Towards AC-induced optimum control of dynamical localization

It is shown that optimum control of dynamical localization (quantum suppression of classical diffusion) in the context of ultracold atoms in periodically shaken optical lattices subjected to time-periodic forces having equidistant zeros depends on the \textit{impulse} transmitted by the external force over half-period rather than on the force amplitude. This result provides a useful principle for optimally controlling dynamical localization in general periodic systems, which is capable of experimental realization.Comment: 7 pages, 6 figure

Numerical studies of light-matter interaction driven by plasmonic fields: the velocity gauge

Theoretical approaches to strong field phenomena driven by plasmonic fields are based on the length gauge formulation of the laser-matter coupling. From the theoretical viewpoint it is known there exists no preferable gauge and consequently the predictions and outcomes should be independent of this choice. The use of the length gauge is mainly due to the fact that the quantity obtained from finite elements simulations of plasmonic fields is the plasmonic enhanced laser electric field rather than the laser vector potential. In this paper we develop, from first principles, the velocity gauge formulation of the problem and we apply it to the high-order harmonic generation (HHG) in atoms. A comparison to the results obtained with the length gauge is made. It is analytically and numerically demonstrated that both gauges give equivalent descriptions of the emitted HHG spectra resulting from the interaction of a spatially inhomogeneous field and the single active electron (SAE) model of the helium atom. We discuss, however, advantages and disadvantages of using different gauges in terms of numerical efficiency.Comment: 19 pages, 5 figures, submitted to Journal of Computational Physic

Impulse-induced localized nonlinear modes in an electrical lattice

Intrinsic localized modes, also called discrete breathers, can exist under certain conditions in one-dimensional nonlinear electrical lattices driven by external harmonic excitations. In this work, we have studied experimentally the efectiveness of generic periodic excitations of variable waveform at generating discrete breathers in such lattices. We have found that this generation phenomenon is optimally controlled by the impulse transmitted by the external excitation (time integral over two consecutive zerosComment: 5 pages, 8 figure

An intrinsic Proper Generalized Decomposition for parametric symmetric elliptic problems

We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension which realizes the best approximation in mean of the error with respect to the parameter in the quadratic norm associated to the elliptic operator, between the exact solution and the Galerkin solution calculated on the subspace. This is analogous to the best approximation property of the Proper Orthogonal Decomposition (POD) subspaces, excepting that in our case the norm is parameter-depending, and then the POD optimal sub-spaces cannot be characterized by means of a spectral problem. We apply a deflation technique to build a series of approximating solutions on finite-dimensional optimal subspaces, directly in the on-line step. We prove that the partial sums converge to the continuous solutions, in mean quadratic elliptic norm.Comment: 18 page