David Gontier — Page 3

arXiv2013

$N$-representability in non-collinear spin-polarized density functional theory

The $N$-representability problem for non-collinear spin-polarized densities was left open in the pioneering work of von Barth and Hedin setting up the Kohn-Sham density functional theory for magnetic compounds. In this letter, we demonstrate that, contrarily to the non-polarized case, the sets of pure and mixed state $N$-representable densities are different in general. We provide a simple characterization of the latter by means of easily checkable necessary and sufficient conditions on the components $ρ^{αβ} (\br)$ of the spin-polarized density.

math-ph↗

arXiv2013

Sampling based on timing: Time encoding machines on shift-invariant subspaces

Sampling information using timing is a new approach in sampling theory. The question is how to map amplitude information into the timing domain. One such encoder, called time encoding machine, was introduced by Lazar and Toth in [23] for the special case of band-limited functions. In this paper, we extend their result to the general framework of shift-invariant subspaces. We prove that time encoding machines may be considered as non-uniform sampling devices, where time locations are unknown a priori. Using this fact, we show that perfect representation and reconstruction of a signal with a time encoding machine is possible whenever this device satisfies some density property. We prove that this method is robust under timing quantization, and therefore can lead to the design of simple and energy efficient sampling devices.

cs.IT↗