Exponentially Accelerated Approach to Stationarity in Markovian Open Quantum Systems through the Mpemba Effect

Ergodicity-breaking and slow relaxation are intriguing aspects of nonequilibrium dynamics both in classical quantum settings. These phenomena typically associated with phase transitions, e.g. the emergence metastable regimes near a first-order transition or scaling vicinity critical points. Despite being fundamental interest divergent time scales hindrance when trying to explore steady-state properties. Here we show that Markovian open systems can be accelerated exponentially by devising an optimal unitary transformation is applied system immediately before actual dynamics. This initial "rotation" engineered such way state becomes orthogonal slowest decaying dynamical mode. We illustrate our idea -- which inspired so-called Mpemba effect, i.e., water freezing faster initially heated up showing how achieve exponential speed-up convergence stationarity Dicke models, avoid all-to-all interacting spin system.