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.
Highlights
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
We 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
We are required to evolve the full non-linear gravitational dynamics of the EinsteinMaxwell theory coupled with the complex scalar field in asymptotic AdS space with the initial perturbations somewhat different from those used in the previous studies on the nonequilibrium condensation process or the quench process of the ground states of holographic superconductors [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33], or the holographic isotropization of non-Abelian plasma [34, 35]
Summary
We consider the holographic s-wave superconductor described by the Einstein-Maxwellcomplex scalar field theory with a negative cosmological constant. The asymptotic behaviors of the fields provide the boundary conditions which are used to solve the evolution equations. The equations of motion for the redefined fields can be derived from eq (2.10)–(2.16) and the corresponding boundary conditions at the AdS boundary can be obtained from the asymptotic expansions (2.18). With these in hand, we can evolve the whole system from arbitrary initial data and extract the time dependent behaviors of the scalar field, the superconducting order parameter, and the geometry of the background hairy black hole
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