Correlations of quantum curvature and variance of Chern numbers

We analyse the correlation function of the quantum curvature in complex quantum systems, using a random matrix model to provide an exemplar of a universal correlation function. We show that the correlation function diverges as the inverse of the distance at small separations. We also define and analyse a correlation function of mixed states, showing that it is finite but singular at small separations. A scaling hypothesis on a universal form for both types of correlations is supported by Monte-Carlo simulations. We relate the correlation function of the curvature to the variance of Chern integers which can describe quantised Hall conductance.

Correlation between the spatial distribution and colony size was common for monogenetic bacteria in laboratory conditions

Background Geographically separated population growth of microbes is a common phenomenon in microbial ecology. Colonies are representative of the morphological characteristics of this structured population growth. Pattern formation by single colonies has been intensively studied, whereas the spatial distribution of colonies is poorly investigated. Results The present study describes a first trial to address the questions of whether and how the spatial distribution of colonies determines the final colony size using the model microorganism Escherichia coli, colonies of which can be grown under well-controlled laboratory conditions. A computational tool for image processing was developed to evaluate colony density, colony size and size variation, and the Voronoi diagram was applied for spatial analysis of colonies with identical space resources. A positive correlation between the final colony size and the Voronoi area was commonly identified, independent of genomic and nutritional differences, which disturbed the colony size and size variation. Conclusions This novel finding of a universal correlation between the spatial distribution and colony size not only indicated the fair distribution of spatial resources for monogenetic colonies growing with identical space resources but also indicated that the initial localization of the microbial colonies decided by chance determined the fate of the subsequent population growth. This study provides a valuable example for quantitative analysis of the complex microbial ecosystems by means of experimental ecology.

Critical domain: Universality, ε-expansion

In Chapter 15, the scaling behaviour of correlation functions at criticality, T = Tc, has been derived. This chapter is devoted to the critical domain, where the correlation length is large with respect to the microscopic scale, but finite. In dimensions d < 4, above Tc, the property of strong scaling is derived: in the critical domain above Tc, all correlation functions, after rescaling, can be expressed in terms of universal correlation functions, in which the scale of distance is provided by the correlation length. However, because the correlation length is singular at Tc, in this formalism, the critical temperature cannot be crossed. Alternatively, one can expand correlation functions in formal power series of the deviation (T −Tc) from the critical temperature, in presence of a magnetic field. The sum of the expansion satisfies renormalization group (RG) equations also valid for T < Tc and in a magnetic field, from which follow scaling properties in the whole critical domain. The universal two-point function can be expanded when T approaches Tc, using the short-distance expansion (SDE). A few terms of the ϵ expansion (ϵ is the deviation from dimension 4) of a few universal quantities are reported. Calculations at fixed dimension and summation of perturbative expansions are described. The conformal bootstrap based on the SDE and conformal invariance at the infrared (IR) fixed point provides an alternative method to determine critical exponents.

Possible evidence of a universal radio/X-ray correlation in a near-complete sample of hard X-ray selected seyfert galaxies

