An Introduction to Topological Insulators

Electronic bands in crystals are described by an ensemble of Bloch wave functions indexed by momenta defined in the first Brillouin Zone, and their associated energies. In an insulator, an energy gap around the chemical potential separates valence bands from conduction bands. The ensemble of valence bands is then a well defined object, which can possess non-trivial or twisted topological properties. In the case of a twisted topology, the insulator is called a topological insulator. We introduce this notion of topological order in insulators as an obstruction to define the Bloch wave functions over the whole Brillouin Zone using a single phase convention. Several simple historical models displaying a topological order in dimension two are considered. Various expressions of the corresponding topological index are finally discussed.Comment: 46 pages, 29 figures. This papers aims to be a pedagogical review on topological insulators. It was written for the topical issue of "Comptes Rendus de l'Acad\'emie des Sciences - Physique" devoted to topological insulators and Dirac matte

Demutualization and enforcement incentives at self-regulatory financial exchanges

n the last few years, many of the world’s largest financial exchanges have converted from mutual, not-for-profit organizations to publicly-traded, for-profit firms. In most cases, these exchanges have substantial responsibilities with respect to enforcing various regulations that protect investors from dishonest agents. We examine how the incentives to enforce such regulations change as an exchange converts from mutual to for-profit status. In contrast to oft-stated concerns, we find that, in many circumstances, an exchange that maximizes shareholder (rather than member) income has a greater incentive to aggressively enforce these types of regulations

Towards a learning-theoretic analysis of spike-timing dependent plasticity

This paper suggests a learning-theoretic perspective on how synaptic plasticity benefits global brain functioning. We introduce a model, the selectron, that (i) arises as the fast time constant limit of leaky integrate-and-fire neurons equipped with spiking timing dependent plasticity (STDP) and (ii) is amenable to theoretical analysis. We show that the selectron encodes reward estimates into spikes and that an error bound on spikes is controlled by a spiking margin and the sum of synaptic weights. Moreover, the efficacy of spikes (their usefulness to other reward maximizing selectrons) also depends on total synaptic strength. Finally, based on our analysis, we propose a regularized version of STDP, and show the regularization improves the robustness of neuronal learning when faced with multiple stimuli.Comment: To appear in Adv. Neural Inf. Proc. System

Hydrodynamic and mass transfer efficiency of ceramic foam packing applied to distillation.

In addition to a high void volume and specific area, solid foams possess other properties (low density, good thermal, mechanical, electrical, and acoustical behaviour) that make them attractive for applications such as heat exchangers and reformers. Applications using foams as catalysts or structured catalyst supports have demonstrated higher performance than classical catalysts. Several studies have explored the hydrodynamic behaviour of foams in monophasic and counter current systems and have reported very low pressure drops. This paper describes the application of ceramic foam to distillation. The β-SiC foam contains 5 pores per inch (PPI) with a 91% void volume and a surface area of 640 m2/m3. Performance parameters including pressure drop for the dry and wet packing, flooding behaviour, and dynamic liquid hold-up were measured in a column of 150 mm internal diameter. The mass transfer efficiency in terms of the height equivalent to theoretical plate (HETP) was determined by total reflux experiments using a mixture of n-heptane and cyclohexane at atmospheric pressure. The experimental results were used to develop a set of correlations describing pressure drop and liquid hold-up in terms of a dimensionless number. The hydrodynamic performance and mass transfer efficiency were compared with classical packing materials used in distillation

A cavity-QED scheme for Heisenberg-limited interferometry

We propose a Ramsey interferometry experiment using an entangled state of N atoms to reach the Heisenberg limit for the estimation of an atomic phase shift if the atom number parity is perfectly determined. In a more realistic situation, due to statistical fluctuations of the atom source and the finite detection efficiency, the parity is unknown. We then achieve about half the Heisenberg limit. The scheme involves an ensemble of circular Rydberg atoms which dispersively interact successively with two initially empty microwave cavities. The scheme does not require very high-Q cavities. An experimental realization with about ten entangled Rydberg atoms is achievable with state of art apparatuses.Comment: 13 pages, 7 figure

Parallel Transport and Band Theory in Crystals

We show that different conventions for Bloch Hamiltonians on non-Bravais lattices correspond to different natural definitions of parallel transport of Bloch eigenstates. Generically the Berry curvatures associated with these parallel transports differ, while physical quantities are naturally related to a canonical choice of the parallel transport.Comment: 5 pages, 1 figure ; minor updat

Networks of ⋅/G/∞\cdot/G/\infty Server Queues with Shot-Noise-Driven Arrival Intensities

We study infinite-server queues in which the arrival process is a Cox process (or doubly stochastic Poisson process), of which the arrival rate is given by shot noise. A shot-noise rate emerges as a natural model, if the arrival rate tends to display sudden increases (or: shots) at random epochs, after which the rate is inclined to revert to lower values. Exponential decay of the shot noise is assumed, so that the queueing systems are amenable for analysis. In particular, we perform transient analysis on the number of customers in the queue jointly with the value of the driving shot-noise process. Additionally, we derive heavy-traffic asymptotics for the number of customers in the system by using a linear scaling of the shot intensity. First we focus on a one dimensional setting in which there is a single infinite-server queue, which we then extend to a network setting