11,517 research outputs found
Multivariate Orthogonal Polynomials and Modified Moment Functionals
Multivariate orthogonal polynomials can be introduced by using a moment
functional defined on the linear space of polynomials in several variables with
real coefficients. We study the so-called Uvarov and Christoffel modifications
obtained by adding to the moment functional a finite set of mass points, or by
multiplying it times a polynomial of total degree 2, respectively. Orthogonal
polynomials associated with modified moment functionals will be studied, as
well as the impact of the modification in useful properties of the orthogonal
polynomials. Finally, some illustrative examples will be given
Phase diagram of an extended Agassi model
Background: The Agassi model is an extension of the Lipkin-Meshkov-Glick
model that incorporates the pairing interaction. It is a schematic model that
describes the interplay between particle-hole and pair correlations. It was
proposed in the 1960's by D. Agassi as a model to simulate the properties of
the quadrupole plus pairing model.
Purpose: The aim of this work is to extend a previous study by Davis and
Heiss generalizing the Agassi model and analyze in detail the phase diagram of
the model as well as the different regions with coexistence of several phases.
Method: We solve the model Hamiltonian through the Hartree-Fock-Bogoliubov
(HFB) approximation, introducing two variational parameters that play the role
of order parameters. We also compare the HFB calculations with the exact ones.
Results: We obtain the phase diagram of the model and classify the order of
the different quantum phase transitions appearing in the diagram. The phase
diagram presents broad regions where several phases, up to three, coexist.
Moreover, there is also a line and a point where four and five phases are
degenerated, respectively.
Conclusions: The phase diagram of the extended Agassi model presents a rich
variety of phases. Phase coexistence is present in extended areas of the
parameter space. The model could be an important tool for benchmarking novel
many-body approximations.Comment: Accepted for publication in PR
An extended Agassi model: algebraic structure, phase diagram, and large size limit
The Agassi model is a schematic two-level model that involves pairing and
monopole-monopole interactions. It is, therefore, an extension of the well
known Lipkin-Meshkov-Glick (LMG) model. In this paper we review the algebraic
formulation of an extension of the Agassi model as well as its bosonic
realization through the Schwinger representation. Moreover, a mean-field
approximation for the model is presented and its phase diagram discussed.
Finally, a analysis, with proportional to the degeneracy of each
level, is worked out to obtain the thermodynamic limit of the ground state
energy and some order parameters from the exact Hamiltonian diagonalization for
finite.Comment: Accepted in Physica Scripta. Focus on SSNET 201
Density, structure and dynamics of water: the effect of Van der Waals interactions
It is known that ab initio molecular dynamics (AIMD) simulations of liquid
water, based on the generalized gradient approximation (GGA) to density
functional theory (DFT), yield structural and diffusive properties in
reasonable agreement with experiment only if artificially high temperatures are
used in the simulations. The equilibrium density, at normal conditions, of DFT
water has been recently shown by Schmidt et al. [J. Phys. chem. B, 113, 11959
(2009)] to be underestimated by different GGA functionals for exchange and
correlation, and corrected by the addition of interatomic pair potentials to
describe van derWaals (vdW) interactions. In this contribution we present a
DFTAIMD study of liquid water using several GGA functionals as well as the van
der Waals density functional (vdW-DF) of Dion et al. [Phys. Rev. Lett. 92,
246401(2004)]. As expected, we find that the density of water is grossly
underestimated by GGA functionals. When a vdW-DF is used, the density improves
drastically and the experimental diffusivity is reproduced without the need of
thermal corrections. We analyze the origin of the density differences between
all the functionals. We show that the vdW-DF increases the population of
non-H-bonded interstitial sites, at distances between the first and second
coordination shells. However, it excessively weakens the H-bond network,
collapsing the second coordination shell. This structural problem is partially
associated to the choice of GGA exchange in the vdW-DF. We show that a
different choice for the exchange functional is enough to achieve an overall
improvement both in structure and diffusivity.Comment: 11 pages, 9 figures, submitted. Revised versio
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