Title: Scaling of non-adiabaticity in disordered quench of quantum Rabi model close to phase transition

Abstract: Dynamics of a system exhibits non-adiabaticity even for slow quenches near critical points. We analyze the response to disorder in quenches on a non-adiabaticity quantifier for the quantum Rabi model, which possesses a phase transition between normal and superradiant phases. We consider a disordered version of a quench in the Rabi model, in which the system residing in the ground state of an initial Hamiltonian of the normal phase is quenched to the final Hamiltonian corresponding to the critical point. The disorder is inserted either in the total time the quench or in the quench parameter itself. We solve the corresponding quantum dynamics numerically, and find that the non-adiabatic effects are unaffected by the presence of disorder in the total time of the quench. This result is then independently confirmed by the application of adiabatic perturbation theory and the Kibble- Zurek mechanism. For the disorder in the quench parameter, we report a monotonic increase in the adiabaticity with the strength of the disorder. Lastly, we consider a quench where the final Hamiltonian is chosen as the average over the disordered final Hamiltonians, and show that this quench is more adiabatic than the average of the quenches with the disorder in final Hamiltonian.