Quantum-Mechanical Nonperturbative Response of Driven Chaotic Mesoscopic Systems

Consider a time-dependent Hamiltonian $H(Q,P;x(t\left)\right)$ with periodic driving $x\left(t\right)=A\sin \left(\Omega t\right)$. It is assumed that the classical dynamics is chaotic, and that its power spectrum extends over some frequency range $|\omega |<{\omega }_{\mathrm{cl}}$. Both classical and quantum-mechanical (QM) linear response theory (LRT) predict a relatively large response for $\Omega <{\omega }_{\mathrm{cl}}$, 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 $A>\mathrm{}{A}_{\mathrm{prt}}$, where $A_{\mathrm{prt}}\propto ħ$, the system may have a relatively strong response for $\Omega >{\omega }_{\mathrm{cl}}$ due to QM nonperturbative effect.