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

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

2000-04-03

arxiv.org/abs/cond-mat/0004022v2

Phys. Rev. Lett 85, 4839 (2000).

Physics

Condensed Matter

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

Scientific paper

10.1103/PhysRevLett.85.4839

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.

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