Quantum-mechanical non-perturbative response of Driven Chaotic Mesoscopic Systems (1998-2002)

Consider a time-dependent Hamiltonian H(Q,P;x(t)) with periodic driving x(t)=ε sin(Ω t). It is assumed that the classical dynamics is chaotic, and that its power-spectrum extends over some frequency range |ω|cl. Both classical and quantum-mechanical (QM) linear response theory (LRT) predict a relatively large response for Ω < ωcl, and a relatively small response otherwise, independently of the driving amplitude ε. We define a non-perturbative regime in the ,ε) space, where LRT fails, and demonstrate this failure numerically. For ε>εprt, where εprtα hbar, the system may have a relatively strong response for Ω>ωcl, and the shape of the response function becomes ε dependent.

[1] D. Cohen and T. Kottos, Phys. Rev. Lett. 85, 4839 (2000). [arXiv] [pdf]
[2] D. Cohen, Phys. Rev. Lett. 82, 4951 (1999). [arXiv] [pdf]
[3] D. Cohen, Annals of Physics 283, 175 (2000). [arXiv] [pdf]
[4] D. Cohen and T. Kottos, J. Phys. A 36, 10151 (2003). [arXiv] [pdf]


regimes