19,092 research outputs found
Regional Policy and Convergence in Europe: The Case of Backward Regions
This paper analyzes the performance of regions whose development is lagging behind since the institutionalization of the EU regional policy, (1989). Results from a panel data model with fixed effects prove that backward regions have been catching up with the EU average income since the launching of the first programming period, the so called Delors'I package, 1989-1993
Quasi-Exactly Solvable N-Body Spin Hamiltonians with Short-Range Interaction Potentials
We review some recent results on quasi-exactly solvable spin models
presenting near-neighbors interactions. These systems can be understood as
cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial
modification of the exchange operator formalism is used to obtain several
infinite families of eigenfunctions of these models in closed form.Comment: This is a contribution to the Proc. of workshop on Geometric Aspects
of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in
SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
A Haldane-Shastry spin chain of BC_N type in a constant magnetic field
We compute the spectrum of the trigonometric Sutherland spin model of BC_N
type in the presence of a constant magnetic field. Using Polychronakos's
freezing trick, we derive an exact formula for the partition function of its
associated Haldane-Shastry spin chain.Comment: LaTeX, 13 page
Quasi-Exactly Solvable Potentials on the Line and Orthogonal Polynomials
In this paper we show that a quasi-exactly solvable (normalizable or
periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a
family of weakly orthogonal polynomials which obey a three-term recursion
relation. In particular, we prove that (normalizable) exactly-solvable
one-dimensional systems are characterized by the fact that their associated
polynomials satisfy a two-term recursion relation. We study the properties of
the family of weakly orthogonal polynomials defined by an arbitrary
one-dimensional quasi-exactly solvable Hamiltonian, showing in particular that
its associated Stieltjes measure is supported on a finite set. From this we
deduce that the corresponding moment problem is determined, and that the -th
moment grows like the -th power of a constant as tends to infinity. We
also show that the moments satisfy a constant coefficient linear difference
equation, and that this property actually characterizes weakly orthogonal
polynomial systems.Comment: 22 pages, plain TeX. Please typeset only the file orth.te
Nonequilibrium Phase Transitions in Directed Small-World Networks
Many social, biological, and economic systems can be approached by complex
networks of interacting units. The behaviour of several models on small-world
networks has recently been studied. These models are expected to capture the
essential features of the complex processes taking place on real networks like
disease spreading, formation of public opinion, distribution of wealth, etc. In
many of these systems relations are directed, in the sense that links only act
in one direction (outwards or inwards). We investigate the effect of directed
links on the behaviour of a simple spin-like model evolving on a small-world
network. We show that directed networks may lead to a highly nontrivial phase
diagram including first and second-order phase transitions out of equilibrium.Comment: 4 pages, RevTeX format, 4 postscript figs, uses eps
The Berry-Tabor conjecture for spin chains of Haldane-Shastry type
According to a long-standing conjecture of Berry and Tabor, the distribution
of the spacings between consecutive levels of a "generic'' integrable model
should follow Poisson's law. In contrast, the spacings distribution of chaotic
systems typically follows Wigner's law. An important exception to the
Berry-Tabor conjecture is the integrable spin chain with long-range
interactions introduced by Haldane and Shastry in 1988, whose spacings
distribution is neither Poissonian nor of Wigner's type. In this letter we
argue that the cumulative spacings distribution of this chain should follow the
"square root of a logarithm'' law recently proposed by us as a characteristic
feature of all spin chains of Haldane-Shastry type. We also show in detail that
the latter law is valid for the rational counterpart of the Haldane-Shastry
chain introduced by Polychronakos.Comment: LaTeX with revtex4, 6 pages, 6 figure
- …