Two-level interacting boson models beyond the mean field

The phase diagram of two-level boson Hamiltonians, including the Interacting Boson Model (IBM), is studied beyond the standard mean field approximation using the Holstein-Primakoff mapping. The limitations of the usual intrinsic state (mean field) formalism concerning finite-size effects are pointed out. The analytic results are compared to numerics obtained from exact diagonalizations. Excitation energies and occupation numbers are studied in different model space regions (Casten triangle for IBM) and especially at the critical points.Comment: 14 pages, 13 figure

Finite-size scaling exponents in the interacting boson model

We investigate the finite-size scaling exponents for the critical point at the shape phase transition from U(5) (spherical) to O(6) (deformed $\gamma$-unstable) dynamical symmetries of the Interacting Boson Model, making use of the Holstein-Primakoff boson expansion and the continuous unitary transformation technique. We compute exactly the leading order correction to the ground state energy, the gap, the expectation value of the $d$-boson number in the ground state and the $E2$ transition probability from the ground state to the first excited state, and determine the corresponding finite-size scaling exponents.Comment: 4 pages, 3 figures, published versio

Assessment of lot shape in business park design

Planning and developing a business park is a complex task, whichdemands integration across various fields of design and knowledge. The first choice to be made in the design process is relate to the zoning process and the definition of the lot layout and landscape. These first decisions will constrain all subsequent decisions concerning utilities, facilities and amenities. For this reason, the assessment of those issues is crucial for the perception of the overall quality of the business park design. The main goal of this work is to present a simple indicator which can assess the lot shape in order to optimize the building form and costs, the use of its open areas, the layout and the economic spacing of roads and the service routes. The indicator lot shape evaluatesthe performance of the lot design solutions according to the concept of compactness

Air quality in the North of Portugal.

Air pollution in urban areas is a major topic of concern in many large cities. In Portugal, a monitoring network measures relevant pollutants for zones and agglomerations. The measurements of two zones and four agglomerations located in the North of Portugal were used to diagnose the pollution level and the relative air quality. It was found that, despite the need for densification of the network of monitoring stations, ozone (O3) and particulate matter (PM10) reach significant levels in a number of days during the year. Some recommendations are made regarding the inclusion of planning and mitigation actions in the Regional and Municipal Master Plan

Relationship between X(5)-models and the interacting boson model

The connections between the X(5)-models (the original X(5) using an infinite square well, X(5)-$\beta^8$, X(5)-$\beta^6$, X(5)-$\beta^4$, and X(5)-$\beta^2$), based on particular solutions of the geometrical Bohr Hamiltonian with harmonic potential in the $\gamma$ degree of freedom, and the interacting boson model (IBM) are explored. This work is the natural extension of the work presented in [1] for the E(5)-models. For that purpose, a quite general one- and two-body IBM Hamiltonian is used and a numerical fit to the different X(5)-models energies is performed, later on the obtained wave functions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce well the results for energies and B(E2) transition rates obtained with all these X(5)-models, although the agreement is not so impressive as for the E(5)-models. From the fitted IBM parameters the corresponding energy surface can be extracted and it is obtained that, surprisingly, only the X(5) case corresponds in the moderate large N limit to an energy surface very close to the one expected for a critical point, while the rest of models seat a little farther.Comment: Accepted in Physical Review

The β4\beta^4 potential at the U(5)-O(6) critical point of the Interacting Boson Model

Exact numerical results of the interacting boson model Hamiltonian along the integrable line from U(5) to O(6) are obtained by diagonalization within boson seniority subspaces. The matrix Hamiltonian reduces to a block tridiagonal form which can be diagonalized for large number of bosons. We present results for the low energy spectrum and the transition probabilities for systems up to 10000 bosons, which confirm that at the critical point the system is equally well described by the Bohr Hamiltonian with a $\beta^4$ potential.Comment: To be published in PR

On the relation between E(5)−E(5)-models and the interacting boson model

The connections between the $E(5)-$models (the original E(5) using an infinite square well, $E(5)-\beta^4$, $E(5)-\beta^6$ and $E(5)-\beta^8$), based on particular solutions of the geometrical Bohr Hamiltonian with $\gamma$-unstable potentials, and the interacting boson model (IBM) are explored. For that purpose, the general IBM Hamiltonian for the $U(5)-O(6)$ transition line is used and a numerical fit to the different $E(5)-$models energies is performed, later on the obtained wavefunctions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce very well all these $E(5)-$models. The agreement is the best for $E(5)-\beta^4$ and reduces when passing through $E(5)-\beta^6$, $E(5)-\beta^8$ and E(5), where the worst agreement is obtained (although still very good for a restricted set of lowest lying states). The fitted IBM Hamiltonians correspond to energy surfaces close to those expected for the critical point. A phenomenon similar to the quasidynamical symmetry is observed

Integrability of Lie systems and some of its applications in physics

The geometric theory of Lie systems will be used to establish integrability conditions for several systems of differential equations, in particular Riccati equations and Ermakov systems. Many different integrability criteria in the literature will be analyzed from this new perspective and some applications in physics will be given.Comment: 16 page