There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the $s$-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.

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Theory of ultracold atomic Fermi gases

Color Superconductivity in Dense, But Not Asymptotically Dense, Quark Matter (M Alford & K Rajagopal) Larkin-Ovchinnikov-Fulde-Ferrell Phases in QCD (G Nardulli) Phase Diagram of Neutral Quark Matter at Moderate Densities (S B Ruster et al.) Spontaneous Nambu-Goldstone Current Generation Driven by Mismatch (M Huang) The CFL Phase and ms: An Effective Field Theory Approach (T Schafer) Nuclear Superconductivity in Compact Stars: BCS Theory and Beyond (A Sedrakian & J W Clark) Pairing Properties of Dressed Nucleons in Infinite Matter (W H Dickhoff & H Muther) Pairing in Higher Angular Momentum States: Spectrum of Solutions of the 3P2-3F2 Pairing Model (M V Zverev et al.) Four-Particle Condensates in Nuclear Systems (G Ropke & P Schuck) Realization, Characterization, and Detection of Novel Superfluid Phases with Pairing Between Unbalanced Fermion Species (K Yang) Phase Transition in Unbalanced Fermion Superfluids (H Caldas).

Pairing in fermionic systems : basic concepts and modern applications

Axions from cooling compact stars: Pair-breaking processes

We present a model of the compact star in Cassiopea A that accounts for its unusually fast cooling behavior. This feature is interpreted as an enhancement in the neutrino emission triggered by a transition from a fully gapped, two-flavor, color-superconducting phase to a crystalline phase or an alternative gapless, color-superconducting phase. By fine-tuning a single parameter -- the temperature of this transition -- a specific cooling scenario can be selected that fits the Cas A data. Such a scenario requires a massive $M\sim 2M_{\odot}$ star and is, therefore, distinctive from models invoking canonical 1.4 $M_{\odot}$ mass star with nucleonic pairing alone.

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Rapid cooling of the compact star in Cassiopea A as a phase transition in dense QCD

The three-flavor crystalline color-superconducting (CCS) phase of quantum chromodynamics (QCD) is a candidate phase for the ground state of cold matter at moderate densities above the density of the deconfinement phase transition. Apart from being a superfluid, the CCS phase has properties of a solid, such as a lattice structure and a shear modulus, and hence the ability to sustain multipolar deformations in gravitational equilibrium. We construct equilibrium configurations of hybrid stars composed of nuclear matter at low, and CCS quark matter at high, densities. Phase equilibrium between these phases is possible only for rather stiff equations of state of nuclear matter and large couplings in the effective Nambu--Jona-Lasinio Lagrangian describing the CCS state. We identify a new branch of stable CCS hybrid stars within a broad range of central densities which, depending on the details of the equations of state, either bifurcate from the nuclear sequence of stars when the central density exceeds that of the deconfinement phase transition or form a new family of configurations separated from the purely nuclear sequence by an instability region. The maximum masses of our nonrotating hybrid configurations are consistent with the presently available astronomical bounds. The sequences of hybrid configurations that rotatemore » near the mass-shedding limit are found to be more compact and thus support substantially larger spins than their same mass nuclear counterparts.« less

Equilibrium sequences of nonrotating and rapidly rotating crystalline color-superconducting hybrid stars

We describe the microphysics, phenomenology, and astrophysical implication of a $B$-field induced unpairing effect that may occur in magnetars, if the local $B$ field in the core of a magnetar exceeds a critical value ${H}_{c2}$. Using the Ginzburg-Landau theory of superconductivity, we derive the ${H}_{c2}$ field for proton condensate taking into the correction $(\ensuremath{\le}30%)$ which arises from its coupling to the background neutron condensate. The density dependence of pairing of proton condensate implies that ${H}_{c2}$ is maximal at the crust-core interface and decreases towards the center of the star. As a consequence, magnetar cores with homogenous constant fields will be partially superconducting for ``medium-field'' magnetars $({10}^{15}\ensuremath{\le}B\ensuremath{\le}5\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{G})$ whereas ``strong-field'' magnetars $(Bg5\ifmmode\times\else\texttimes\fi{}{10}^{16}\text{G})$ will be void of superconductivity. The neutrino emissivity of a magnetar's core changes in a twofold manner: (i) the $B$-field assisted direct Urca process is enhanced by orders of magnitude, because of the unpairing effect in regions where $B\ensuremath{\ge}{H}_{c2}$; (ii) the Cooper-pair breaking processes on protons vanish in these regions and the overall emissivity by the pair-breaking processes is reduced by a factor of only a few.

Armen Sedrakian

Papers

Pairing in fermionic systems : basic concepts and modern applications

Axions from cooling compact stars: Pair-breaking processes

Rapid cooling of the compact star in Cassiopea A as a phase transition in dense QCD

Equilibrium sequences of nonrotating and rapidly rotating crystalline color-superconducting hybrid stars

Magnetar superconductivity versus magnetism: Neutrino cooling processes