27 research outputs found
The structure of the density-potential mapping. Part I: Standard density-functional theory
The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review aims at clarifying the status of the Hohenberg-Kohn theorem within DFT and Part II at different extensions of the theory that include magnetic fields. We collect evidence that the Hohenberg-Kohn theorem does not so much form the basis of DFT, but is rather the consequence of a more comprehensive mathematical framework. Such results are especially useful when it comes to the construction of generalized DFTs
Range of applicability of the Hu-Paz-Zhang master equation
We investigate a case of the Hu-Paz-Zhang master equation of the
Caldeira-Leggett model without Lindblad form obtained in the weak-coupling
limit up to the second-order perturbation. In our study, we use Gaussian
initial states to be able to employ a sufficient and necessary condition, which
can expose positivity violations of the density operator during the time
evolution. We demonstrate that the evolution of the non-Markovian master
equation has problems when the stationary solution is not a positive operator,
i.e., does not have physical interpretation. We also show that solutions always
remain physical for small-times of evolution. Moreover, we identify a strong
anomalous behavior, when the trace of the solution is diverging. We also
provide results for the corresponding Markovian master equation and show that
positivity violations occur for various types of initial conditions even when
the stationary solution is a positive operator. Based on our numerical results,
we conclude that this non-Markovian master equation is superior to the
corresponding Markovian one.Comment: 14 pages, 19 figure
On the Online Bin Packing Problem
A new framework for analyzing online bin packing algorithms is presented. This framework presents a unified way of explaining the performance of algorithms based on the Harmonic approach [3, 5, 8, 10, 11, 12]. Within this framework, it is shown that a new algorithm, Harmonic++, has asymptotic performance ratio at most 1.58889. It is also shown that the analysis of Harmonic+1 presented in [11] is incorrect; this is a fundamental logical flaw, not an error in calculation or an omitted case. The asymptotic performance ratio of Harmonic+1 is at least 1.59217. Thus Harmonic++ provides the best upper bound for the online bin packing problem to date