Quantum-Mechanical Non-Perturbative Response of Driven Chaotic Mesoscopic Systems

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 $A_{prt}\propto \hslash$, the system may have a relatively strong response for $\Omega >{\omega }_{cl}$, and the shape of the response function becomes $A$ dependent.

4 pages, 2 figures, revised version with much better introduction

References in corpus (3)

• Chaos and energy spreading for time-Dependent Hamiltonians, and the various Regimes in the theory of Quantum Dissipation
• Quantum dissipation due to the interaction with chaotic degrees-of-freedom and the correspondence principle
• Wavepacket dynamics in energy space, RMT and quantum-classical correspondence

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