67 research outputs found
Geometric Duality for Convex Vector Optimization Problems
Geometric duality theory for multiple objective linear programming problems
turned out to be very useful for the development of efficient algorithms to
generate or approximate the whole set of nondominated points in the outcome
space. This article extends the geometric duality theory to convex vector
optimization problems.Comment: 21 page
Configuration mixing in Pb : band structure and electromagnetic properties
In the present paper, we carry out a detailed analysis of the presence and
mixing of various families of collective bands in Pb. Making use of the
interacting boson model, we construct a particular intermediate basis that can
be associated with the unperturbed bands used in more phenomenological studies.
We use the E2 decay to construct a set of collective bands and discuss in
detail the B(E2)-values. We also perform an analysis of these theoretical
results (Q, B(E2)) to deduce an intrinsic quadrupole moment and the associated
quadrupole deformation parameter, using an axially deformed rotor model.Comment: submitted to pr
Configuration mixing in the neutron-deficient Pb isotopes
In this article we report the results of detailed interacting boson model
calculations with configuration mixing for the neutron-deficient Pb isotopes.
Calculated energy levels and values for Pb are discussed
and some care is suggested concerning the current classification on the basis
of level systematics of the and states in Pb.
Furthermore, quadrupole deformations are extracted for Pb and the
mixing between the different families (0p-0h, 2p-2h, and 4p-4h) is discussed in
detail. Finally, the experimental and the theoretical level systematics are
compared.Comment: to be published in Phys. Rev.
Markov Processes, Hurst Exponents, and Nonlinear Diffusion Equations with application to finance
We show by explicit closed form calculations that a Hurst exponent H that is
not 1/2 does not necessarily imply long time correlations like those found in
fractional Brownian motion. We construct a large set of scaling solutions of
Fokker-Planck partial differential equations where H is not 1/2. Thus Markov
processes, which by construction have no long time correlations, can have H not
equal to 1/2. If a Markov process scales with Hurst exponent H then it simply
means that the process has nonstationary increments. For the scaling solutions,
we show how to reduce the calculation of the probability density to a single
integration once the diffusion coefficient D(x,t) is specified. As an example,
we generate a class of student-t-like densities from the class of quadratic
diffusion coefficients. Notably, the Tsallis density is one member of that
large class. The Tsallis density is usually thought to result from a nonlinear
diffusion equation, but instead we explicitly show that it follows from a
Markov process generated by a linear Fokker-Planck equation, and therefore from
a corresponding Langevin equation. Having a Tsallis density with H not equal to
1/2 therefore does not imply dynamics with correlated signals, e.g., like those
of fractional Brownian motion. A short review of the requirements for
fractional Brownian motion is given for clarity, and we explain why the usual
simple argument that H unequal to 1/2 implies correlations fails for Markov
processes with scaling solutions. Finally, we discuss the question of scaling
of the full Green function g(x,t;x',t') of the Fokker-Planck pde.Comment: to appear in Physica
Phase transitions in the interacting boson model
A geometric analysis of the interacting boson model is performed. A
coherent-state is used in terms of three types of deformation: axial quadrupole
(), axial hexadecapole () and triaxial (). The
phase-transitional structure is established for a schematic hamiltonian
which is intermediate between four dynamical symmetries of U(15), namely the
spherical , the (prolate and oblate) deformed
and the -soft SO(15) limits. For realistic choices
of the hamiltonian parameters the resulting phase diagram has properties close
to what is obtained in the version of the model and, in particular, no
transition towards a stable triaxial shape is found.Comment: 19 pages, 5 figures, submitted to J. Phys.
Magnetic Dipole Sum Rules for Odd-Mass Nuclei
Sum rules for the total- and scissors-mode M1 strength in odd-A nuclei are
derived within the single-j interacting boson-fermion model. We discuss the
physical content and geometric interpretation of these sum rules and apply them
to ^{167}Er and ^{161}Dy. We find consistency with the former measurements but
not with the latter.Comment: 13 pages, Revtex, 1 figure, Phys. Rev. Lett. in pres
IBM-1 description of the fission products Ru
IBM-1} calculations for the fission products Ru have been
carried out. The even-even isotopes of Ru can be described as transitional
nuclei situated between the U(5) (spherical vibrator) and SO(6)
(-unstable rotor) symmetries of the Interacting Boson Model. At first,
a Hamiltonian with only one- and two-body terms has been used. Excitation
energies and (E2) ratios of gamma transitions have been calculated. A
satisfactory agreement has been obtained, with the exception of the odd-even
staggering in the quasi- bands of Ru. The observed pattern
is rather similar to the one for a rigid triaxial rotor. A calculation based on
a Hamiltonian with three-body terms was able to remove this discrepancy. The
relation between the IBM and the triaxial rotor model was also examined.Comment: 22 pages, 8 figure
Quantum phase transitions in the interacting boson model
This review is focused on various properties of quantum phase transitions
(QPTs) in the Interacting Boson Model (IBM) of nuclear structure. The model in
its infinite-size limit exhibits shape-phase transitions between spherical,
deformed prolate, and deformed oblate forms of the ground state. Finite-size
precursors of such behavior are verified by robust variations of nuclear
properties (nuclear masses, excitation energies, transition probabilities for
low lying levels) across the chart of nuclides. Simultaneously, the model
serves as a theoretical laboratory for studying diverse general features of
QPTs in interacting many-body systems, which differ in many respects from
lattice models of solid-state physics. We outline the most important fields of
the present interest: (a) The coexistence of first- and second-order phase
transitions supports studies related to the microscopic origin of the QPT
phenomena. (b) The competing quantum phases are characterized by specific
dynamical symmetries and novel symmetry related approaches are developed to
describe also the transitional dynamical domains. (c) In some parameter
regions, the QPT-like behavior can be ascribed also to individual excited
states, which is linked to the thermodynamic and classical descriptions of the
system. (d) The model and its phase structure can be extended in many
directions: by separating proton and neutron excitations, considering
odd-fermion degrees of freedom or different particle-hole configurations, by
including other types of bosons, higher order interactions, and by imposing
external rotation. All these aspects of IBM phase transitions are relevant in
the interpretation of experimental data and important for a fundamental
understanding of the QPT phenomenon.Comment: a review article, 71 pages, 18 figure
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