Nonequilibrium dynamical transition process between excited states of holographic superconductors

TL;DR

This paper investigates the non-equilibrium dynamical transitions between excited states of holographic superconductors using Einstein-Maxwell-scalar theory, revealing how systems evolve through metastable states to reach the ground state.

Contribution

It introduces a detailed analysis of the transition dynamics between excited states in holographic superconductors, including the role of metastable intermediate states and the evolution landscape.

Findings

Intermediate states are metastable and evolve towards the ground state.

System undergoes a cascade of transitions between different excited states.

Global landscape view characterizes the transition pathways and state weights.

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.