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Quench Dynamics and Emergence of Phase Separation in Two-Component Atomic Bose Gases at Zero Temperature and above the BEC Critical Temperature

We study the dynamics of two-component atomic Bose gases initially in a mixture encountering a sudden quench of the inter-species interactions. The dynamics above the critical temperature $T_c$ is studied using a leading order large-N approximation that predicted a phase transition from mixing to phase separation as a function of the inter-species coupling. Here we explore the dynamics of this phase transition following a quench and compare our results to those found at zero temperature using the time-dependent Gross-Pitaevskii equations which ignore quantum and thermal fluctuations. In the regime above $T_c$ where no condensate is present, however, the time evolution of the densities following the quench exhibits features similar to that found at zero temperature where only the condensates contribute to the densities. When the inter-species interaction jumps above the critical value, we observe dynamical transitions from a homogeneous mixture to a phase-separated structure for both cases. Our simulations suggest that at temperatures above $T_c$ where no condensate is present this dynamical transition should still be observable in experiments.