Adaptive stepsize and instabilities in complex Langevin dynamics

Stochastic quantization offers the opportunity to simulate field theories with a complex action. In some theories unstable trajectories are prevalent when a constant stepsize is employed. We construct algorithms for generating an adaptive stepsize in complex Langevin simulations and find that unstable trajectories are completely eliminated. To illustrate the generality of the approach, we apply it to the three-dimensional XY model at nonzero chemical potential and the heavy dense limit of QCD.Comment: 12 pages, several eps figures; clarification and minor corrections added, to appear in PL

An Online Bibliography on Scheme Evolution

We briefly motivate and present a new online bibliography on schema evolution, an area which has recently gained much interest in both research and practice

Data Warehousing Scenarios for Model Management

Model management is a framework for supporting meta-data related applications where models and mappings are manipulated as first class objects using operations such as Match, Merge, ApplyFunction, and Compose. To demonstrate the approach, we show how to use model management in two scenarios related to loading data warehouses. The case study illustrates the value of model management as a methodology for approaching meta-data related problems. It also helps clarify the required semantics of key operations. These detailed scenarios provide evidence that generic model management is useful and, very likely, implementable

Tests of the Efficient Markets Hypothesis

This paper surveys various statistical methods that have been proposed for the examination of the efficiency of financial markets and proposes a novel procedure for testing the predictability of a time series. For illustration, this procedure is applied to Austrian stock return series

Optical control of internal electric fields in band-gap graded InGaN nanowires

InGaN nanowires are suitable building blocks for many future optoelectronic devices. We show that a linear grading of the indium content along the nanowire axis from GaN to InN introduces an internal electric field evoking a photocurrent. Consistent with quantitative band structure simulations we observe a sign change in the measured photocurrent as a function of photon flux. This negative differential photocurrent opens the path to a new type of nanowire-based photodetector. We demonstrate that the photocurrent response of the nanowires is as fast as 1.5 ps

Bose-Einstein condensation at constant temperature

We present a novel experimental approach to Bose-Einstein condensation by increasing the particle number of the system at almost constant temperature. In particular the emergence of a new condensate is observed in multi-component F=1 spinor condensates of 87-Rb. Furthermore we develop a simple rate-equation model for multi-component BEC thermodynamics at finite temperature which well reproduces the measured effects.Comment: 4 pages, 3 figures, RevTe

Extensions and block decompositions for finite-dimensional representations of equivariant map algebras

Suppose a finite group acts on a scheme $X$ and a finite-dimensional Lie algebra $\mathfrak{g}$. The associated equivariant map algebra is the Lie algebra of equivariant regular maps from $X$ to $\mathfrak{g}$. The irreducible finite-dimensional representations of these algebras were classified in previous work with P. Senesi, where it was shown that they are all tensor products of evaluation representations and one-dimensional representations. In the current paper, we describe the extensions between irreducible finite-dimensional representations of an equivariant map algebra in the case that $X$ is an affine scheme of finite type and $\mathfrak{g}$ is reductive. This allows us to also describe explicitly the blocks of the category of finite-dimensional representations in terms of spectral characters, whose definition we extend to this general setting. Applying our results to the case of generalized current algebras (the case where the group acting is trivial), we recover known results but with very different proofs. For (twisted) loop algebras, we recover known results on block decompositions (again with very different proofs) and new explicit formulas for extensions. Finally, specializing our results to the case of (twisted) multiloop algebras and generalized Onsager algebras yields previously unknown results on both extensions and block decompositions.Comment: 41 pages; v2: minor corrections, formatting changed to match published versio

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator, this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the first experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realising 1+1-dimensional quantum electrodynamics (Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which have a direct and efficient implementation on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulating high-energy theories with atomic physics experiments, the long-term vision being the extension to real-time quantum simulations of non-Abelian lattice gauge theories