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2009 Student HPC Competition Title: Of Nuclear Shapes in Systems with Random Interactions By: Volha Abramkina

Abstract

Application of random matrix theory (RMT) to physics originated in nuclear physics and was inspired by Wigner back in the 1950s [3]. The idea behind the RMT approach is a replacement of the actual Hamiltonian matrix by an ensemble of random matrices with the same global properties as the original Hamiltonian, looking for manifestation of generic features. A two-body random ensemble, employed in our calculations, bridges random matrix approach and one of the most successful nuclear models, shell model. The imposed symmetries such as conservation of angular momentum, isospin, and parity together with complex many-body dynamics generate features in the low-lying spectra similar to those of real nuclei. In our work we investigate formation of the mean eld in ensembles with random interactions with a particular focus on shape collectivities.

Such a statistical approach demands a diagonalization of a large number of sparse matrices. With each matrices being lled independently, parallelization of a code is extremely simple. Using HPC was a great help, it allowed to collect a large number of data and made possible to study phenomena not previously investigated because of computational limitations.