Phase separation in the vicinity of "quantum critical" doping concentration: implications for high temperature superconductors

A general quantitative measure of the tendency towards phase separation is introduced for systems exhibiting phase transitions or crossovers controlled by charge carrier concentration. This measure is devised for the situations when the quantitative knowledge of various contributions to free energy is incomplete, and is applied to evaluate the chances of electronic phase separation associated with the onset of antiferromagnetic correlations in high-temperature cuprate superconductors. The experimental phenomenology of lanthanum- and yittrium-based cuprates was used as input to this analysis. It is also pointed out that Coulomb repulsion between charge carriers separated by the distances of 1-3 lattice periods strengthens the tendency towards phase separation by accelerating the decay of antiferromagnetic correlations with doping. Overall, the present analysis indicates that cuprates are realistically close to the threshold of phase separation -- nanoscale limited or even macroscopic with charge density varying between adjacent crystal planes

Comment on "Proposed molecular test of local hidden-variables theories"

Lo and Shimony have proposed a molecular test of local hidden-variables theories, which should eliminate a loophole arising in all tests dealing with photons. It is pointed out that the proposed correction for accidental coincidences invalidates the test. Conditions for the reliability of the experiment are stated

Analog Computer Research

Contains reports on three research projects

Asymptotic and intermediate long-time behavior of nuclear free induction decays in polycrystalline solids and powders

Free induction decay (FID) measured by nuclear magnetic resonance (NMR) in a polycrystalline solid is the isotropic average of the FIDs for individual single crystallites. It has been recently proposed theoretically and verified experimentally that the long-time behavior of single-crystal FIDs has the universal form of exponentially decaying sinusoidal oscillations. Polycrystalline averaging complicates the situation theoretically, while the available experimental evidence is also ambiguous. Exponentially decaying sinusoidal oscillations have been observed for Xe-129 in polycrystalline solid xenon but not for F-19 in the powder of CaF2. In this paper, we present the first principles FID calculations for the powders of both CaF2 and solid xenon. In both cases, the asymptotic long-time behavior has the expected form of exponentially decaying sinusoidal oscillations, which is determined by the single crystallite FID with the slowest exponential decay. However, this behavior appears only at rather small values of the signal that have not yet been measured in experiments. At intermediate times accessible experimentally, a polycrystalline FID depends on the distribution of the exponential decay constants and oscillation frequencies for single crystallite FIDs. In CaF2, these parameters are relatively broadly distributed, and as a result, the sinusoidal long-time oscillations become somewhat washed out. In contrast, the single crystallite parameters are more clustered in solid xenon, and, as a result, the experimentally observable range is characterized by well-defined oscillation frequency and exponential decay constant even though both of these parameters do not represent the true long-time behavior. The above difference of the intermediate FID behavior originates from the difference of the crystal structures of solid xenon and CaF2.Comment: 16 pages, 5 figure

Generalized multi-SNP mediation intersection–union test

To elucidate the molecular mechanisms underlying genetic variants identified from genome-wide association studies (GWAS) for a variety of phenotypic traits encompassing binary, continuous, count, and survival outcomes, we propose a novel and flexible method to test for mediation that can simultaneously accommodate multiple genetic variants and different types of outcome variables. Specifically, we employ the intersection–union test approach combined with the likelihood ratio test to detect mediation effect of multiple genetic variants via some mediator (e.g., the expression of a neighboring gene) on outcome. We fit high-dimensional generalized linear mixed models under the mediation framework, separately under the null and alternative hypothesis. We leverage Laplace approximation to compute the marginal likelihood of outcome and use coordinate descent algorithm to estimate corresponding parameters. Our extensive simulations demonstrate the validity of our proposed methods and substantial, up to 97%, power gains over alternative methods. Applications to real data for the study of Chlamydia trachomatis infection further showcase advantages of our methods. We believe our proposed methods will be of value and general interest in this post-GWAS era to disentangle the potential causal mechanism from DNA to phenotype for new drug discovery and personalized medicine

Self-dual gravity

Self-dual gravity is a diffeomorphism invariant theory in four dimensions that describes two propagating polarisations of the graviton and has a negative mass dimension coupling constant. Nevertheless, this theory is not only renormalisable but quantum finite, as we explain. We also collect various facts about self-dual gravity that are scattered across the literature

Analog Computer Research

Contains reports on four research projects

Violations of local realism with quNits up to N=16

Predictions for systems in entangled states cannot be described in local realistic terms. However, after admixing some noise such a description is possible. We show that for two quNits (quantum systems described by N dimensional Hilbert spaces) in a maximally entangled state the minimal admixture of noise increases monotonically with N. The results are a direct extension of those of Kaszlikowski et. al., Phys. Rev. Lett. {\bf 85}, 4418 (2000), where results for $N\leq 9$ were presented. The extension up to N=16 is possible when one defines for each N a specially chosen set of observables. We also present results concerning the critical detectors efficiency beyond which a valid test of local realism for entangled quNits is possible.Comment: 5 pages, 3 ps picture