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We consider quantum spin systems in which a central spin is singled out andinteracts nonlocally with all other bath spins. These systems show complexstationary phenomena and very distinct dynamical regimes which, despite thecollective nature of the interaction, are still largely not understood. Here,we derive exact analytical results on the emergent dynamical behavior of openquantum central spin systems. The latter crucially depends on the scaling ofthe interaction strength with the bath size. For scalings with the inversesquare root of the bath size (typical of one-to-many interactions), the systembehaves, in the thermodynamic limit, as an open quantum (spin-boson)Jaynes-Cummings model, whose bosonic mode encodes the quantum fluctuations ofthe bath spins. In this regime, non-Gaussian correlations are dynamicallygenerated and persist at stationarity. For scalings with the inverse bath size,the emergent dynamics is instead of mean-field type. Our work provides afundamental understanding of the different dynamical regimes of central spinsystems and opens up the possibility of efficiently exploring theirnonequilibrium behavior. It further highlights a non-mean-field theory that maybecome relevant for open quantum many-body systems in general.

Non-Gaussian dynamics of quantum fluctuations and mean-field limit in open quantum central spin systems