Quantum-mechanical nonperturbative response of driven chaotic mesoscopic systems

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