Arezky H. Rodríguez

Tsallis Entropy and the transition to scaling in fragmentation

By using the maximum entropy principle with Tsallis entropy we obtain a fragment size distribution function which undergoes a transition to scaling. This distribution function reduces to those obtained by other authors using Shannon entropy. The treatment is easily generalisable to any process of fractioning with suitable constraints.

Excited states in the infinite quantum lens potential: conformal mapping and moment quantization methods

The conformal mapping method (CMM) and the eigenvalue moment method (EMM) are employed to study the eigenvalue problem defined by a free particle in a quantum lens geometry. The characteristics of the spectrum and the corresponding spatial properties of wavefunctions are studied for varying symmetry quantization numbers and lens parameter values. It is shown that the states belong to two independent Hilbert subspaces corresponding to even and odd azimuthal, m, quantum numbers. The CMM analysis is used to reduce the Dirichlet problem for the Helmholtzs equation into a 2D problem defined by a region with semicircular geometry. This approach allows one to obtain explicit analytical solutions in terms of the lens geometry. In the case of small geometry deformations (relative to the semicircular case), the solutions can be found by a perturbative method. The exact and approximate solutions are compared for different values of the lens parameters. We compare these results with those derived through the EMM approach, which, although more computationally expensive, can yield converging lower and upper bounds. The particular formulation developed here differs significantly from an earlier application of EMM to the ground state case (within each symmetry class). Accordingly, we develop the new formulation and apply it to a limited number of states in order to confirm the results derived by the other, aforementioned, methods.

Dimensional crossover in fragmentation

Experiments in which thick clay plates and glass rods are fractured have revealed different behavior of fragment mass distribution function in the small and large fragment regions. In this paper we explain this behavior using non-extensive Tsallis statistics and show how the crossover between the two regions is caused by the change in the fragments’ dimensionality during the fracture process. We obtain a physical criterion for the position of this crossover and an expression for the change in the power-law exponent between the small and large fragment regions. These predictions are in good agreement with the experiments on thick clay plates.

Electroreflectance spectroscopy in self-assembled quantum dots: lens symmetry

Modulated electroreflectance spectroscopy

Some electronic and optical properties of self-assembled quantum dots: asymmetries in a lens domain

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Quantum lens in an external electric field: Anomalous photoluminescence behavior

of semiconductor self-assembled quantum dots is investigated. The structure is modeled as dots with lens shape geometry and circular cross section. A microscopic description of the electroreflectance spectrum and optical response in terms of an external electric field (

AC-Stark effect in a semi-spherical quantum dot

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Induced Monoculture In Axelrod Model With Clever Mass Media

) and lens geometry have been considered. The field and lens symmetry dependence of all experimental parameters involved in the

Stark Effect in Self‐Assembled Quantum Dots with Lens Shape

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Reply to Comment on ‘Excited states in the infinite quantum lens potential: conformal mapping and moment quantization methods’

spectrum have been considered. Using the effective mass formalism the energies and the electronic states as a function of