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

abstract

  • 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.

publication date

  • January 1, 2000