Construction of G_2-instantons via twisted connected sums

We propose a method to construct G_2-instantons over a compact twisted connected sum G_2-manifold, applying a gluing result of S\'a Earp and Walpuski to instantons over a pair of 7-manifolds with a tubular end (see arXiv:1310.7933). In our example, the moduli spaces of the ingredient instantons are non-trivial, and their images in the moduli space over the asymptotic cross-section K3 surface intersect transversely. Such a pair of asymptotically stable holomorphic bundles is obtained using a twisted version of the Hartshorne-Serre construction, which can be adapted to produce other examples. Moreover, their deformation theory and asymptotic behaviour are explicitly understood, results which may be of independent interest.Comment: 22 pages. Final version to appear in Mathematical Research Letter

Thermalization of a Lipkin-Meshkov-Glick model coupled to a bosonic bath

We derive a Lindblad master equation that approximates the dynamics of a Lipkin-Meshkov-Glick (LMG) model weakly coupled to a bosonic bath. By studying the time evolution of operators under the adjoint master equation we prove that, for large system sizes, these operators attain their thermal equilibrium expectation values in the long-time limit, and we calculate the rate at which these values are approached. Integrability of the LMG model prevents thermalization in the absence of a bath, and our work provides an explicit proof that the bath indeed restores thermalization. Imposing thermalization on this otherwise non-thermalizing model outlines an avenue towards probing the unconventional thermodynamic properties predicted to occur in ultracold-atom-based realizations of the LMG model.Comment: 10 pages, 3 figure

Origin of the structural phase transition in Li7La3Zr2O12

Garnet-type Li7La3Zr2O12 (LLZO) is a solid electrolyte material with a low-conductivity tetragonal and a high-conductivity cubic phase. Using density-functional theory and variable cell shape molecular dynamics simulations, we show that the tetragonal phase stability is dependent on a simultaneous ordering of the Li ions on the Li sublattice and a volume-preserving tetragonal distortion that relieves internal structural strain. Supervalent doping introduces vacancies into the Li sublattice, increasing the overall entropy and reducing the free energy gain from ordering, eventually stabilizing the cubic phase. We show that the critical temperature for cubic phase stability is lowered as Li vacancy concentration (dopant level) is raised and that an activated hop of Li ions from one crystallographic site to another always accompanies the transition. By identifying the relevant mechanism and critical concentrations for achieving the high conductivity phase, this work shows how targeted synthesis could be used to improve electrolytic performance

Transport properties in resonant tunneling heterostructures

We use an adiabatic approximation in terms of instantaneous resonances to study the steady-state and time-dependent transport properties of interacting electrons in biased resonant tunneling heterostructures. This approach leads, in a natural way, to a transport model of large applicability consisting of reservoirs coupled to regions where the system is described by a nonlinear Schr\"odinger equation. From the mathematical point of view, this work is non-rigorous but may offer some fresh and interesting problems involving semiclassical approximation, adiabatic theory, non-linear Schr\"odinger equations and dynamical systems.Comment: 25 pages including 9 postscript figures; requires REVTeX 3.0, psfig; uuencoded gz-compressed .tar file; preprint 1133 April 96 Ecole Polytechnique to be published in J. Math. Phys. october 199

The puzzle of non-participation in continuing training : an empirical study of chronic vs. temporary non-participation

"Although participation in continuing vocational training is often found to be associated with considerable individual benefits, a puzzlingly large number of people still do not take part in training. In order to solve the puzzle we distinguish between temporary and chronic non-participants. Previous studies have shown that training participants and non-participants differ in unobservable characteristics and therefore self-select into training or not. We show that even non-participants cannot be treated as a homogeneous group: there are those who never take part in training (chronic non-participants) and those who are not currently taking part (temporary (non-)participants). Using a unique data set of non-participants commissioned by the German 'Expert Commission on Financing Lifelong Learning' and covering a very large number of individuals not taking part in training, we separate and compare chronic and temporary non-participants. By estimating a sample selection model using maximum likelihood estimation we take potential selection effects into account: temporary (non-)participants may be more motivated or may have different inherent skills than chronic nonparticipants. We find that chronic non-participants would have higher costs than temporary (non-)participants and their short-term benefits associated with their current jobs would be lower. However, in the long run even chronic non-participants would benefit similarly from participation due to improved prospects on the labor market. The results indicate that chronic non-participants either misperceive future developments or suffer from an exceptionally high discount rate, which in turn leads in their view to a negative cost-benefit ratio for training." (Author's abstract, IAB-Doku) ((en)) Additional Information Kurzfassung (deutsch) Executive summary (English)Weiterbildung, Teilnehmer, Bildungsbeteiligung, Bildungsinvestitionen, Bildungsertrag, Kosten-Nutzen-Analyse, Bildungsökonomie

Unbiased All-Optical Random-Number Generator

The generation of random bits is of enormous importance in modern information science. Cryptographic security is based on random numbers which require a physical process for their generation. This is commonly performed by hardware random number generators. These exhibit often a number of problems, namely experimental bias, memory in the system, and other technical subtleties, which reduce the reliability in the entropy estimation. Further, the generated outcome has to be post-processed to "iron out" such spurious effects. Here, we present a purely optical randomness generator, based on the bi-stable output of an optical parametric oscillator. Detector noise plays no role and no further post-processing is required. Upon entering the bi-stable regime, initially the resulting output phase depends on vacuum fluctuations. Later, the phase is rigidly locked and can be well determined versus a pulse train, which is derived from the pump laser. This delivers an ambiguity-free output, which is reliably detected and associated with a binary outcome. The resulting random bit stream resembles a perfect coin toss and passes all relevant randomness measures. The random nature of the generated binary outcome is furthermore confirmed by an analysis of resulting conditional entropies.Comment: 10 pages, 4 figure