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The Mixed Phase of Charged AdS Black holes

We study the mixed phase of charged AdS black hole and radiation when the total energy is fixed below the threshold to produce a stable charged black hole branch. The coexistence conditions for the charged AdS black hole and radiation are derived for the generic case when radiation particles carry charge. The phase diagram of the mixed phase is demonstrated for both fixed potential and charge ensemble. In the dual gauge picture, they correspond to the mixed phase of quark-gluon plasma~(QGP) and hadron gas in the fixed chemical potential and density ensemble respectively. In the nuclei and heavy ion collisions at intermediate energies, the mixed phase of exotic QGP and hadron gas could be produced. The mixed phase will condensate and evaporate into the hadron gas as the fireball expands.