Higher spin Richardson-Gaudin model with time-dependent coupling: Exact dynamics

We determine the exact asymptotic many-body wavefunction of a spin-$s$ Richardson-Gaudin model with a coupling inversely proportional to time, for time evolution starting from the ground state at $t=0^{+}$ and for arbitrary $s$. Contrary to common belief, the resulting wavefunction cannot be derived from the spin-$1\mathrm{/}2$ case by merging spins, but instead requires independent treatment for each spin size. The steady state is non-thermal and, in contrast to the spin-$1\mathrm{/}2$ case, does not conform to a natural Generalized Gibbs Ensemble. We show that mean-field theory is exact for any product of a finite number of spin operators on different sites. We discuss how these findings can be probed in cavity QED and trapped ion experiments.