# Quantum-Mechanical Non-Perturbative Response and the Limitations of Linear Response Theory Academic Article

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• Overview
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• 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.