Quantum gravity effects on statistics and compact star configurations

The thermodynamics of classical and quantum ideal gases based on the Generalized uncertainty principle (GUP) are investigated. At low temperatures, we calculate corrections to the energy and entropy. The equations of state receive small modifications. We study a system comprised of a zero temperature ultra-relativistic Fermi gas. It turns out that at low Fermi energy $\varepsilon_F$, the degenerate pressure and energy are lifted. The Chandrasekhar limit receives a small positive correction. We discuss the applications on configurations of compact stars. As $\varepsilon_F$ increases, the radius, total number of fermions and mass first reach their nonvanishing minima and then diverge. Beyond a critical Fermi energy, the radius of a compact star becomes smaller than the Schwarzschild one. The stability of the configurations is also addressed. We find that beyond another critical value of the Fermi energy, the configurations are stable. At large radius, the increment of the degenerate pressure is accelerated at a rate proportional to the radius.Comment: V2. discussions on the stability of star configurations added, 17 pages, 2 figures, typos corrected, version to appear in JHE

How classical is the quantum universe?

We discuss two topics that are usually considered to be exclusively "quantum": the Schroedinger equation, and the uncertainty principle. We show (or rather recall) that the Schroedinger equation can be derived from Hamilton's equations using the metaplectic representation. We also show that the uncertainty principle, stated in the form of the Robertson-Schroedinger-Heisenberg inequalities can be formulated in perfectly classical terms using the topological notion of symplectic capacity

Thermodynamic curvature and black holes

I give a relatively broad survey of thermodynamic curvature $R$, one spanning results in fluids and solids, spin systems, and black hole thermodynamics. $R$ results from the thermodynamic information metric giving thermodynamic fluctuations. $R$ has a unique status in thermodynamics as being a geometric invariant, the same for any given thermodynamic state. In fluid and solid systems, the sign of $R$ indicates the character of microscopic interactions, repulsive or attractive. $|R|$ gives the average size of organized mesoscopic fluctuating structures. The broad generality of thermodynamic principles might lead one to believe the same for black hole thermodynamics. This paper explores this issue with a systematic tabulation of results in a number of cases.Comment: 27 pages, 10 figures, 7 tables, 78 references. Talk presented at the conference Breaking of Supersymmetry and Ultraviolet Divergences in extended Supergravity, in Frascati, Italy, March 27, 2013. v2 corrects some small problem

Order and Stochastic Dynamics in Drosophila Planar Cell Polarity

Cells in the wing blade of Drosophila melanogaster exhibit an in-plane polarization causing distal orientation of hairs. Establishment of the Planar Cell Polarity (PCP) involves intercellular interactions as well as a global orienting signal. Many of the genetic and molecular components underlying this process have been experimentally identified and a recently advanced system-level model has suggested that the observed mutant phenotypes can be understood in terms of intercellular interactions involving asymmetric localization of membrane bound proteins. Among key open questions in understanding the emergence of ordered polarization is the effect of stochasticity and the role of the global orienting signal. These issues relate closely to our understanding of ferromagnetism in physical systems. Here we pursue this analogy to understand the emergence of PCP order. To this end we develop a semi-phenomenological representation of the underlying molecular processes and define a “phase diagram” of the model which provides a global view of the dependence of the phenotype on parameters. We show that the dynamics of PCP has two regimes: rapid growth in the amplitude of local polarization followed by a slower process of alignment which progresses from small to large scales. We discuss the response of the tissue to various types of orienting signals and show that global PCP order can be achieved with a weak orienting signal provided that it acts during the early phase of the process. Finally we define and discuss some of the experimental predictions of the model

Radio & Optical Interferometry: Basic Observing Techniques and Data Analysis

Astronomers usually need the highest angular resolution possible, but the blurring effect of diffraction imposes a fundamental limit on the image quality from any single telescope. Interferometry allows light collected at widely-separated telescopes to be combined in order to synthesize an aperture much larger than an individual telescope thereby improving angular resolution by orders of magnitude. Radio and millimeter wave astronomers depend on interferometry to achieve image quality on par with conventional visible and infrared telescopes. Interferometers at visible and infrared wavelengths extend angular resolution below the milli-arcsecond level to open up unique research areas in imaging stellar surfaces and circumstellar environments. In this chapter the basic principles of interferometry are reviewed with an emphasis on the common features for radio and optical observing. While many techniques are common to interferometers of all wavelengths, crucial differences are identified that will help new practitioners avoid unnecessary confusion and common pitfalls. Concepts essential for writing observing proposals and for planning observations are described, depending on the science wavelength, angular resolution, and field of view required. Atmospheric and ionospheric turbulence degrades the longest-baseline observations by significantly reducing the stability of interference fringes. Such instabilities represent a persistent challenge, and the basic techniques of phase-referencing and phase closure have been developed to deal with them. Synthesis imaging with large observing datasets has become a routine and straightforward process at radio observatories, but remains challenging for optical facilities. In this context the commonly-used image reconstruction algorithms CLEAN and MEM are presented. Lastly, a concise overview of current facilities is included as an appendix.Comment: 45 pages, 14 Figures; an abridged version of a chapter to appear in Volume 2 of Planets, Stars and Stellar Systems, to be published in 2011 by Springe

Active Fluids Within the Unified Coloured Noise Approximation

Active matter is made of active particles which are able to convert energy from the environment into directed persistent motion. They can be modelled by stochastic differential equations subject to persistent noise. Run and tumble and active Brownian particle (ABP) models have been first proposed and still are considered closer to experimental observations but do not allow for much analytical progress. The Gaussian coloured noise (GCN) model, introduced as a time coarse-grained version of the ABP can be tuned to have the same variance of the active force as the ABP, which leads to a simpler analytical treatment. Finally, the UCNA can be considered as a Markovian reduction of the GCN. We give a simple derivation of the governing equation and analyse some of its recent applications ranging from the study of the swim pressure, its relation to the mobility, to the state induced by a moving object