Phase structure and quasinormal modes of a charged AdS dilaton black hole

We investigate the phase structure of a charged AdS dilaton black hole in the extended phase space which takes the cosmological constant, i.e. the AdS-Lambda parameter, as pressures. Through both thermal ensemble and quasinormal mode analysis, we find that stable phase of the black hole with nontrivial dilaton profiles always exists for both large and small couplings when the AdS-Lambda is considered as dynamical degrees of freedom. This forms somewhat of a contrast with previous works. Our results provide new examples for the parallelism or equivalences between thermal ensemble methods and dynamic perturbation analysis for black hole phase structures.