28,233 research outputs found
Accurate calculation of resonances in multiple-well oscillators
Quantum--mechanical multiple--well oscillators exhibit curious complex
eigenvalues that resemble resonances in models with continuum spectra. We
discuss a method for the accurate calculation of their real and imaginary
parts
Estimates for the Sobolev trace constant with critical exponent and applications
In this paper we find estimates for the optimal constant in the critical
Sobolev trace inequality S\|u\|^p_{L^{p_*}(\partial\Omega) \hookrightarrow
\|u\|^p_{W^{1,p}(\Omega)} that are independent of . This estimates
generalized those of [3] for general . Here is the
critical exponent for the immersion and is the space dimension. Then we
apply our results first to prove existence of positive solutions to a nonlinear
elliptic problem with a nonlinear boundary condition with critical growth on
the boundary, generalizing the results of [16]. Finally, we study an optimal
design problem with critical exponent.Comment: 22 pages, submitte
The Geography of Non-formal Manifolds
We show that there exist non-formal compact oriented manifolds of dimension
and with first Betti number if and only if and
, or and . Moreover, we present explicit
examples for each one of these cases.Comment: 8 pages, one reference update
Phase diagram of a polydisperse soft-spheres model for liquids and colloids
The phase diagram of soft spheres with size dispersion has been studied by
means of an optimized Monte Carlo algorithm which allows to equilibrate below
the kinetic glass transition for all sizes distribution. The system
ubiquitously undergoes a first order freezing transition. While for small size
dispersion the frozen phase has a crystalline structure, large density
inhomogeneities appear in the highly disperse systems. Studying the interplay
between the equilibrium phase diagram and the kinetic glass transition, we
argue that the experimentally found terminal polydispersity of colloids is a
purely kinetic phenomenon.Comment: Version to be published in Physical Review Letter
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
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
Separation and fractionation of order and disorder in highly polydisperse systems
Microcanonical Monte Carlo simulations of a polydisperse soft-spheres model
for liquids and colloids have been performed for very large polydispersity, in
the region where a phase-separation is known to occur when the system (or part
of it) solidifies. By studying samples of different sizes, from N=256 to N=864,
we focus on the nature of the two distinct coexisting phases. Measurements of
crystalline order in particles of different size reveal that the solid phase
segregates between a crystalline solid with cubic symmetry and a disordered
phase. This phenomenon is termed fractionation.Comment: 8 pages, 5 figure
Heavy mesons in the Quark Model
Since the discovery of the , the quark model was very successful in
describing the spectrum and properties of heavy mesons including only
components. However since 2003, with the discovery of the , many
states that can not be accommodated on the naive quark model have been
discovered, and they made unavoidable to include higher Fock components on the
heavy meson states. We will give an overview of the success of the quark model
for heavy mesons and point some of the states that are likely to be more
complicated structures such as meson-meson molecules.Comment: Contribution to the Proceedings of the 15th International Workshop on
Meson Physics - MESON201
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