Lieb-Robinson Bounds in Quantum Many-Body Physics

We give an overview of recent results on Lieb-Robinson bounds and some of their applications in the study of quantum many-body models in condensed matter physics.Comment: Lecture Notes for the school "Entropy and the Quantum", 16-20 March 2009, Tucson, Arizona

Locality Estimates for Quantum Spin Systems

We review some recent results that express or rely on the locality properties of the dynamics of quantum spin systems. In particular, we present a slightly sharper version of the recently obtained Lieb-Robinson bound on the group velocity for such systems on a large class of metric graphs. Using this bound we provide expressions of the quasi-locality of the dynamics in various forms, present a proof of the Exponential Clustering Theorem, and discuss a multi-dimensional Lieb-Schultz-Mattis Theorem.Comment: Contribution for the proceedings of ICMP XV, Rio de Janeiro, 200

On the dynamics of lattice systems with unbounded on-site terms in the Hamiltonian

We supply the mathematical arguments required to complete the proofs of two previously published results: Lieb-Robinson bounds for the dynamics of quantum lattice systems with unbounded on-site terms in the Hamiltonian and the existence of the thermodynamic limit of the dynamics of such systems

Recent Progress in Quantum Spin Systems

Some recent developments in the theory of quantum spin systems are reviewed.Comment: To appear in Markov Processes and Related Fields (J.T. Lewis special edition

Pulsed source of spectrally uncorrelated and indistinguishable photons at telecom wavelengths

We report on the generation of indistinguishable photon pairs at telecom wavelengths based on a type-II parametric down conversion process in a periodically poled potassium titanyl phosphate (PPKTP) crystal. The phase matching, pump laser characteristics and coupling geometry are optimised to obtain spectrally uncorrelated photons with high coupling efficiencies. Four photons are generated by a counter- propagating pump in the same crystal and anlysed via two photon interference experiments between photons from each pair source as well as joint spectral and g^(2) measurements. We obtain a spectral purity of 0.91 and coupling efficiencies around 90% for all four photons without any filtering. These pure indistinguishable photon sources at telecom wavelengths are perfectly adapted for quantum network demonstrations and other multi-photon protocols

Testing Optimal Punishment Mechanisms under Price Regulation: the Case of the Retail Market for Gasoline

We analyse the effects of a price floor on price wars (or deep price cuts) in the retail market for gasoline. Bertrand supergame oligopoly models predict that price wars should last longer in the presence of price floors. In 1996, the introduction of a price floor in the Quebec retail market for gasoline serves as a natural experiment with which to test this prediction. We use a Markov Switching Model with two latent states to simultaneously identify the periods of price-collusion/price-war and estimate the parameters characterizing each state. Results support the prediction that price floors reduce the intensity of price wars but increase their expected duration.price regulation, oligopoly supergame, Markov switching model, gasoline

Tracking ancient beach-lines inland: 2600-year-old dentate-stamped ceramics at Hopo, Vailala River region, Papua New Guinea

The Lapita expansion took Austronesian seafaring peoples with distinctive pottery eastward from the Bismarck Archipelago to western Polynesia during the late second millennium BC, marking the first stage in the settlement of Oceania. Here it is shown that a parallel process also carried Lapita pottery and people many hundreds of kilometres westward along the southern shore of Papua New Guinea. The key site is Hopo, now 4.5km inland owing to the progradation of coastal sand dunes, but originally on the sea edge. Pottery and radiocarbon dates indicate Lapita settlement in this location c.600 BC, and suggest that the long-distance maritime networks linking the entire southern coast of Papua New Guinea in historical times may trace their origin to this period

Political Predation and Economic Development

We analyze a game between citizens and governments, whose type (benevolent or predatory) is unknown to the public. Opportunistic governments mix between predation and restraint. As long as restraint is observed, political expectations improve, people enter the modern sector, and the economy grows. Once there is predation, the reputation of the government is ruined and the economy collapses. If citizens are unable to overthrow this government, the collapse is durable. Otherwise, a new government is drawn and the economy can rebound. Consistent with stylized facts, equilibrium political and economic histories are random, unstable, and exhibit long-term divergence.