THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

The isolated electronic spin system of the nitrogen-vacancy (NV) centre in diamond offers unique possibilities to be employed as a nanoscale sensor for detection and imaging of weak magnetic fields. Magnetic imaging with nanometric resolution and field detection capabilities in the nanotesla range are enabled by the atomic-size and exceptionally long spin-coherence times of this naturally occurring defect. The exciting perspectives that ensue from these characteristics have triggered vivid experimental activities in the emerging field of 'NV magnetometry'. It is the purpose of this article to review the recent progress in high-sensitivity nanoscale NV magnetometry, generate an overview of the most pertinent results of the last years and highlight perspectives for future developments. We will present the physical principles that allow for magnetic field detection with NV centres and discuss first applications of NV magnetometers that have been demonstrated in the context of nano magnetism, mesoscopic physics and the life sciences.

https://iopscience.iop.org/article/10.1088/0034-4885/77/5/056503/pdf

Magnetometry with nitrogen-vacancy defects in diamond

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.

QCD and strongly coupled gauge theories: challenges and perspectives

Galactic history is written in the white dwarf stars. Their surface properties hint at interiors composed of matter under extreme conditions. In the forty years since their discovery, pulsating white dwarf stars have moved from side-show curiosities to center stage as important tools for unraveling the deep mysteries of the Universe. Innovative observational techniques and theoretical modeling tools have breathed life into precision asteroseismology. We are just learning to use this powerful tool, confronting theoretical models with observed frequencies and their time rate-of-change. With this tool, we calibrate white dwarf cosmochronology; we explore equations of state; we measure stellar masses, rotation rates, and nuclear reaction rates; we explore the physics of interior crystallization; we study the structure of the progenitors of Type Ia supernovae, and we test models of dark matter. The white dwarf pulsations are at once the heartbeat of galactic history and a window into unexplored and exotic physics.

Pulsating White Dwarf Stars and Precision Asteroseismology

The relativistic fluid is a highly successful model used to describe the dynamics of many-particle, relativistic systems. It takes as input basic physics from microscopic scales and yields as output predictions of bulk, macroscopic motion. By inverting the process, an understanding of bulk features can lead to insight into physics on the microscopic scale. Relativistic fluids have been used to model systems as “small” as heavy ions in collisions, and as large as the Universe itself, with “intermediate” sized objects like neutron stars being considered along the way. The purpose of this review is to discuss the mathematical and theoretical physics underpinnings of the relativistic (multiple) fluid model. We focus on the variational principle approach championed by Brandon Carter and his collaborators, in which a crucial element is to distinguish the momenta that are conjugate to the particle number density currents. This approach differs from the “standard” text-book derivation of the equations of motion from the divergence of the stress-energy tensor in that one explicitly obtains the relativistic Euler equation as an “integrability” condition on the relativistic vorticity. We discuss the conservation laws and the equations of motion in detail, and provide a number of (in our opinion) interesting and relevant applications of the general theory.

/pdf/relativistic-fluid-dynamics-physics-for-many-different-50u1t44jg7.pdf

Relativistic fluid dynamics: physics for many different scales

We consider an instability of rapidly rotating neutron stars in low-mass x-ray binaries (LMXBs) with respect to excitation of r modes (which are analogous to Earth's Rossby waves controlled by the Coriolis force). We argue that finite temperature effects in the superfluid core of a neutron star lead to a resonance coupling and enhanced damping (and hence stability) of oscillation modes at certain stellar temperatures. Using a simple phenomenological model we demonstrate that neutron stars with high spin frequency may spend a substantial amount of time at these "resonance" temperatures. This finding allows us to explain puzzling observations of hot rapidly rotating neutron stars in LMXBs and to predict a new class of hot, nonaccreting, rapidly rotating neutron stars, some of which may have already been observed and tentatively identified as quiescent LMXB candidates. We also impose a new theoretical limit on the neutron star spin frequency, which can explain the cutoff spin frequency ∼730  Hz, following from the statistical analysis of accreting millisecond x-ray pulsars. In addition to explaining the observations, our model provides a new tool to constrain superdense matter properties by comparing measured and theoretically predicted resonance temperatures.

Instability windows and evolution of rapidly rotating neutron stars.

In a previous paper [M. E. Gusakov, A. I. Chugunov, and E. M. Kantor, Phys. Rev. Lett. 112, 151101 (2014)], we introduced a new scenario that explains the existence of rapidly rotating warm neutron stars (NSs) observed in low-mass x-ray binaries (LMXBs). Here it is described in more detail. The scenario takes into account the interaction between superfluid inertial modes and the normal (quadrupole) $m=2$ $r$ mode, which can be driven unstable by the Chandrasekhar-Friedman-Schutz (CFS) mechanism. This interaction can only occur at some fixed ``resonance'' stellar temperatures; it leads to formation of the ``stability peaks'' which stabilize a star in the vicinity of these temperatures. We demonstrate that a NS in LMXB spends a substantial fraction of time on the stability peak, that is, in the region of stellar temperatures and spin frequencies that has been previously thought to be CFS unstable with respect to excitation of $r$ modes. We also find that the spin frequencies of NSs are limited by the CFS instability of normal (octupole) $m=3$ $r$ mode rather than by $m=2$ $r$ mode. This result agrees with the predicted value of the cutoff spin frequency $\ensuremath{\sim}730\text{ }\text{ }\mathrm{Hz}$ in the spin distribution of accreting millisecond x-ray pulsars. In addition, we analyze evolution of a NS after the end of the accretion phase and demonstrate that millisecond pulsars can be born in LMXBs within our scenario. Besides millisecond pulsars, our scenario also predicts a new class of LMXB descendants---hot and rapidly rotating nonaccreting NSs (``hot widows''/HOFNARs). Further comparison of the proposed theory with observations of rotating NSs can impose new important constraints on the properties of superdense matter.

