Nonequilibrium dynamical transition process between excited states of holographic superconductors

Abstract

We study the dynamics of the holographic s-wave superconductors described by the Einstein-Maxwell-complex scalar field theory with a negative cosmological constant. If the eigenfunction of the linearized equation of motion of the scalar field in the planar RNAdS black hole background is chosen as the initial data, the bulk system will evolve to the intermediate state that corresponds to the excited state superconductor on the boundary. The process can be regarded as the non-equilibrium condensation process of the excited state of holographic superconductor. When the linear superposition of the eigenfunctions is chosen as the initial data, the system will go through a series of the intermediate states corresponding to different overtone numbers, which can be regarded as the dynamical transition process between the excited states of holographic superconductor. Because the intermediate states are metastable, the bulk system eventually evolves to the stationary state that corresponds the ground state of the holographic superconductor. We also provide a global and physical picture of the evolution dynamics of the black hole and the corresponding superconducting phase transition from the funneled landscape view, quantifying the weights of the states and characterizing the transitions and cascades towards the ground state.

Excited states of holographic superconductors with backreaction

“…Thus, excited states are usually unstable or metastable. In [40], the authors found that the system will go through a series of the intermediate states corresponding to different excited states, and intermediate states can keep stable for a long time. Because the intermediate states are metastable, the system will eventually evolve to the ground state of holographic superconductor.…”

On the triplet of holographic phase transition

“…All foregoing holographic superconductors are in the ground state. In recent years there exhibits a new trend studying holographic superconductors, in which the ground state arises together with other excited states [11], namely, the number of excited states depends on the value of chemical potential µ. For example, for µ = 4.064 there is only the ground states while µ = 35 there appear six excited states.…”

Spontaneously translational symmetry breaking in the excited states of holographic superconductor

“…However, we have to mention that our method of introducing translational symmetry breaking was based on excited states, where we have not found solutions in ground state with such broken symmetry. Even though, the excited states might represent new bound states of interactions between quasi-particles excited above the ground state, as studied in [43], were found to be meta-stable; given considerable time, these excited states would evolve back to the ground state. Therefore, before recovering real experiments or finding new phenomenon via excited states, it is necessary to find solutions in these states that can be stable.…”

“…Recent studies in [40,41] have presented a family of solutions in excited state where the profiles of scalar field solutions have multiple nodes along the holographic direction, while they also show additional peaks and poles in optical conductivity. Semianalytical studies toward the excited state are presented in [42], while nonequilibrium process of these states have been studied in detail in [43]. Moreover, they have been generalized to the framework of dRGT massive gravity model in [44] as well.…”