In search of grammaticalization in synchronic dialect data: General extenders in north-east England

In this paper, we draw on a socially stratified corpus of dialect data collected in north-east England to test recent proposals that grammaticalization processes are implicated in the synchronic variability of general extenders (GEs), i.e., phrase- or clause-final constructions such as and that and or something. Combining theoretical insights from the framework of grammaticalization with the empirical methods of variationist sociolinguistics, we operationalize key diagnostics of grammaticalization (syntagmatic length, decategorialization, semantic-pragmatic change) as independent factor groups in the quantitative analysis of GE variability. While multivariate analyses reveal rapid changes in apparent time to the social conditioning of some GE variants in our data, they do not reveal any evidence of systematic changes in the linguistic conditioning of variants in apparent time that would confirm an interpretation of ongoing grammaticalization. These results lead us to questio

Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation

We show that gauge invariant quantum link models, Abelian and non-Abelian, can be exactly described in terms of tensor networks states. Quantum link models represent an ideal bridge between high-energy to cold atom physics, as they can be used in cold-atoms in optical lattices to study lattice gauge theories. In this framework, we characterize the phase diagram of a (1+1)-d quantum link version of the Schwinger model in an external classical background electric field: the quantum phase transition from a charge and parity ordered phase with non-zero electric flux to a disordered one with a net zero electric flux configuration is described by the Ising universality class.Comment: 9 pages, 9 figures. Published versio

Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks

Tensor network algorithms provide a suitable route for tackling real-time dependent problems in lattice gauge theories, enabling the investigation of out-of-equilibrium dynamics. We analyze a U(1) lattice gauge theory in (1+1) dimensions in the presence of dynamical matter for different mass and electric field couplings, a theory akin to quantum-electrodynamics in one-dimension, which displays string-breaking: the confining string between charges can spontaneously break during quench experiments, giving rise to charge-anticharge pairs according to the Schwinger mechanism. We study the real-time spreading of excitations in the system by means of electric field and particle fluctuations: we determine a dynamical state diagram for string breaking and quantitatively evaluate the time-scales for mass production. We also show that the time evolution of the quantum correlations can be detected via bipartite von Neumann entropies, thus demonstrating that the Schwinger mechanism is tightly linked to entanglement spreading. To present the variety of possible applications of this simulation platform, we show how one could follow the real-time scattering processes between mesons and the creation of entanglement during scattering processes. Finally, we test the quality of quantum simulations of these dynamics, quantifying the role of possible imperfections in cold atoms, trapped ions, and superconducting circuit systems. Our results demonstrate how entanglement properties can be used to deepen our understanding of basic phenomena in the real-time dynamics of gauge theories such as string breaking and collisions.Comment: 15 pages, 25 figures. Published versio

Collateral, liquidity and debt sustainability

We study the sustainability of public debt in a closed production economy where a benevolent government chooses fiscal policies, including haircuts on its outstanding debt, in a discretionary manner. Government bonds are held by domestic agents to smooth consumption over time and because they provide collateral and liquidity services. We characterize a recursive equilibrium where public debt amounts to a sizeable fraction of output in steady state and is nevertheless fully serviced by the government. In a calibrated economy, steady state debt amounts to around 84% of output, the government's default threshold is at around 94% of output, and the haircut on outstanding debt at this threshold is around 40%. Both reputational costs of default and contemporaneous costs due to lost collateral and liquidity are essential to generate these empirically plausible predictions

The tractability frontier of well-designed SPARQL queries

We study the complexity of query evaluation of SPARQL queries. We focus on the fundamental fragment of well-designed SPARQL restricted to the AND, OPTIONAL and UNION operators. Our main result is a structural characterisation of the classes of well-designed queries that can be evaluated in polynomial time. In particular, we introduce a new notion of width called domination width, which relies on the well-known notion of treewidth. We show that, under some complexity theoretic assumptions, the classes of well-designed queries that can be evaluated in polynomial time are precisely those of bounded domination width

New bulk scalar field solutions in brane worlds

We use nonlinear perturbation theory to obtain new solutions for brane world models that incorporate a massive bulk scalar field. We then consider tensor perturbations and show that Newtonian gravity is recovered on the brane for both a light scalar field and for a bulk field with large negative mass. This latter result points to the viability of higher-derivative theories of gravity in the context of bulk extra dimensions.Comment: 4+\epsilon pages, no figure

Quantum Spin Lenses in Atomic Arrays

We propose and discuss `quantum spin lenses', where quantum states of delocalized spin excitations in an atomic medium are `focused' in space in a coherent quantum process down to (essentially) single atoms. These can be employed to create controlled interactions in a quantum light-matter interface, where photonic qubits stored in an atomic ensemble are mapped to a quantum register represented by single atoms. We propose Hamiltonians for quantum spin lenses as inhomogeneous spin models on lattices, which can be realized with Rydberg atoms in 1D, 2D and 3D, and with strings of trapped ions. We discuss both linear and non-linear quantum spin lenses: in a non-linear lens, repulsive spin-spin interactions lead to focusing dynamics conditional to the number of spin excitations. This allows the mapping of quantum superpositions of delocalized spin excitations to superpositions of spatial spin patterns, which can be addressed by light fields and manipulated. Finally, we propose multifocal quantum spin lenses as a way to generate and distribute entanglement between distant atoms in an atomic lattice array.Comment: 13 pages, 9 figure