Testing Local Lorentz and Position Invariance and Variation of Fundamental Constants by searching the Derivative of the Comparison Frequency Between a Cryogenic Sapphire Oscillator and Hydrogen Maser

The cryogenic sapphire oscillator (CSO) at the Paris Observatory has been continuously compared to various Hydrogen Masers since 2001. The early data sets were used to test Local Lorentz Invariance in the Robertson-Mansouri-Sexl (RMS) framework by searching for sidereal modulations with respect to the Cosmic Microwave Background, and represent the best Kennedy-Thorndike experiment to date. In this work we present continuous operation over a period of greater than six years from September 2002 to December 2008 and present a more precise way to analyze the data by searching the time derivative of the comparison frequency. Due to the long-term operation we are able to search both sidereal and annual modulations. The results gives P_{KT} = \beta_{RMS}-\alpha_{RMS}-1 = -1.7(4.0) \times 10^{-8} for the sidereal and -23(10) \times 10^{-8} for the annual term, with a weighted mean of -4.8(3.7) \times 10^{-8}, a factor of 8 better than previous. Also, we analyze the data with respect to a change in gravitational potential for both diurnal and annual variations. The result gives \beta_{H-Maser} - \beta_{CSO} = -2.7(1.4) \times 10^{-4} for the annual and -6.9(4.0) \times 10^{-4} for the diurnal terms, with a weighted mean of -3.2(1.3) \times 10^{-4}. This result is two orders of magnitude better than other tests that use electromagnetic resonators. With respect to fundamental constants a limit can be provided on the variation with ambient gravitational potential and boost of a combination of the fine structure constant (\alpha), the normalized quark mass (m_q), and the electron to proton mass ratio (m_e/m_p), setting the first limit on boost dependence of order 10^{-10}.Comment: Fixed typo

Test of constancy of speed of light with rotating cryogenic optical resonators

A test of Lorentz invariance for electromagnetic waves was performed by comparing the resonance frequencies of two optical resonators as a function of orientation in space. In terms of the Robertson-Mansouri-Sexl theory, we obtain $\beta-\delta-1/2=(+0.5\pm 3\pm 0.7) E-10$, a ten-fold improvement compared to the previous best results. We also set a first upper limit for a so far unknown parameter of the Standard Model Extension test theory, $|(\tilde{\kappa}_{e-})^{ZZ}| < 2\cdot E-14$.Comment: 4 pages, 2 figures, accepted for publication Phys. Rev. A (2005

Auswirkungen der Schuldenbremse auf die hessischen Landesfinanzen

The debt brake recently introduced into the German constitution forces the German federal states (Länder) to run structurally balanced budgets form 2020 onwards. The study is preoccupied with the potential effects of the debt brakes on the budget of the federal state of Hessen in the transition period until 2020. Although there is substantial leeway as to the exact specification of technical details the results show that even under favourable conditions fiscal policy in Hessen would be forced into severe restriction. Under more unfavourable conditions the ability of the Hessian government to act may be called into question.

Scoring Aave Accounts for Creditworthiness

Scoring the creditworthiness of accounts that interact with decentralized financial (DeFi) protocols remains an important yet unsolved problem. In this paper, we propose a credit scoring system for those accounts that have interacted with the Aave v2 liquidity protocol. The key component of this system is a tree-based binary classifier that predicts "position delinquency." To the community, we provide our method, results, and the (abridged) dataset on which this system is built

Improved test of Lorentz Invariance in Electrodynamics using Rotating Cryogenic Sapphire Oscillators

We present new results from our test of Lorentz invariance, which compares two orthogonal cryogenic sapphire microwave oscillators rotating in the lab. We have now acquired over 1 year of data, allowing us to avoid the short data set approximation (less than 1 year) that assumes no cancelation occurs between the $\tilde{\kappa}_{e-}$ and $\tilde{\kappa}_{o+}$ parameters from the photon sector of the standard model extension. Thus, we are able to place independent limits on all eight $\tilde{\kappa}_{e-}$ and $\tilde{\kappa}_{o+}$ parameters. Our results represents up to a factor of 10 improvement over previous non rotating measurements (which independently constrained 7 parameters), and is a slight improvement (except for $\tilde{\kappa}_{e-}^{ZZ}$) over results from previous rotating experiments that assumed the short data set approximation. Also, an analysis in the Robertson-Mansouri-Sexl framework allows us to place a new limit on the isotropy parameter $P_{MM}=\delta-\beta+{1/2}$ of $9.4(8.1)\times10^{-11}$, an improvement of a factor of 2.Comment: Accepted for publication in Phys. Rev.

