Analytic Solution for the Ground State Energy of the Extensive Many-Body Problem

A closed form expression for the ground state energy density of the general extensive many-body problem is given in terms of the Lanczos tri-diagonal form of the Hamiltonian. Given the general expressions of the diagonal and off-diagonal elements of the Hamiltonian Lanczos matrix, $\alpha_n(N)$ and $\beta_n(N)$, asymptotic forms $\alpha(z)$ and $\beta(z)$ can be defined in terms of a new parameter $z\equiv n/N$ ($n$ is the Lanczos iteration and $N$ is the size of the system). By application of theorems on the zeros of orthogonal polynomials we find the ground-state energy density in the bulk limit to be given in general by ${\cal E}_0 = {\rm inf}\,\left[\alpha(z) - 2\,\beta(z)\right]$.Comment: 10 pages REVTex3.0, 3 PS figure

Towards visualisation of central-cell-effects in scanning-tunnelling-microscope images of subsurface dopant qubits in silicon

Atomic-scale understanding of phosphorous donor wave functions underpins the design and optimisation of silicon based quantum devices. The accuracy of large-scale theoretical methods to compute donor wave functions is dependent on descriptions of central-cell-corrections, which are empirically fitted to match experimental binding energies, or other quantities associated with the global properties of the wave function. Direct approaches to understanding such effects in donor wave functions are of great interest. Here, we apply a comprehensive atomistic theoretical framework to compute scanning tunnelling microscopy (STM) images of subsurface donor wave functions with two central-cell-correction formalisms previously employed in the literature. The comparison between central-cell models based on real-space image features and the Fourier transform profiles indicate that the central-cell effects are visible in the simulated STM images up to ten monolayers below the silicon surface. Our study motivates a future experimental investigation of the central-cell effects via STM imaging technique with potential of fine tuning theoretical models, which could play a vital role in the design of donor-based quantum systems in scalable quantum computer architectures.Comment: Nanoscale 201

Quantum Error Correction on Linear Nearest Neighbor Qubit Arrays

A minimal depth quantum circuit implementing 5-qubit quantum error correction in a manner optimized for a linear nearest neighbor architecture is described. The canonical decomposition is used to construct fast and simple gates that incorporate the necessary swap operations. Simulations of the circuit's performance when subjected to discrete and continuous errors are presented. The relationship between the error rate of a physical qubit and that of a logical qubit is investigated with emphasis on determining the concatenated error correction threshold.Comment: 4 pages, 5 figure

Bench-to-bedside review: Nitric oxide in critical illness – update 2008

Nitric oxide (NO) is a unique and nearly ubiquitous molecule that is widely utilized as a signaling molecule in cells throughout the body. NO is highly diffusible, labile, and multiply reactive, suiting it well for its role as an important regulator of a number of diverse biologic processes, including vascular tone and permeability, platelet adhesion, neurotransmission, and mitochondrial respiration. NO can protect cells against antioxidant injury, can inhibit leukocyte adhesion, and can participate in antimicrobial defense, but can also have deleterious effects, including inhibition of enzyme function, promotion of DNA damage, and activation of inflammatory processes. This molecule's chemistry dictates its biologic activity, which can be both direct and indirect. In addition, NO has bimodal effects in a number of cells, maintaining homeostasis at low doses, and participating in pathophysiology in others. Perturbation of NO regulation is involved in the most important and prevalent disease processes in critical care units, including sepsis, acute lung injury, and multiple organ failure. Given that NO is ubiquitous, highly diffusible, and promiscuously reactive, its regulation is complex. The NO concentration, kinetics, and localization, both inside and outside the cell, are clearly crucial factors. In the present update we review a selection of studies that have yielded important information on these complex but important issues. Interpretation of these and other studies aimed at elucidating physiologic and pathophysiologic roles of NO must take this complexity into account. A full review of the role of NO in these diseases is beyond the scope of the current manuscript; the present article will focus on recent advances in understanding the complex role of NO in health and disease

Measurable quantum geometric phase from a rotating single spin

We demonstrate that the internal magnetic states of a single nitrogen-vacancy defect, within a rotating diamond crystal, acquire geometric phases. The geometric phase shift is manifest as a relative phase between components of a superposition of magnetic substates. We demonstrate that under reasonable experimental conditions a phase shift of up to four radians could be measured. Such a measurement of the accumulation of a geometric phase, due to macroscopic rotation, would be the first for a single atom-scale quantum system.Comment: 5 pages, 2 figures: Accepted for publication in Physical Review Letter