### abstract

- Consider a time-dependent Hamiltonian $H(Q,P;x(t))$ with periodic driving $x(t)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}A\mathrm{sin}(\ensuremath{\Omega}t)$. It is assumed that the classical dynamics is chaotic, and that its power spectrum extends over some frequency range $|\ensuremath{\omega}|<{\ensuremath{\omega}}_{\mathrm{cl}}$. Both classical and quantum-mechanical (QM) linear response theory (LRT) predict a relatively large response for $\ensuremath{\Omega}<{\ensuremath{\omega}}_{\mathrm{cl}}$, and a relatively small response otherwise, independent of the driving amplitude $A$. We define a nonperturbative regime in the $(\ensuremath{\Omega},A)$ space, where LRT fails, and demonstrate this failure numerically. For $A>{A}_{\mathrm{prt}}$, where ${A}_{\mathrm{prt}}\ensuremath{\propto}\ensuremath{\Elzxh}$, the system may have a relatively strong response for $\ensuremath{\Omega}>{\ensuremath{\omega}}_{\mathrm{cl}}$ due to QM nonperturbative effect.