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|<ωcl.
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 (Ω,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]