Quantum-Mechanical Nonperturbative Response of Driven Chaotic Mesoscopic Systems

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