Non-equilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission

We analyze in detail the heating of bosonic atoms in an optical lattice due to incoherent scattering of light from the lasers forming the lattice. Because atoms scattered into higher bands do not thermalize on the timescale of typical experiments, this process cannot be described by the total energy increase in the system alone (which is determined by single-particle effects). The heating instead involves an important interplay between the atomic physics of the heating process and the many-body physics of the state. We characterize the effects on many-body states for various system parameters, where we observe important differences in the heating for strongly and weakly interacting regimes, as well as a strong dependence on the sign of the laser detuning from the excited atomic state. We compute heating rates and changes to characteristic correlation functions based both on perturbation theory calculations, and a time-dependent calculation of the dissipative many-body dynamics. The latter is made possible for 1D systems by combining time-dependent density matrix renormalization group (t-DMRG) methods with quantum trajectory techniques.Comment: 17 pages, 14 figure

Measuring entanglement growth in quench dynamics of bosons in an optical lattice

We discuss a scheme to measure the many-body entanglement growth during quench dynamics with bosonic atoms in optical lattices. By making use of a 1D or 2D setup in which two copies of the same state are prepared, we show how arbitrary order Renyi entropies can be extracted using tunnel-coupling between the copies and measurement of the parity of on-site occupation numbers, as has been performed in recent experiments. We illustrate these ideas for a Superfluid-Mott insulator quench in the Bose-Hubbard model, and also for hard-core bosons, and show that the scheme is robust against imperfections in the measurements.Comment: 4+ pages plus supplementary materia

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

Incidence of the Tomonaga-Luttinger liquid state on the NMR spin lattice relaxation in Carbon Nanotubes

We report 13C nuclear magnetic resonance measurements on single wall carbon nanotube (SWCNT) bundles. The temperature dependence of the nuclear spin-lattice relaxation rate, 1/T1, exhibits a power-law variation, as expected for a Tomonage-Luttinger liquid (TLL). The observed exponent is smaller than that expected for the two band TLL model. A departure from the power law is observed only at low T, where thermal and electronic Zeeman energy merge. Extrapolation to zero magnetic field indicates gapless spin excitations. The wide T range on which power-law behavior is observed suggests that SWCNT is so far the best realization of a one-dimensional quantum metal.Comment: 5 pages, 4 figure

Central bank independence and the monetary instrument problem

We study the monetary instrument problem in a model of optimal discretionary fiscal and monetary policy. The policy problem is cast as a dynamic game between the central bank, the fiscal authority, and the private sector. We show that, as long as there is a conflict of interest between the two policy-makers, the central bank's monetary instrument choice critically affects the Markov-perfect Nash equilibrium of this game. Focusing on a scenario where the fiscal authority is impatient relative to the monetary authority, we show that the equilibrium allocation is typically characterized by a public spending bias if the central bank uses the nominal money supply as its instrument. If it uses instead the nominal interest rate, the central bank can prevent distortions due to fiscal impatience and implement the same equilibrium allocation that would obtain under cooperation of two benevolent policy authorities. Despite this property, the welfare-maximizing choice of instrument depends on the economic environment under consideration. In particular, the money growth instrument is to be preferred whenever fiscal impatience has positive welfare effects, which is easily possible under lack of commitment

Optimal Fiscal and Monetary Policy Without Commitment

This paper studies optimal fiscal and monetary policy in a stochastic economy with imperfectly competitive product markets and a discretionary government. We find that, in the flexible price economy, optimal time-consistent policy implements the Friedman rule independently of the degree of imperfect competition. This result is in contrast to the Ramsey literature, where the Friedman rule emerges as the optimal policy only if markets are perfectly competitive. Second, once nominal rigidities are introduced, the Friedman rule ceases to be optimal, inflation rates are low and stable, and tax rates are relatively volatile. Finally, optimal time-consistent policy under sticky prices does not generate the near-random walk behavior of taxes and real debt that can be observed under optimal policy in the Ramsey problem. A common reason for these results is that the discretionary government, in an effort to asymptotically eliminate its time-consistency problem, accumulates a large net asset position such that it can finance its expenditures via the associated interest earnings

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