Consider a time-dependent Hamiltonian $H(Q,P;x(t))$ with periodic driving $x(t)=A\sin(\Omega t)$. It is assumed that the classical dynamics is chaotic, and that its power-spectrum extends over some frequency range $|\omega|<\omega_{ cl}$. 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, independently of the driving amplitude $A$. We define a non-perturbative regime in the $(\Omega,A)$ space, where LRT fails, and demonstrate this failure numerically. For $A>A_{ prt}$, where $A_{ prt}\propto\hbar$, the system may have a relatively strong response for $\Omega>\omega_{ cl}$, and the shape of the response function becomes $A$ dependent.
Categories: cond-mat