Many-body position operator in lattice fermionic systems with periodic boundary conditions

A total position operator $X$ in the position representation is derived for lattice fermionic systems with periodic boundary conditions. The operator is shown to be Hermitian, the generator of translations in momentum space, and its time derivative is shown to correspond to the total current operator in a periodic system. The operator is such that its moments can be calculated up to any order. To demonstrate its utility finite size scaling is applied to the Brinkman-Rice transition as well as metallic and insulating Gutzwiller wavefunctions.Comment: to appear in Journal of Physics A: Mathematical and General (reference will be added later

Linear-scaling density-functional simulations of charged point defects in Al2O3 using hierarchical sparse matrix algebra

We present calculations of formation energies of defects in an ionic solid (Al(2)O(3)) extrapolated to the dilute limit, corresponding to a simulation cell of infinite size. The large-scale calculations required for this extrapolation are enabled by developments in the approach to parallel sparse matrix algebra operations, which are central to linear-scaling density-functional theory calculations. The computational cost of manipulating sparse matrices, whose sizes are determined by the large number of basis functions present, is greatly improved with this new approach. We present details of the sparse algebra scheme implemented in the ONETEP code using hierarchical sparsity patterns, and demonstrate its use in calculations on a wide range of systems, involving thousands of atoms on hundreds to thousands of parallel processes

Electrostatic considerations affecting the calculated HOMO-LUMO gap in protein molecules.

A detailed study of energy differences between the highest occupied and lowest unoccupied molecular orbitals (HOMO-LUMO gaps) in protein systems and water clusters is presented. Recent work questioning the applicability of Kohn-Sham density-functional theory to proteins and large water clusters (E. Rudberg, J. Phys.: Condens. Mat. 2012, 24, 072202) has demonstrated vanishing HOMO-LUMO gaps for these systems, which is generally attributed to the treatment of exchange in the functional used. The present work shows that the vanishing gap is, in fact, an electrostatic artefact of the method used to prepare the system. Practical solutions for ensuring the gap is maintained when the system size is increased are demonstrated. This work has important implications for the use of large-scale density-functional theory in biomolecular systems, particularly in the simulation of photoemission, optical absorption and electronic transport, all of which depend critically on differences between energies of molecular orbitals.Comment: 13 pages, 4 figure

Accurate and efficient method for the treatment of exchange in a plane-wave basis.

Published versio

Linear-scaling time-dependent density-functional theory beyond the Tamm-Dancoff approximation: Obtaining efficiency and accuracy with in situ optimised local orbitals.

We present a solution of the full time-dependent density-functional theory (TDDFT) eigenvalue equation in the linear response formalism exhibiting a linear-scaling computational complexity with system size, without relying on the simplifying Tamm-Dancoff approximation (TDA). The implementation relies on representing the occupied and unoccupied subspaces with two different sets of in situ optimised localised functions, yielding a very compact and efficient representation of the transition density matrix of the excitation with the accuracy associated with a systematic basis set. The TDDFT eigenvalue equation is solved using a preconditioned conjugate gradient algorithm that is very memory-efficient. The algorithm is validated on a small test molecule and a good agreement with results obtained from standard quantum chemistry packages is found, with the preconditioner yielding a significant improvement in convergence rates. The method developed in this work is then used to reproduce experimental results of the absorption spectrum of bacteriochlorophyll in an organic solvent, where it is demonstrated that the TDA fails to reproduce the main features of the low energy spectrum, while the full TDDFT equation yields results in good qualitative agreement with experimental data. Furthermore, the need for explicitly including parts of the solvent into the TDDFT calculations is highlighted, making the treatment of large system sizes necessary that are well within reach of the capabilities of the algorithm introduced here. Finally, the linear-scaling properties of the algorithm are demonstrated by computing the lowest excitation energy of bacteriochlorophyll in solution. The largest systems considered in this work are of the same order of magnitude as a variety of widely studied pigment-protein complexes, opening up the possibility of studying their properties without having to resort to any semiclassical approximations to parts of the protein environment.T.J.Z. acknowledges the support of EPSRC under Grant No. EP/J017639/1 and the ARCHER eCSE programme. M.C.P. and P.D.H. acknowledge the support of EPSRC under Grant No. EP/J015059/1. The underlying data of this publication can be accessed via the following persistent URI: https://www.repository.cam.ac.uk/handle/1810/251293This is the author accepted manuscript. The final version is available from AIP via http://dx.doi.org/10.1063/1.493628

“It’s like my life but more, and better!” - Playing with the Cathaby Shark Girls: MMORPGs, young people and fantasy-based social play

This article is available open access through the publisher’s website at the link below. Copyright @ 2011 A B Academic Publishers.Digital technology has opened up a range of new on-line leisure spaces for young people. Despite their popularity, on-line games and Massive Multiplayer Online Role Playing Games in particular are still a comparatively under-researched area in the fields of both Education and more broadly Youth Studies. Drawing on a Five year ethnographic study, this paper considers the ways that young people use the virtual spaces offered by MMORPGs. This paper suggests that MMORPGs represent significant arenas within which young people act out a range of social narratives through gaming. It argues that MMORPG have become important fantasy spaces which offer young people possibilities to engage in what were formally material practices. Although this form of play is grounded in the everyday it also extends material practices and offers new and unique forms of symbolic experimentation, thus I argue that game-play narratives cannot be divorced from the everyday lives of their participants

Quantum Monte Carlo calculations of the surface energy of an electron gas

Published versio

O(N) methods in electronic structure calculations

Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.Comment: 85 pages, 15 figures, 488 references. Resubmitted to Rep. Prog. Phys (small changes

Gas Accretion and Giant Lyman-alpha Nebulae

Several decades of observations and discoveries have shown that high-redshift AGN and massive galaxies are often surrounded by giant Lyman-alpha nebulae extending in some cases up to 500 kpc in size. In this review, I discuss the properties of the such nebulae discovered at z>2 and their connection with gas flows in and around the galaxies and their halos. In particular, I show how current observations are used to constrain the physical properties and origin of the emitting gas in terms of the Lyman-alpha photon production processes and kinematical signatures. These studies suggest that recombination radiation is the most viable scenario to explain the observed Lyman-alpha luminosities and Surface Brightness for the large majority of the nebulae and imply that a significant amount of dense, ionized and cold clumps should be present within and around the halos of massive galaxies. Spectroscopic studies suggest that, among the giant Lyman-alpha nebulae, the one associated with radio-loud AGN should have kinematics dominated by strong, ionized outflows within at least the inner 30-50 kpc. Radio-quiet nebulae instead present more quiescent kinematics compatible with stationary situation and, in some cases, suggestive of rotating structures. However, definitive evidences for accretion onto galaxies of the gas associated with the giant Lyman-alpha emission are not unambiguously detected yet. Deep surveys currently ongoing using other bright, non-resonant lines such as Hydrogen H-alpha and HeII1640 will be crucial to search for clearer signatures of cosmological gas accretion onto galaxies and AGN.Comment: Invited review to appear in Gas Accretion onto Galaxies, Astrophysics and Space Science Library, eds. A. J. Fox & R. Dave', to be published by Springe