Stochastic density functional theory

Linear-scaling implementations of density functional theory (DFT) reach their intended efficiency regime only when applied to systems having a physical size larger than the range of their Kohn-Sham density matrix (DM). This causes a problem since many types of large systems of interest have a rather broad DM range and are therefore not amenable to analysis using DFT methods. For this reason, the recently proposed stochastic DFT (sDFT), avoiding exhaustive DM evaluations, is emerging as an attractive alternative linear-scaling approach. This review develops a general formulation of sDFT in terms of a (non)orthogonal basis representation and offers an analysis of the statistical errors (SEs) involved in the calculation. Using a new Gaussian-type basis-set implementation of sDFT, applied to water clusters and silicon nanocrystals, it demonstrates and explains how the standard deviation and the bias depend on the sampling rate and the system size in various types of calculations. We also develop basis-set embedded-fragments theory, demonstrating its utility for reducing the SEs for energy, density of states and nuclear force calculations. Finally, we discuss the algorithmic complexity of sDFT, showing it has CPU wall-time linear-scaling. The method parallelizes well over distributed processors with good scalability and therefore may find use in the upcoming exascale computing architectures

Thermal-assisted Anisotropy and Thermal-driven Instability in the Superfluidity state of Two-Species Polar Fermi Gas

We study the superfluid state of two-species heteronuclear Fermi gases with isotropic contact and anisotropic long-range dipolar interactions. By explicitly taking account of Fock exchange contribution, we derive self-consistent equations describing the pairing states in the system. Exploiting the symmetry of the system, we developed an efficient way of solving the self-consistent equations by exploiting the symmetries. We find that the temperature tends to increase the anisotropy of the pairing state, which is rather counterintuitive. We study the anisotropic properties of the system by examining the angular dependence of the number density distribution, the excitation spectrum and the pair correlation function. The competing effects of the contact interaction and the dipolar interaction upon the anisotropy are revealed. We derive and compute the superfluid mass density $\rho_{ij}$ for the system. Astonishingly, we find that $\rho_{zz}$ becomes negative above some certain temperature $T^*$($T<T_c$), signaling some instability of the system. This suggests that the elusive FFLO state may be observed in experiments, due to an anisotropic state with a spontaneously generated superflow.Comment: 7 pages, 5 figure

Doping the holographic Mott insulator

Mott insulators form because of strong electron repulsions, being at the heart of strongly correlated electron physics. Conventionally these are understood as classical "traffic jams" of electrons described by a short-ranged entangled product ground state. Exploiting the holographic duality, which maps the physics of densely entangled matter onto gravitational black hole physics, we show how Mott-insulators can be constructed departing from entangled non-Fermi liquid metallic states, such as the strange metals found in cuprate superconductors. These "entangled Mott insulators" have traits in common with the "classical" Mott insulators, such as the formation of Mott gap in the optical conductivity, super-exchange-like interactions, and form "stripes" when doped. They also exhibit new properties: the ordering wave vectors are detached from the number of electrons in the unit cell, and the DC resistivity diverges algebraically instead of exponentially as function of temperature. These results may shed light on the mysterious ordering phenomena observed in underdoped cuprates.Comment: 27 pages, 9 figures. Accepted in Nature Physic

Decoding the urban grid: or why cities are neither trees nor perfect grids

In a previous paper (Figueiredo and Amorim, 2005), we introduced the continuity lines, a compressed description that encapsulates topological and geometrical properties of urban grids. In this paper, we applied this technique to a large database of maps that included cities of 22 countries. We explore how this representation encodes into networks universal features of urban grids and, at the same time, retrieves differences that reflect classes of cities. Then, we propose an emergent taxonomy for urban grids

Steering in computational science: mesoscale modelling and simulation

This paper outlines the benefits of computational steering for high performance computing applications. Lattice-Boltzmann mesoscale fluid simulations of binary and ternary amphiphilic fluids in two and three dimensions are used to illustrate the substantial improvements which computational steering offers in terms of resource efficiency and time to discover new physics. We discuss details of our current steering implementations and describe their future outlook with the advent of computational grids.Comment: 40 pages, 11 figures. Accepted for publication in Contemporary Physic