The admissible KMS bundles on classifiable C^⁎-algebras

Abstract Given any unital, finite, classifiable $\mathrm{C}^*$ -algebra A with real rank zero and any compact simplex bundle with the fibre at zero being homeomorphic to the space of tracial states on A , we show that there exists a flow on A realizing this simplex. Moreover, we show that given any unital $\mathrm{UCT}$ Kirchberg algebra A and any proper simplex bundle with empty fibre at zero, there exists a flow on A realizing this simplex.