44 research outputs found
Criticality in the configuration-mixed interacting boson model : (1) mixing
The case of U(5)-- mixing in the
configuration-mixed Interacting Boson Model is studied in its mean-field
approximation. Phase diagrams with analytical and numerical solutions are
constructed and discussed. Indications for first-order and second-order shape
phase transitions can be obtained from binding energies and from critical
exponents, respectively
The quadrupole collective model from a Cartan-Weyl perspective
The matrix elements of the quadrupole variables and canonic conjugate
momenta, emerging from collective nuclear models are calculated within a
basis. Using a harmonic oscillator implementation of the
SU(1,1) degree of freedom, it can be shown that the matrix elements of the
quadrupole phonon creation and annihilation operators can be calculated in a
pure algebraic way, making use of an intermediate state method.Comment: Special issue of journal of physics for the QTS5 conferenc
A theoretical description of energy spectra and two-neutron separation energies for neutron-rich zirconium isotopes
Very recently the atomic masses of neutron-rich Zr isotopes, from Zr
to Zr, have been measured with high precision. Using a schematic
Interacting Boson Model (IBM) Hamiltonian, the evolution from spherical to
deformed shapes along the chain of Zr isotopes, describing at the same time the
excitation energies as well as the two-neutron separation energies, can be
rather well reproduced. The interplay between phase transitions and
configuration mixing of intruder excitations in this mass region is succinctly
addressed.Comment: Accepted in European Journal of Physics
A primal-dual semidefinite programming algorithm tailored to the variational determination of the two-body density matrix
The quantum many-body problem can be rephrased as a variational determination
of the two-body reduced density matrix, subject to a set of N-representability
constraints. The mathematical problem has the form of a semidefinite program.
We adapt a standard primal-dual interior point algorithm in order to exploit
the specific structure of the physical problem. In particular the matrix-vector
product can be calculated very efficiently. We have applied the proposed
algorithm to a pairing-type Hamiltonian and studied the computational aspects
of the method. The standard N-representability conditions perform very well for
this problem.Comment: 24 pages, 5 figures, submitted to the Journal of Computational
Physic
Solution of the Bohr hamiltonian for soft triaxial nuclei
The Bohr-Mottelson model is solved for a generic soft triaxial nucleus,
separating the Bohr hamiltonian exactly and using a number of different
model-potentials: a displaced harmonic oscillator in , which is solved
with an approximated algebraic technique, and Coulomb/Kratzer,
harmonic/Davidson and infinite square well potentials in , which are
solved exactly. In each case we derive analytic expressions for the
eigenenergies which are then used to calculate energy spectra.
Here we study the chain of osmium isotopes and we compare our results with
experimental information and previous calculations.Comment: 13 pages, 9 figure
A Birkhoff connection between quantum circuits and linear classical reversible circuits
Birkhoff's theorem tells how any doubly stochastic matrix can be decomposed as a weighted sum of permutation matrices. Similar theorems on unitary matrices reveal a connection between quantum circuits and linear classical reversible circuits. It triggers the question whether a quantum computer can be regarded as a superposition of classical reversible computers
Quadrupole collective variables in the natural Cartan-Weyl basis
The matrix elements of the quadrupole collective variables, emerging from
collective nuclear models, are calculated in the natural Cartan-Weyl basis of
O(5) which is a subgroup of a covering structure. Making
use of an intermediate set method, explicit expressions of the matrix elements
are obtained in a pure algebraic way, fixing the -rotational structure
of collective quadrupole models.Comment: submitted to Journal of Physics
Soft triaxial rotor in the vicinity of and its extensions
The collective Bohr hamiltonian is solved for the soft triaxial rotor around
with a displaced harmonic oscillator potential in and
a Kratzer-like potential in . The properties of the spectrum are
outlined and a generalization for the more general triaxial case with
is proposed.Comment: Contribution to ENAM '04 conference. 2 pages, 2 figur