Empirical signatures of quantum phasetransitions and universal properties of criticalpoint descriptions and dynamical symmetries

摘要

Recently, a new signature for quantum phase transitional regions has been discussed.This signature, based on degeneracies of yrast and intrinsic excitations, can distinguish first andsecond order phase transitions, and is valid not only at or near the analytic critical points describedby X(5) and E(5), but along the phase transitional line connecting them as well. In addition, a studyof a number of recent analytic solutions to the Bohr Hamiltonian and of the dynamical symmetriesof the IBA Hamiltonian has revealed a set of extremely simple and general analytic formulas thatdescribe the energies of 0~+ states. For the case of flat-bottomed geometrical potentials, the formuladepends solely on the number of relevant dimensions. For the IBA (large boson number limit) asingle formula describes all three dynamical symmetries.