The Emergence of Collective Phenomena in Systems with Random Interactions

• Other Authors: Abramkina, Volha (authoraut)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Physics
• Online Access: http://purl.flvc.org/fsu/fd/FSU_migr_etd-0104

Emergent phenomena are one of the most profound topics in modern science, addressing the ways that collectivities and complex patterns appear due to multiplicity of components and simple interactions. Ensembles of random Hamiltonians allow one to explore emergent phenomena in a statistical way. In this work we adopt a shell model approach with a two-body interaction Hamiltonian. The sets of the two-body interaction strengths are selected at random, resulting in the two-body random ensemble (TBRE). Symmetries such as angular momentum, isospin, and parity entangled with complex many-body dynamics result in surprising order discovered in the spectrum of low-lying excitations. The statistical patterns exhibited in the TBRE are remarkably similar to those observed in real nuclei. Signs of almost every collective feature seen in nuclei, namely, pairing superconductivity, deformation, and vibration, have been observed in random ensembles. In what follows a systematic investigation of nuclear shape collectivities in random ensembles is conducted. The development of the mean field, its geometry, multipole collectivities and their dependence on the underlying two-body interaction are explored. Apart from the role of static symmetries such as SU(2) angular momentum and isospin groups, the emergence of dynamical symmetries including the seniority SU(2), rotational symmetry, as well as the Elliot SU(3) is shown to be an important precursor for the existence of geometric collectivities. === A Thesis submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctorate of Philosophy in Physics. === Degree Awarded: Summer Semester, 2011. === Date of Defense: May 17, 2011. === Shell Model, Quadrupole Collectivity, Random Interactions === Includes bibliographical references. === Alexander Volya, Professor Directing Thesis; Giray Okten, University Representative; Simon Capstick, Committee Member; Grigory Rogachev, Committee Member; Per Arne Rikvold, Committee Member.