Universality of the Lyapunov regime for the Loschmidt echo

The Loschmidt echo (LE) is a magnitude that measures the sensitivity of quantum dynamics to perturbations in the Hamiltonian. For a certain regime of the parameters, the LE decays exponentially with a rate given by the Lyapunov exponent of the underlying classically chaotic system. We develop a semiclassical theory, supported by numerical results in a Lorentz gas model, which allows us to establish and characterize the universality of this Lyapunov regime. In particular, the universality is evidenced by the semiclassical limit of the Fermi wavelength going to zero, the behavior for times longer than Ehrenfest time, the insensitivity with respect to the form of the perturbation and the behavior of individual (non-averaged) initial conditions. Finally, by elaborating a semiclassical approximation to the Wigner function, we are able to distinguish between classical and quantum origin for the different terms of the LE. This approach renders an understanding for the persistence of the Lyapunov regime after the Ehrenfest time, as well as a reinterpretation of our results in terms of the quantum--classical transition.Comment: 33 pages, 17 figures, uses Revtex

Advances, Challenges and Opportunities in 3D CMOS Sequential Integration

3D sequential integration enables the full use of the third dimension thanks to its high alignment performance. In this paper, we address the major challenges of 3D sequential integration: in particular, the control of molecular bonding allows us to obtain pristine quality top active layer. With the help of Solid Phase Epitaxy, we can match the performance of top FET, processed at low temperature (600°C), with the bottom FET devices. Finally, the development of a stable salicide enables to retain bottom performance after top FET processing. Overcoming these major technological issues offers a wide range of applications

Impact of scaling on electrostatics of germanium-channel MOSFET-analytical study.

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