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arXiv:nucl-th/0310031 · Symmetries in Nuclear Structure

INTEGRABILITY AND QUANTUM PHASE TRANSITIONS IN INTERACTING BOSON MODELS

J. Dukelsky, J. M. Arias, J. E. García-Ramos, Stuart Pittel

Published Apr 1, 2004• 0 citations
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Abstract

The exact solution of the boson pairing hamiltonian given by Richardson in the sixties is used to study the phenomena of level crossings and quantum phase transitions in the integrable regions of the sd and sdg interacting boson models.
DOI
10.1142/9789812702760_0019

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The exact solution of the BCS pairing Hamiltonian was found by Richardson in 1963. While little attention was paid to this exactly solvable model in the remainder of the 20th century, there was a burst of work at the beginning of this century focusing on its applications in different areas of quantum physics. We review the history of this exact solution and discuss recent developments related to the Richardson-Gaudin class of integrable models, focussing on the role of these various models in nuclear physics.