Deriving uniform semiclassical approximations for one-dimensional fermionic systems

Dynamical classic limit: Dissipative vs conservative systems

We analyze the nonlinear dynamics of a quartic semiclassical system able to describe the interaction of matter with a field. We do it in both dissipative and conservative scenarios. In particular, we study the classical limit of both frameworks and compare the associated features. In the two environments, we heavily use a system's invariant, related to the Uncertainty Principle, that helps to determine how the dynamics tends to the pertinent classical limit. We exhibit the convergence to the classical limit and also verify that the Uncertainty Principle is complied with during the entire process, even in the presence of dissipation.

Deriving approximate functionals with asymptotics

Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB expansion in one dimension, and modern approaches to asymptotic expansions. A mathematical framework for analyzing asymptotic behavior for the sums of energies unites both corrections to the gradient expansion of DFT and hyperasymptotics of sums. Simple examples are given for the model problem of orbital-free DFT in one dimension. In some cases, errors can be made as small as 10-32 Hartree suggesting that, if these new ingredients can be applied, they might produce approximate functionals that are much more accurate than those in current use. A variation of the Euler-Maclaurin formula generalizes previous results.

Semilocal Pauli-Gaussian Kinetic Functionals for Orbital-Free Density Functional Theory Calculations of Solids

Kinetic energy (KE) approximations are key elements in orbital-free density functional theory. To date, the use of nonlocal functionals, possibly employing system-dependent parameters, has been considered mandatory in order to obtain satisfactory accuracy for different solid-state systems, whereas semilocal approximations are generally regarded as unfit to this aim. Here, we show that, instead, properly constructed semilocal approximations, the Pauli-Gaussian (PG) KE functionals, especially at the Laplacian level of theory, can indeed achieve similar accuracy as nonlocal functionals and can be accurate for both metals and semiconductors, without the need for system-dependent parameters.