Transition metal oxides using quantum Monte Carlo

The transition metal-oxygen bond appears prominently throughout chemistry and solid-state physics. Many materials, from biomolecules to ferroelectrics to the components of supernova remnants contain this bond in some form. Many of these materials' properties strongly depend on fine details of the TM-O bond and intricate correlation effects, which make accurate calculations of their properties very challenging. We present quantum Monte Carlo, an explicitly correlated class of methods, to improve the accuracy of electronic structure calculations over more traditional methods like density functional theory. We find that unlike s-p type bonding, the amount of hybridization of the d-p bond in TM-O materials is strongly dependant on electronic correlation.Comment: 20 pages, 4 figures, to appear as a topical review in J. Physics: Condensed Matte

Direct estimation of functionals of density operators by local operations and classical communication

We present a method of direct estimation of important properties of a shared bipartite quantum state, within the "distant laboratories" paradigm, using only local operations and classical communication. We apply this procedure to spectrum estimation of shared states, and locally implementable structural physical approximations to incompletely positive maps. This procedure can also be applied to the estimation of channel capacity and measures of entanglement

How well can we measure supermassive black hole spin?

Being one of only two fundamental properties black holes possess, the spin of supermassive black holes (SMBHs) is of great interest for understanding accretion processes and galaxy evolution. However, in these early days of spin measurements, consistency and reproducibility of spin constraints have been a challenge. Here we focus on X-ray spectral modelling of active galactic nuclei (AGN), examining how well we can truly return known reflection parameters such as spin under standard conditions. We have created and fit over 4000 simulated Seyfert 1 spectra each with 375$\pm$1k counts. We assess the fits with reflection fraction of $R$ = 1 as well as reflection-dominated AGN with $R$ = 5. We also examine the consequence of permitting fits to search for retrograde spin. In general, we discover that most parameters are over-estimated when spectroscopy is restricted to the 2.5 - 10.0 keV regime and that models are insensitive to inner emissivity index and ionization. When the bandpass is extended out to 70keV, parameters are more accurately estimated. Repeating the process for $R$ = 5 reduces our ability to measure photon index ($\sim$3 to 8 per cent error and overestimated), but increases precision in all other parameters -- most notably ionization, which becomes better constrained ($\pm$45 erg cm $\rm{s^{-1}}$) for low ionization parameters ($\xi$$<$200 erg cm $\rm{s^{-1}}$). In all cases, we find the spin parameter is only well measured for the most rapidly rotating supermassive black holes (i.e. $a$ $>$ 0.8 to about $\pm$0.10) and that inner emissivity index is never well constrained. Allowing our model to search for retrograde spin did not improve the results.Comment: Accepted for publication in MNRAS. 13 pages, 7 figure

From Schr\"odinger's Equation to the Quantum Search Algorithm

The quantum search algorithm is a technique for searching N possibilities in only sqrt(N) steps. Although the algorithm itself is widely known, not so well known is the series of steps that first led to it, these are quite different from any of the generally known forms of the algorithm. This paper describes these steps, which start by discretizing Schr\"odinger's equation. This paper also provides a self-contained introduction to the quantum search algorithm from a new perspective.Comment: Postscript file, 16 pages. This is a pedagogical article describing the invention of the quantum search algorithm. It appeared in the July, 2001 issue of American Journal of Physics (AJP

Symmetric Multiplets in Quantum Algebras

We consider a modified version of the coproduct for \U(\su_q(2)) and show that in the limit when $q \rightarrow 1$, there exists an essentially non-cocommutative coproduct. We study the implications of this non-cocommutativity for a system of two spin-$1/2$ particles. Here it is shown that, unlike the usual case, this non-trivial coproduct allows for symmetric and anti-symmetric states to be present in the multiplet. We surmise that our analysis could be related to the ferromagnetic and antiferromagnetic cases of the Heisenberg magnets.Comment: Needs subeqnarray.sty. To be published in Mod Phys Lett.