The Dynamical Stability Of Holographic Superfluid Phase Transitions

Anti-de Sitter/Conformal field theory(AdS/CFT)correspondence provides a very useful tool for studying strongly coupled quantum filed theory,and has achieved many excellent results in applications such as Quantum field theory(QFT)and condensed matter physics.The holographic superconductor model is one of the most successful applications of AdS/CFT correspondence to condensed matter physics,and its proposal provides a new path for people to study strong coupling high-temperature superconductor.In addition to typical 2nd order phase transition,complex phase transition models such as 1st order phase transition,0th order phase transition,and reentrant phase transition can also be realized in the holographic superconductor model.This article mainly introduces the author’s research on use of self-interaction potential terms to realize various types of phase transition behaviors,including 2nd order,1st order,0th order and cave of wind(COW),and studies the dynamical stability problems of these transitions.We first introduce the holographic superconductor model with two self-interaction terms λ|ψ|4 and τ|ψ|6.By changing the values of parameters λ and τ,0th,1st and 2nd order and cave of wind phase transition can be realized in the probe limit.By systematically studying the regulatory effects of λ and τ parameters on phase transition behavior,we provide the parameter ranges for various types of phase transitions.By calculating the thermodynamical potential of the equilibrium state,the landscape behavior of the system can be guessed,and qualitative predications of the system’s can be made.In the holographic superconductor model,the dynamic stability can be obtained by calculating the quasi-normal modes of the gravitational system.We specifically calculated the quasi-normal modes for various types of phase transitions and compared them with the results of the landscape analysis.We found that the results of the quasi-normal modes under homogeneous perturbations(k=0)perfectly coincide with the results of the canonical ensemble.landscape analysis.Specifically,for 0th order phase transition,we found that both landscape analysis and quasi-normal modes calculation indicate instability,and therefore,the 0th order phase transition cannot occur in reality.We also calculated the quasi-normal modes under inhomogeneous perturbations(k≠0)and found that the unstable region is larger than that given by homogeneous perturbations,and the dividing point between the stable region and unstable region of inhomogeneous perturbations coincides with the turning point of the condensation curve of grand canonical ensemble.As an example,we detailed the relationship between stability under homogeneous and inhomogeneous perturbations and two different ensembles for a 1st order phase transition.