Fermi Liquids and the Luttinger Integral

The Luttinger Theorem, which relates the electron density to the volume of the Fermi surface in an itinerant electron system, is taken to be one of the essential features of a Fermi liquid. The microscopic derivation of this result depends on the vanishing of a certain integral, the Luttinger integral $I_{\rm L}$, which is also the basis of the Friedel sum rule for impurity models, relating the impurity occupation number to the scattering phase shift of the conduction electrons. It is known that non-zero values of $I_{\rm L}$ with $I_{\rm L}=\pm\pi/2$, occur in impurity models in phases with non-analytic low energy scattering, classified as singular Fermi liquids. Here we show the same values, $I_{\rm L}=\pm\pi/2$, occur in an impurity model in phases with regular low energy Fermi liquid behavior. Consequently the Luttinger integral can be taken to characterize these phases, and the quantum critical points separating them interpreted as topological.Comment: 5 pages 7 figure

On the prevalence of bridged macrocyclic pyrroloindolines formed in regiodivergent alkylations of tryptophan.

A Friedel-Crafts alkylation is described that efficiently transforms tryptophan-containing peptides into macrocycles of varying ring connectivity. Factors are surveyed that influence the distribution of regioisomers, with a focus on indole C3-alkylations leading to bridged endo-pyrroloindolines. We probe the stability and stereochemistry of these pyrroloindolines, study their rearrangement to C2-linked indolic macrocycles, and demonstrate a scalable, stereoselective synthesis of this compound class. Placing the macrocyclization in sequence with further template-initiated annulation leads to extraordinary polycyclic products and further demonstrates the potential for this chemistry to drive novel peptidomimetic lead discovery programs

Tree-Independent Dual-Tree Algorithms

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings.Comment: accepted in ICML 201

Weighted-density approximation for general nonuniform fluid mixtures

In order to construct a general density-functional theory for nonuniform fluid mixtures, we propose an extension to multicomponent systems of the weighted-density approximation (WDA) of Curtin and Ashcroft [Phys. Rev. A 32, 2909 (1985)]. This extension corrects a deficiency in a similar extension proposed earlier by Denton and Ashcroft [Phys. Rev. A 42, 7312 (1990)], in that that functional cannot be applied to the multi-component nonuniform fluid systems with spatially varying composition, such as solid-fluid interfaces. As a test of the accuracy of our new functional, we apply it to the calculation of the freezing phase diagram of a binary hard-sphere fluid, and compare the results to simulation and the Denton-Ashcroft extension.Comment: 4 pages, 4 figures, to appear in Phys. Rev. E as Brief Repor

Supersymmetry Breaking Triggered by Monopoles

We investigate N = 1 supersymmetric gauge theories where monopole condensation triggers supersymmetry breaking in a metastable vacuum. The low-energy effective theory is an O'Raifeartaigh-like model of the kind investigated recently by Shih where the R-symmetry can be spontaneously broken. We examine several implementations with varying degrees of phenomenological interest.Comment: 20 pages, 4 figures (v2: minor clarifications and typos fixed

Bursts in a fiber bundle model with continuous damage

We study the constitutive behaviour, the damage process, and the properties of bursts in the continuous damage fiber bundle model introduced recently. Depending on its two parameters, the model provides various types of constitutive behaviours including also macroscopic plasticity. Analytic results are obtained to characterize the damage process along the plastic plateau under strain controlled loading, furthermore, for stress controlled experiments we develop a simulation technique and explore numerically the distribution of bursts of fiber breaks assuming infinite range of interaction. Simulations revealed that under certain conditions power law distribution of bursts arises with an exponent significantly different from the mean field exponent 5/2. A phase diagram of the model characterizing the possible burst distributions is constructed.Comment: 9 pages, 11 figures, APS style, submitted for publicatio