Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices

Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and $PT$-symmetric examples are studied, a Hatano-Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.Comment: 20 pages, 8 figures, typos corrected, slightly extended, accepted for publication in New Journal of Physics in Focus Issue on Parity-Time Symmetry in Optics and Photonic

Instant restore after a media failure

Media failures usually leave database systems unavailable for several hours until recovery is complete, especially in applications with large devices and high transaction volume. Previous work introduced a technique called single-pass restore, which increases restore bandwidth and thus substantially decreases time to repair. Instant restore goes further as it permits read/write access to any data on a device undergoing restore--even data not yet restored--by restoring individual data segments on demand. Thus, the restore process is guided primarily by the needs of applications, and the observed mean time to repair is effectively reduced from several hours to a few seconds. This paper presents an implementation and evaluation of instant restore. The technique is incrementally implemented on a system starting with the traditional ARIES design for logging and recovery. Experiments show that the transaction latency perceived after a media failure can be cut down to less than a second and that the overhead imposed by the technique on normal processing is minimal. The net effect is that a few "nines" of availability are added to the system using simple and low-overhead software techniques

Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances

We study the properties of coupled linear and nonlinear resonances. The fundamental phenomena and the level crossing scenarios are introduced for a nonlinear two-level system with one decaying state, describing the dynamics of a Bose-Einstein condensate in a mean-field approximation (Gross-Pitaevskii or nonlinear Schroedinger equation). An important application of the discussed concepts is the dynamics of a condensate in tilted optical lattices. In particular the properties of resonance eigenstates in double-periodic lattices are discussed, in the linear case as well as within mean-field theory. The decay is strongly altered, if an additional period-doubled lattice is introduced. Our analytic study is supported by numerical computations of nonlinear resonance states, and future applications of our findings for experiments with ultracold atoms are discussed.Comment: 12 pages, 17 figure

Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer

We investigate an $N$-particle Bose-Hubbard dimer with an additional effective decay term in one of the sites. A mean-field approximation for this non-Hermitian many-particle system is derived, based on a coherent state approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in particular the fixed point structures showing characteristic modifications of the self-trapping transition, are analyzed. The mean-field dynamics is found to be in reasonable agreement with the full many-particle evolution.Comment: 4 pages, 3 figures, published versio

Conditions Under Which Index Models Are Useful

This paper summarizes the key conditions under which the index method is valuable for forecasting and describes the procedures one should use when developing index models. The paper also addresses the specific concern of selecting inferior candidates when using the bio-index as a nomination helper. Political decision-makers should not use the bioindex as a stand-alone method but should combine forecasts from a variety of different methods that draw upon different information

Comparing Face-to-Face Meetings, Nominal Groups, Delphi and Prediction Markets on an Estimation Task

We conducted laboratory experiments to analyze the accuracy of three structured approaches (nominal groups, Delphi, and prediction markets) compared to traditional face-to-face meetings (FTF). We recruited 227 participants (11 groups per method) that had to solve a quantitative judgment task that did not involve distributed knowledge. This task consisted of ten factual questions, which required percentage estimates. While, overall, we did not find statistically significant differences in accuracy between the four methods, the results differed somewhat at the individual question level. Delphi was as accurate as FTF for eight questions and outperformed FTF for two questions. By comparison, prediction markets were unable to outperform FTF for any of the ten questions but were inferior for three questions. The relative performance of nominal groups and FTF was mixed and differences were small. We also compared the results from the three structured approaches to prior individual estimates and staticized groups. The three structured approaches were more accurate than participants’ prior individual estimates. Delphi was also more accurate than staticized groups. Nominal groups and prediction markets provided little additional value compared to a simple average of forecast. In addition, we examined participants’ perceptions of the group and the group process. Participants rated personal communication more favorable than computer-mediated interaction. Group interaction in FTF and nominal groups was perceived as highly cooperative and effective. Prediction markets were rated least favorable. Prediction market participants were least satisfied with the group process and perceived their method as most difficult

Predicting Elections from the Most Important Issue: A Test of the Take-the-Best Heuristic

We used the take-the-best heuristic to develop a model to forecast the popular twoparty vote shares in U.S. presidential elections. The model draws upon information about how voters expect the candidates to deal with the most important issue facing the country. We used cross-validation to calculate a total of 1,000 out-of-sample forecasts, one for each of the last 100 days of the ten U.S. presidential elections from 1972 to 2008. Ninety-seven percent of forecasts correctly predicted the winner of the popular vote. The model forecasts were competitive compared to forecasts from methods that incorporate substantially more information (e.g., econometric models and the Iowa Electronic Markets). The purpose of the model is to provide fast advice on which issues candidates should stress in their campaign

Predicting Elections from Biographical Information about Candidates: A Test of the Index Method

We used 59 biographical variables to create a “bio-index” for forecasting U.S. presidential elections. The bio-index method counts the number of variables for which a candidate rates favourably, and the forecast is that the candidate with the highest score would win the popular vote. The bio-index relies on different information and includes more variables than traditional econometric election forecasting models. The method can be used in combination with simple linear regression to estimate a relationship between the index score of the candidate of the incumbent party and his share of the popular vote. The study tested the model for the 29 U.S. presidential elections from 1896 to 2008. The model‟s forecasts, calculated by cross-validation, correctly predicted the popular vote winner for 27 of the 29 elections; this performance compares favourably to forecasts from polls (15 out of 19), prediction markets (22 out of 26), and three econometric models (12 to 13 out of 15 to 16). Out-of-sample forecasts of the two-party popular vote for the four elections from 1996 to 2008 yielded a forecast error almost as low as the best of seven econometric models. The model can help parties to select the candidates running for office, and it can help to improve on the accuracy of election forecasting, especially for longer-term forecasts

Main Memory Implementations for Binary Grouping

An increasing number of applications depend on efficient storage and analysis features for XML data. Hence, query optimization and efficient evaluation techniques for the emerging XQuery standard become more and more important. Many XQuery queries require nested expressions. Unnesting them often introduces binary grouping. We introduce several algorithms implementing binary grouping and analyze their time and space complexity. Experiments demonstrate their performance