Quantum-Mechanical Non-Perturbative Response of Driven Chaotic Mesoscopic Systems

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