ABSTRACT Because the disc–jet coupling likely depends on various properties of sources probed, the sample control is always an important but challenging task. In this work, we re-analysed the INTEGRAL hard X-ray-selected sample of Seyfert galaxies. We only consider sources that have measurements in black hole (BH) mass, and luminosities in radio and X-rays. Our final sample includes 64 (out of the original 79) sources, consists of both bright active galactic nucleus and low-luminosity ones. The 2–10 keV X-ray Eddington ratio LX/LEdd locates in the range between ∼10−4.5 and ∼10−0.5. We first find that, because of the similarity in the LHX/LX distribution, the X-ray origin of radio-loud Seyferts may be the same to that of radio-quiet (RQ) ones, where we attribute to the hot accretion flow (or similarly, the corona). We then investigate the connections between luminosities in radio and X-rays. Since our sample suffers a selection bias of a BH mass MBH dependence on LX/LEdd, we focus on the correlation slope ξX between the radio (at 1.4 GHz) and X-ray luminosities in Eddington unit, i.e. $({L_{\rm R}}/{L_{\rm Edd}}) \propto ({L_{\rm X}}/{L_{\rm Edd}})^{\xi _{\rm X}}$. We classify the sources according to various properties, i.e. 1) Seyfert classification, 2) radio loudness, and 3) radio morphology. We find that, despite these differences in classification, all the sources in our sample are consistent with a universal correlation slope ξX (note that the normalization may be different), with ξX = 0.77 ± 0.10. This is unexpected, considering various possible radio emitters in RQ systems. For the jet (either relativistic and well collimated, or sub-relativistic and weakly collimated) interpretation, our result may suggest a common/universal but to be identified jet launching mechanism among all the Seyfert galaxies, while properties like BH spin and magnetic field strength only play secondary roles. We further estimate the jet production efficiency ηjet of Seyfert galaxies, which is $\eta _{\rm jet}\approx 1.9^{+0.9}_{-1.5}\times 10^{-4}$ on average. We also find that ηjet increases as the system goes fainter. Alternative scenarios for the radio emission in RQ systems are also discussed.

Galactic and cosmological fast radio bursts as scaled-up solar radio bursts

Fast radio bursts (FRBs) are bright milliseconds radio transients with large dispersion measures. Recently, FRB 200428 was detected in temporal coincidence with a hard X-ray flare from the Galactic magnetar SGR 1935+2154, which supports that at least some FRBs are from magnetar activity. Interestingly, a portion of X-ray flares from magnetar XTE J1810-197 and the Sun are also accompanied by radio bursts. Many features of Galactic FRB 200428 and cosmological FRBs resemble solar radio bursts. However, a common physical origin among FRBs, magnetar radio pulses and solar radio bursts has not yet been established. Here we report a universal correlation between X-ray luminosity and radio luminosity over twenty orders of magnitude among solar type III radio bursts, XTE J1810-197 and Galactic FRB 200428. This universal correlation reveals that the energetic electrons which produce the X-ray flares and those which cause radio emissions have a common origin, which can give stringent limits on the generation process of radio bursts. Moreover, we find similar occurrence frequency distributions of energy, duration and waiting time for solar radio bursts, SGR 1935+2154 and repeating FRB 121102, which also support the tight correlation and the X-ray flares temporally associated with radio bursts. All of these distributions can be understood by avalanche models of self-organized criticality systems. The universal correlation and statistical similarities indicate that the Galactic FRB 200428 and FRBs seen at cosmological distances can be treated as scaled-up solar radio bursts.

Correlation between the Spatial Distribution and Colony size Was Common for Monogenetic Bacteria in Laboratory Conditions.

Background: Geographically separated population growth of microbes is a common phenomenon in microbial ecology. Colonies are representative of the morphological characteristics of this structured population growth. Pattern formation by single colonies has been intensively studied, whereas the spatial distribution of colonies is poorly investigated. Results: The present study describes a first trial to address the questions of whether and how the spatial distribution of colonies determines the final colony size using the model microorganism Escherichia coli, colonies of which can be grown under well-controlled laboratory conditions. A computational tool for image processing was developed to evaluate colony density, colony size and size variation, and the Voronoi diagram was applied for spatial analysis of colonies with identical space resources. A positive correlation between the final colony size and the Voronoi area was commonly identified, independent of genomic and nutritional differences, which disturbed the colony size and size variation. Conclusions: This novel finding of a universal correlation between the spatial distribution and colony size not only indicated the fair distribution of spatial resources for monogenetic colonies growing with identical space resources but also indicated that the initial localization of the microbial colonies decided by chance determined the fate of the subsequent population growth. This study provides a valuable example for quantitative analysis of the complex microbial ecosystems by means of experimental ecology.