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

Gravitational wave observations of GW170817 placed bounds on the tidal deformabilities of compact stars, allowing one to probe equations of state for matter at supranuclear densities. Here we design new parametrizations for hybrid hadron-quark equations of state, which give rise to low-mass twin stars, and test them against GW170817. We find that GW170817 is consistent with the coalescence of a binary hybrid star-neutron star. We also test and find that the I-Love-Q relations for hybrid stars in the third family agree with those for purely hadronic and quark stars within $\ensuremath{\sim}3%$ for both slowly and rapidly rotating configurations, implying that these relations can be used to perform equation-of-state independent tests of general relativity and to break degeneracies in gravitational waveforms for hybrid stars in the third family as well.

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Implications from GW170817 and I-Love-Q relations for relativistic hybrid stars

Microscopic Theory of the Nuclear Equation of State and Neutron Star Structure.- Superfluidity in Neutron Star Matter.- Relativistic Superfluid Models for Rotating Neutron Stars.- The Tensor Virial Method and Its Applications to Self-Gravitating Superfluids.- Neutron Star Crusts.- Kaon Condensation in Neutron Stars.- Phases of QCD at High Baryon Density.- Diquarks in Dense Matter.- Color Superconductivity in Compact Stars.- Strange Quark Stars: Structural Properties and Possible Signatures for Their Existence.- Phase Diagram for Spinning and Accreting Neutron Stars.- Signal of Quark Deconfinement in Millisecond Pulsars and Reconfinement in Accreting X-ray Neutron Stars.- Supernova Explosions and Neutron Star Formation.- Evolution of a Neutron Star from Its Birth to Old Age.- Neutron Star Kicks and Asymmetric Supernovae.- Spin and Magnetism in Old Neutron Stars.- Neutrino Cooling of Neutron Stars: Medium Effects.

Physics of neutron star interiors

The recent measurement of a 1.97 ± 0.04 solar-mass pulsar places a stringent lower bound on the maximum mass of compact stars and therefore challenges the existence of any agents that soften the equation of state of ultra-dense matter. We investigate whether hyperons and/or quark matter can be accommodated in massive compact stars by constructing an equation of state based on a combination of phenomenological relativistic hyper-nuclear density functional and an effective model of quantum chromodynamics (the

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Composition and stability of hybrid stars with hyperons and quark color-superconductivity

The recent measurement of a $197\pm 004$ solar-mass pulsar places a stringent lower bound on the maximum mass of compact stars and therefore challenges the existence of any agents that soften the equation of state of ultra-dense matter We investigate whether hyperons and/or quark matter can be accommodated in massive compact stars by constructing an equation of state based on a combination of phenomenological relativistic hyper-nuclear density functional and an effective model of quantum chromodynamics (the Nambu-Jona-Lasinio model) Stable configurations are obtained with $M \ge 197 M_{\sun}$ featuring hyper-nuclear and quark matter in color superconducting state if the equation of state of nuclear matter is stiff above the saturation density, the transition to quark matter takes place at a few times the nuclear saturation density, and the repulsive vector interactions in quark matter are substantial

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Compact stars may contain quark matter in their interiors at densities exceeding several times the nuclear saturation density. We explore models of such compact stars where there are two first-order phase transitions: the first from nuclear matter to a quark-matter phase, followed at a higher density by another first-order transition to a different quark-matter phase [e.g., from the two-flavor color-superconducting (2SC) to the color-flavor-locked (CFL) phase]. We show that this can give rise to two separate branches of hybrid stars, separated from each other and from the nuclear branch by instability regions, and, therefore, to a new family of compact stars, denser than the ordinary hybrid stars. In a range of parameters, one may obtain twin hybrid stars (hybrid stars with the same masses but different radii) and even triplets where three stars, with inner cores of nuclear matter, 2SC matter, and CFL matter, respectively, all have the same mass but different radii.

Armen Sedrakian

Papers

Implications from GW170817 and I-Love-Q relations for relativistic hybrid stars

Physics of neutron star interiors

Composition and stability of hybrid stars with hyperons and quark color-superconductivity

Composition and stability of hybrid stars with hyperons and quark color-superconductivity

Compact stars with sequential QCD phase transitions