Explaining observations of rapidly rotating neutron stars in low-mass x-ray binaries

We calculate the relativistic entrainment matrix ${Y}_{\mathit{ik}}$ at zero temperature for a nucleon-hyperon mixture composed of neutrons, protons, and \ensuremath{\Lambda} and ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ hyperons, as well as electrons and muons. This matrix is analogous to the entrainment matrix (also termed mass-density matrix or Andreev-Bashkin matrix) of nonrelativistic theory. It is an important ingredient for modeling the pulsations of massive neutron stars with superfluid nucleon-hyperon cores. The calculation is done in the frame of the relativistic Landau Fermi-liquid theory generalized to the case of superfluid mixtures; the matrix ${Y}_{\mathit{ik}}$ is expressed through the Landau parameters of nucleon-hyperon matter. The results are illustrated with a particular example of the $\ensuremath{\sigma}\text{\ensuremath{-}}\ensuremath{\omega}\text{\ensuremath{-}}\ensuremath{\rho}$ mean-field model with scalar self-interactions. Using this model, we calculate the matrix ${Y}_{\mathit{ik}}$ and the Landau parameters. We also analyze the stability of the ground state of nucleon-hyperon matter with respect to small perturbations.

Relativistic entrainment matrix of a superfluid nucleon-hyperon mixture: The zero temperature limit

To put new constraints on the r-mode instability window, we analyse the formation of millisecond pulsars (MSPs) within the recycling scenario, making use of three sets of observations: (a) X-ray observations of neutron stars (NSs) in low-mass X-ray binaries; (b) timing of millisecond pulsars; and (c) X-ray and UV observations of MSPs. As shown in previous works, r-mode dissipation by shear viscosity is not sufficient to explain observational set (a), and enhanced r-mode dissipation at the red-shifted internal temperatures $T^\infty\sim 10^8$ K is required to stabilize the observed NSs. Here, we argue that models with enhanced bulk viscosity can hardly lead to a self-consistent explanation of observational set (a) due to strong neutrino emission, which is typical for these models (unrealistically powerful energy source is required to keep NSs at the observed temperatures). We also demonstrate that the observational set (b), combined with the theory of internal heating and NS cooling, provides evidence of enhanced r-mode dissipation at low temperatures, $T^\infty\sim 2\times 10^7$ K. Observational set (c) allows us to set an upper limit on the internal temperatures of MSPs, $T^\infty<2\times 10^7$ K (assuming a canonical NS with the accreted crust). Recycling scenario can produce MSPs at these temperatures only if r-mode instability is suppressed in the whole MSP spin frequency range ($\nu\lesssim 750$ Hz) at temperatures $2\times 10^7\lesssim T^\infty\lesssim 3 \times 10^7$ K, providing thus a new constraint on the r-mode instability window. These observational constraints are analysed in more details in application to the resonance uplift scenario of Gusakov et al. [Phys. Rev. Lett., 112 (2014), 151101].

R-modes and neutron star recycling scenario

One of the effective mechanisms of neutrino energy losses in red giants, pre-supernovae and in the cores of white dwarfs is the emission of neutrino-antineutrino pairs in the process of plasmon decay. In this paper, we numerically calculate the emissivity due to plasmon decay in a wide range of temperatures 10 7 -10 11 K and densities (2 x 10 2 -10 14 ) gcm -3 . Numerical results are approximated by convenient analytical expressions. We also calculate and approximate by analytical expressions the neutrino luminosity of white dwarfs due to plasmon decay, as a function of their mass and internal temperature. This neutrino luminosity depends on the chemical composition of white dwarfs only through the parameter μ e (the net number of baryons per electron) and is the dominant neutrino luminosity in all white dwarfs at the neutrino cooling stage.

/pdf/the-neutrino-emission-due-to-plasmon-decay-and-neutrino-4kyf13xomp.pdf

Elena M. Kantor

Papers

Instability windows and evolution of rapidly rotating neutron stars.

Explaining observations of rapidly rotating neutron stars in low-mass x-ray binaries

Relativistic entrainment matrix of a superfluid nucleon-hyperon mixture: The zero temperature limit

R-modes and neutron star recycling scenario

The neutrino emission due to plasmon decay and neutrino luminosity of white dwarfs