Quantum Belief Propagation

We present an accurate numerical algorithm, called quantum belief propagation (QBP), for simulation of one-dimensional quantum systems at non-zero temperature. The algorithm exploits the fact that quantum effects are short-range in these systems at non-zero temperature, decaying on a length scale inversely proportional to the temperature. We compare to exact results on a spin-1/2 Heisenberg chain. Even a very modest calculation, requiring diagonalizing only 10-by-10 matrices, reproduces the peak susceptibility with a relative error of less than $10^{-5}$, while more elaborate calculations further reduce the error.Comment: 4 pages, 1 figure; revised time estimates due to improved implementation. Typographical corrections to Eq. 7 made; thanks to David Poulin for pointing out the mistak

Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States

We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer resources required. This modification is based on a principle of "observing" the system outside the light-cone. We apply this method to study spin relaxation in systems started out of equilibrium with initial conditions that give rise to very rapid entanglement growth. We also show that it is possible to approximate time evolution under a local Hamiltonian by a quantum circuit whose light-cone naturally matches the Lieb-Robinson velocity. Asymptotically, these modified methods allow a doubling of the system size that one can obtain compared to direct simulation. We then consider a different problem of thermal properties of disordered spin chains and use quantum belief propagation to average over different configurations. We test this algorithm on one dimensional systems with mixed ferromagnetic and anti-ferromagnetic bonds, where we can compare to quantum Monte Carlo, and then we apply it to the study of disordered, frustrated spin systems.Comment: 19 pages, 12 figure

The literature of low g propellant behavior

Annotated bibliography on low-g liquid propellant behavio

Tip Splittings and Phase Transitions in the Dielectric Breakdown Model: Mapping to the DLA Model

We show that the fractal growth described by the dielectric breakdown model exhibits a phase transition in the multifractal spectrum of the growth measure. The transition takes place because the tip-splitting of branches forms a fixed angle. This angle is eta dependent but it can be rescaled onto an ``effectively'' universal angle of the DLA branching process. We derive an analytic rescaling relation which is in agreement with numerical simulations. The dimension of the clusters decreases linearly with the angle and the growth becomes non-fractal at an angle close to 74 degrees (which corresponds to eta= 4.0 +- 0.3).Comment: 4 pages, REVTex, 3 figure

Random Vibrational Networks and Renormalization Group

We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several real-space renormalization techniques which can be used to describe this dynamics on general networks, drawing on strong disorder techniques developed for regular lattices. The renormalization group is capable of elucidating the localization properties, and provides, even for specific network instances, a fast approximation technique for determining the spectra which compares well with exact results.Comment: 4 pages, 3 figure

An area law for entanglement from exponential decay of correlations

Area laws for entanglement in quantum many-body systems give useful information about their low-temperature behaviour and are tightly connected to the possibility of good numerical simulations. An intuition from quantum many-body physics suggests that an area law should hold whenever there is exponential decay of correlations in the system, a property found, for instance, in non-critical phases of matter. However, the existence of quantum data-hiding state--that is, states having very small correlations, yet a volume scaling of entanglement--was believed to be a serious obstruction to such an implication. Here we prove that notwithstanding the phenomenon of data hiding, one-dimensional quantum many-body states satisfying exponential decay of correlations always fulfil an area law. To obtain this result we combine several recent advances in quantum information theory, thus showing the usefulness of the field for addressing problems in other areas of physics.Comment: 8 pages, 3 figures. Short version of arXiv:1206.2947 Nature Physics (2013

β-Elimination of phosphate and subsequent addition of pyridoxamine as a method for identifying and sequencing peptides containing phosphoseryl residues

AbstractPeptides containing phosphoseryl residues can be modified by removal of the phosphate groups via β-elimination followed by addition of pyridoxamine to the resulting dehydroalanyl residue. Peptides containing the modified residues can be detected at nanomole levels by monitoring absorbance at 328 nm or at picomole levels by monitoring fluorescence. Photolysis of the modified peptide converts the pyridoxamino adduct to a form which can be readily identified after Edman degradation

Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance

We define for quantum many-body systems a quasi-adiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density of states, and thus is away from a quantum phase transition. This continuation takes local operators into local operators, while approximately preserving the ground state expectation values. We apply this continuation to the problem of gauge theories coupled to matter, and propose a new distinction, perimeter law versus "zero law" to identify confinement. We also apply the continuation to local bosonic models with emergent gauge theories. We show that local gauge invariance is topological and cannot be broken by any local perturbations in the bosonic models in either continuous or discrete gauge groups. We show that the ground state degeneracy in emergent discrete gauge theories is a robust property of the bosonic model, and we argue that the robustness of local gauge invariance in the continuous case protects the gapless gauge boson.Comment: 15 pages, 6 figure

Developing the evidence base for adult social care practice: The NIHR School for Social Care Research

In a foreword to 'Shaping the Future of Care Together', Prime Minister Gordon Brown says that a care and support system reflecting the needs of our times and meeting our rising aspirations is achievable, but 'only if we are prepared to rise to the challenge of radical reform'. A number of initiatives will be needed to meet the challenge of improving social care for the growing older population. Before the unveiling of the green paper, The National Institute for Health Research (NIHR) announced that it has provided 15m pounds over a five-year period to establish the NIHR School for Social Care Research. The School's primary aim is to conduct or commission research that will help to improve adult social care practice in England. The School is seeking ideas for research topics, outline proposals for new studies and expert advice in developing research methods

Community Detection as an Inference Problem

We express community detection as an inference problem of determining the most likely arrangement of communities. We then apply belief propagation and mean-field theory to this problem, and show that this leads to fast, accurate algorithms for community detection.Comment: 4 pages, 2 figure