Quantum-Mechanical Nonperturbative Response of Driven Chaotic Mesoscopic Systems

Consider a time-dependent Hamiltonian $H(Q,P;x(t))$ with periodic driving x(t)0ex0ex=0ex0exAsin(Ωt). It is assumed that the classical dynamics is chaotic, and that its power spectrum extends over some frequency range |ω|<ωcl. Both classical and quantum-mechanical (QM) linear response theory (LRT) predict a relatively large response for Ω<ωcl, 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>Aₚᵣₜ, where Aₚᵣₜ∝, the system may have a relatively strong response for Ω>ωcl due to QM nonperturbative effect.