Asymptotics of relative heat traces and determinants on open surfaces of finite area

The goal of this paper is to prove that on surfaces with asymptotically cusp ends the relative determinant of pairs of Laplace operators is well defined. We consider a surface with cusps (M,g) and a metric h on the surface that is a conformal transformation of the initial metric g. We prove the existence of the relative determinant of the pair $(\Delta_{h},\Delta_{g})$ under suitable conditions on the conformal factor. The core of the paper is the proof of the existence of an asymptotic expansion of the relative heat trace for small times. We find the decay of the conformal factor at infinity for which this asymptotic expansion exists and the relative determinant is defined. Following the paper by B. Osgood, R. Phillips and P. Sarnak about extremal of determinants on compact surfaces, we prove Polyakov's formula for the relative determinant and discuss the extremal problem inside a conformal class. We discuss necessary conditions for the existence of a maximizer.Comment: This is the final version of the article before it gets published. 51 page

Color terms: Native language semantic structure and artificial language structure formation in a large-scale online smartphone application

Artificial language games give researchers the opportunity to investigate the emergence and evolution of semantic structure, i.e. the organization of meaning spaces into discrete categories. A possible issue for this approach is that categories might simply carry over from participants’ native languages, a potential bias that has mostly been ignored. We investigate this in a referential communication game by comparing color terms from three different languages to those of an artificial language. Here, we assess the similarity of the semantic structures, and test the influence of the semantic structure on artificial language communication. We compare the in-game communication to a separate online naming task providing us with the native language structure. Our results show that native and artificial language structure overlap at least moderately. Furthermore, communicative behavior and performance were influenced by the shared semantic structure, but only for English-speaking pairs. These results imply a cognitive link between participants’ semantic structures and artificial language structure formation.1. Introduction - Artificial language games, semantic structure, and possible biases - Color terms and categorical facilitation 2. Method - The Color Game -- Participants -- Materials -- Procedure - Online survey -- Participants -- Materials -- Procedure - Predictions 3. Results - Prediction 1 - Prediction 2.1 - Prediction 2.2 - Prediction 2.3 - Prediction 3 4. Discussion 5. Conclusio

Mesoscopic Rydberg Gate based on Electromagnetically Induced Transparency

We demonstrate theoretically a parallelized C-NOT gate which allows to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond timescale. Our scheme relies on the strong and long-ranged interaction between Rydberg atoms triggering Electromagnetically Induced Transparency (EIT). By this we can robustly implement a conditional transfer of all ensemble atoms among two logical states, depending on the state of the control atom. We outline a many body interferometer which allows a comparison of two many-body quantum states by performing a measurement of the control atom.Comment: published versio

A SiGe HEMT Mixer IC with Low Conversion Loss

The authors present the first SiGe HEMT mixer integrated circuit. The active mixer stage, operating up to 10GHz RF, has been designed and realized using a 0.1µ µµ µm gate length transistor technology. The design is based on a new large-signal simulation model developed for the SiGe HEMT. Good agreement between simulation and measurement is reached. The mixer exhibits 4.0dB and 4.7dB conversion loss when down-converting 3.0GHz and 6.0GHz signals, respectively, to an intermediate frequency of 500MHz using high-side injection of 5dBm local oscillator power. Conversion loss is less than 8dB for RF frequencies up to 10GHz with a mixer linearity of –8.8dBm input related 1dB compression point

Enhanced dielectrophoresis of nanocolloids by dimer formation

We investigate the dielectrophoretic motion of charge-neutral, polarizable nanocolloids through molecular dynamics simulations. Comparison to analytical results derived for continuum systems shows that the discrete charge distributions on the nanocolloids have a significant impact on their coupling to the external field. Aggregation of nanocolloids leads to enhanced dielectrophoretic transport, provided that increase in the dipole moment upon aggregation can overcome the related increase in friction. The dimer orientation and the exact structure of the nanocolloid charge distribution are shown to be important in the enhanced transport

Nucleosynthesis and Clump Formation in a Core Collapse Supernova

High-resolution two-dimensional simulations were performed for the first five minutes of the evolution of a core collapse supernova explosion in a 15 solar mass blue supergiant progenitor. The computations start shortly after bounce and include neutrino-matter interactions by using a light-bulb approximation for the neutrinos, and a treatment of the nucleosynthesis due to explosive silicon and oxygen burning. We find that newly formed iron-group elements are distributed throughout the inner half of the helium core by Rayleigh-Taylor instabilities at the Ni+Si/O and C+O/He interfaces, seeded by convective overturn during the early stages of the explosion. Fast moving nickel mushrooms with velocities up to about 4000 km/s are observed. This offers a natural explanation for the mixing required in light curve and spectral synthesis studies of Type Ib explosions. A continuation of the calculations to later times, however, indicates that the iron velocities observed in SN 1987 A cannot be reproduced because of a strong deceleration of the clumps in the dense shell left behind by the shock at the He/H interface.Comment: 8 pages, LaTeX, 2 postscript figures, 2 gif figures, shortened and slightly revised text and references, accepted by ApJ Letter

Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second part, see math-ph/0105046. To appear in Reviews in Mathematical Physic

Trapped-Atom-Interferometer in a Magnetic Microtrap

We propose a configuration of a magnetic microtrap which can be used as an interferometer for three-dimensionally trapped atoms. The interferometer is realized via a dynamic splitting potential that transforms from a single well into two separate wells and back. The ports of the interferometer are neighboring vibrational states in the single well potential. We present a one-dimensional model of this interferometer and compute the probability of unwanted vibrational excitations for a realistic magnetic potential. We optimize the speed of the splitting process in order suppress these excitations and conclude that such interferometer device should be feasible with currently available microtrap technique.Comment: 6 pages, 6 figures, submitted to PR

Ectoplasm & Superspace Integration Measure for 2D Supergravity with Four Spinorial Supercurrents

Building on a previous derivation of the local chiral projector for a two dimensional superspace with eight real supercharges, we provide the complete density projection formula required for locally supersymmetrical theories in this context. The derivation of this result is shown to be very efficient using techniques based on the Ectoplasmic construction of local measures in superspace.Comment: 18 pages, LaTeX; V2: minor changes, typos corrected, references added; V3: version to appear in J. Phys. A: Math. Theor., some comments and references added to address a referee reques

Installing a Fast Orbit Feedback at BESSY

In view of increased processing bandwidth at demanding experiments and the need for rapid compensation of noise spikes and new, yet unknown excitations, a fast orbit feedback aiming at noise suppression in the 1Hz 50Hz range has become mandatory for the 3rd generation light source BESSY II. The fast set point transmission plus the replacement of all corrector power supplies is scheduled as a first step. Later in combination with top up operation orbit stability can be further improved by replacing today s multiplexed analog beam position monitors by state of the art fast digital units. This paper describes how the pilot installation of a small subset of fast corrector power supplies allows to tune performance and study the benefits for today s most sensitive experiment