Defining a day-ahead spot market for unbundled time-specific renewable energy certificates

One option to counteract anthropogenic climate change is to increase the share of renewable electricity supply. Current market structures provide only a limited framework for the creation of “green” electricity tariffs, which are often criticised as “greenwashing”, lacking transparency, and ineffective investment signalling. This paper defines and discusses a day-ahead spot market for tradable (short-term) time-specific renewable energy certificates (REC). Implementing an unbundled spot market for REC promises a more credible provision of renewable electricity, along with a mechanism rewarding flexibility in renewable production and storage as well as tangible investment signals

Dynamical orbital effects of General Relativity on the satellite-to-satellite range and range-rate in the GRACE mission: a sensitivity analysis

We numerically investigate the impact of GTR on the orbital part of the satellite-to-satellite range \rho and range-rate \dot\rho of the twin GRACE A/B spacecrafts through their dynamical equations of motion integrated in an Earth-centered frame over a time span \Delta t=1 d. Instead, the GTR effects connected with the propagation of the electromagnetic waves linking the spacecrafts are neglected. The present-day accuracies in measuring the GRACE biased range and range-rate are \sigma_\rho\sim 1-10 \mum, \sigma_\dot\rho\sim 0.1-1 \mum s^-1; studies for a follow-on of such a mission points toward a range-rate accuracy of the order of \sigma_\dot\rho\sim 1 nm s^-1 or better. The GTR range and range-rate effects turn out to be \Delta\rho=80 \mum and \Delta\dot\rho=0.012 \mum s^-1 (Lense-Thirring), and \Delta\rho=6000 \mum and \Delta\dot\rho=10 \mum s^-1 (Schwarzschild). We also compute the dynamical range and range-rate perturbations caused by the first six zonal harmonic coefficients J_L, L=2,3,4,5,6,7 of the classical multipolar expansion of the terrestrial gravitational potential in order to evaluate their aliasing impact on the relativistic effects. Conversely, we also quantitatively, and preliminarily, assess the possible a-priori \virg{imprinting} of GTR itself, not solved-for in all the GRACE-based Earth's gravity models produced so far, on the estimated values of the low degree zonals of the geopotential. The present sensitivity analysis can also be extended, in principle, to different orbital configurations in order to design a suitable dedicated mission able to accurately measure the relativistic effects considered.Comment: LaTex, 24 pages, 5 figures, 9 tables. Accepted for publication in Advances in Space Research (ASR

Laser cooling scheme for the carbon dimer (12C2)

We report on a scheme for laser cooling of 12 C 2 . We have calculated the branching ratios for cycling and repumping transitions and calculated the number of photon scatterings required to achieve deflection and laser cooling of a beam of C 2 molecules under realistic experimental conditions. Our results demonstrate that C 2 cooling using the Swan ( d 3 Π g ↔ a 3 Π u ) and so-called Duck ( d 3 Π g ↔ c 3 Σ + u ) bands is achievable via techniques similar to state-of-the-art molecular cooling experiments. The Phillips ( A 1 Π u ↔ X 1 Σ + g ) and Ballik-Ramsay ( b 3 Σ − g ↔ a 3 Π u ) bands offer the potential for narrow-line cooling. This work opens up a path to cooling of molecules with carbon-carbon bonds and may pave the way toward quantum control of organic molecules

Atom Interferometers and the Gravitational Redshift

From the principle of equivalence, Einstein predicted that clocks slow down in a gravitational field. Since the general theory of relativity is based on the principle of equivalence, it is essential to test this prediction accurately. Muller, Peters and Chu claim that a reinterpretation of decade old experiments with atom interferometers leads to a sensitive test of this gravitational redshift effect at the Compton frequency. Wolf et al dispute this claim and adduce arguments against it. In this article, we distill these arguments to a single fundamental objection: an atom is NOT a clock ticking at the Compton frequency. We conclude that atom interferometry experiments conducted to date do not yield such sensitive tests of the gravitational redshift. Finally, we suggest a new interferometric experiment to measure the gravitational redshift, which realises a quantum version of the classical clock "paradox".Comment: 18 pages, one figure, improved discussion, corrected typo