of powers of boson monomials, as well as variants of the "ordered"
Bell numbers. For any such B we demonstrate that every positive integral power
of B(m(n)), where m(n) is a quadratic function of n with positive integral
coefficients, is the n-th moment of a positive function on the positive real
axis, given by a weighted infinite sum of log-normal distributions.Comment: 7 pages, 2 Figure
Recommended from our members
Generalization of Richardson-Gaudin models to rank-2 algebras
A generalization of Richardson-Gaudin models to the rank-2 SO(5) and SO(3,2) algebras is used to describe systems of two kinds of fermions or bosons interacting through a pairing force. They are applied to the proton-neutron neutron isovector pairing model and to the Interacting Boson Model 2, in the transition from vibration to gamma-soft nuclei, respectively. In both cases, the integrals of motion and their eigenvalues are obtained
On the dynamics of the glass transition on Bethe lattices
The Glauber dynamics of disordered spin models with multi-spin interactions
on sparse random graphs (Bethe lattices) is investigated. Such models undergo a
dynamical glass transition upon decreasing the temperature or increasing the
degree of constrainedness. Our analysis is based upon a detailed study of large
scale rearrangements which control the slow dynamics of the system close to the
dynamical transition. Particular attention is devoted to the neighborhood of a
zero temperature tricritical point.
Both the approach and several key results are conjectured to be valid in a
considerably more general context.Comment: 56 pages, 38 eps figure
The number of matchings in random graphs
We study matchings on sparse random graphs by means of the cavity method. We
first show how the method reproduces several known results about maximum and
perfect matchings in regular and Erdos-Renyi random graphs. Our main new result
is the computation of the entropy, i.e. the leading order of the logarithm of
the number of solutions, of matchings with a given size. We derive both an
algorithm to compute this entropy for an arbitrary graph with a girth that
diverges in the large size limit, and an analytic result for the entropy in
regular and Erdos-Renyi random graph ensembles.Comment: 17 pages, 6 figures, to be published in Journal of Statistical
Mechanic
The Density Matrix Renormalization Group for finite Fermi systems
The Density Matrix Renormalization Group (DMRG) was introduced by Steven
White in 1992 as a method for accurately describing the properties of
one-dimensional quantum lattices. The method, as originally introduced, was
based on the iterative inclusion of sites on a real-space lattice. Based on its
enormous success in that domain, it was subsequently proposed that the DMRG
could be modified for use on finite Fermi systems, through the replacement of
real-space lattice sites by an appropriately ordered set of single-particle
levels. Since then, there has been an enormous amount of work on the subject,
ranging from efforts to clarify the optimal means of implementing the algorithm
to extensive applications in a variety of fields. In this article, we review
these recent developments. Following a description of the real-space DMRG
method, we discuss the key steps that were undertaken to modify it for use on
finite Fermi systems and then describe its applications to Quantum Chemistry,
ultrasmall superconducting grains, finite nuclei and two-dimensional electron
systems. We also describe a recent development which permits symmetries to be
taken into account consistently throughout the DMRG algorithm. We close with an
outlook for future applications of the method.Comment: 48 pages, 17 figures Corrections made to equation 19 and table
Shortest paths and load scaling in scale-free trees
The average node-to-node distance of scale-free graphs depends
logarithmically on N, the number of nodes, while the probability distribution
function (pdf) of the distances may take various forms. Here we analyze these
by considering mean-field arguments and by mapping the m=1 case of the
Barabasi-Albert model into a tree with a depth-dependent branching ratio. This
shows the origins of the average distance scaling and allows a demonstration of
why the distribution approaches a Gaussian in the limit of N large. The load
(betweenness), the number of shortest distance paths passing through any node,
is discussed in the tree presentation.Comment: 8 pages, 8 figures; v2: load calculations extende
- …