Quantum phase transitions in algebraic and collective models of nuclear structure

Quantum Phase Transitions arising in algebraic and collective models of nuclear structure are reviewed. The concept of quantum phases and phase transitions is described as well as those of critical point symmetries and quasi-dynamical symmetries. Algebraic and collective models are compared and the connections between them are explored. Differences between even–even and odd–even systems are discussed. Several applications of critical point symmetries are given in both the even and odd sectors. Details of the spherical to γ−unstable and spherical to axially deformed quantum shape phase transition are covered in some detail as well as other transitions and alternative approaches.