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

We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices

Cavity Optomechanics

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

This review presents an overview of the thermal properties of mesoscopic structures. The discussion is based on the concept of electron energy distribution, and, in particular, on controlling and probing it. The temperature of an electron gas is determined by this distribution: refrigeration is equivalent to narrowing it, and thermometry is probing its convolution with a function characterizing the measuring device. Temperature exists, strictly speaking, only in quasiequilibrium in which the distribution follows the Fermi-Dirac form. Interesting nonequilibrium deviations can occur due to slow relaxation rates of the electrons, e.g., among themselves or with lattice phonons. Observation and applications of nonequilibrium phenomena are also discussed. The focus in this paper is at low temperatures, primarily below $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, where physical phenomena on mesoscopic scales and hybrid combinations of various types of materials, e.g., superconductors, normal metals, insulators, and doped semiconductors, open up a rich variety of device concepts. This review starts with an introduction to theoretical concepts and experimental results on thermal properties of mesoscopic structures. Then thermometry and refrigeration are examined with an emphasis on experiments. An immediate application of solid-state refrigeration and thermometry is in ultrasensitive radiation detection, which is discussed in depth. This review concludes with a summary of pertinent fabrication methods of presented devices.

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Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications

We show that the topologically protected flat band emerging on a surface of a nodal fermionic system promotes the surface superconductivity due to an infinitely large density of states associated with the flat band. The critical temperature depends linearly on the pairing interaction and can be thus considerably higher than the exponentially small bulk critical temperature. We discuss an example of surface superconductivity in multilayered graphene with rhombohedral stacking.

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High-temperature surface superconductivity in topological flat-band systems

Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. Here we show that in gapless topological media, the bulk-surface and bulk-vortex correspondence is more effective: it produces topologically protected gapless fermions without dispersion—the fiat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines [A. P. Schnyder and S. Ryu, Phys. Rev. B 84, 060504(R) (2011); T. T. Heikkil G. E. Volovik, JETP Lett. 93, 59 (2011)] and in the vortex core in systems with topologically protected Fermi points (Weyl points) [G. E. Volovik, JETP Lett. 93, 66 (2011)]. Flat band has an extremely singular density of states, and we show that this property may give rise in particular to surface superconductivity which could exist even at room temperature.

Flat bands in topological media

Use of nanomechanical resonators has the potential to offer microwave amplification with the minimum possible added noise, namely that due to quantum fluctuations In order to compensate for energy losses, the radio signals used in telecommunications and detection technologies require occasional electrical amplification For specific applications, sensitive amplifiers have been demonstrated that operate near the quantum limit — where the only noise added is due to fundamental quantum fluctuations This paper describes a new concept for amplifying weak electrical signals close to this fundamental limit, using a nanomechanical resonator The system uses a resonator irradiated with microwave light of a frequency tuned so that it sets the resonator in motion with tiny vibrations; these amplify the signal In this proof-of-principle study, signal amplification of 25 decibels is demonstrated, with only 20 fundamental noise quanta added This mechanical amplification approach has the attraction that it is conceptually simple and could feasibly be used in integrated electrical circuits The sensitive measurement of electrical signals is at the heart of modern technology According to the principles of quantum mechanics, any detector or amplifier necessarily adds a certain amount of noise to the signal, equal to at least the noise added by quantum fluctuations1,2 This quantum limit of added noise has nearly been reached in superconducting devices that take advantage of nonlinearities in Josephson junctions3,4 Here we introduce the concept of the amplification of microwave signals using mechanical oscillation, which seems likely to enable quantum-limited operation We drive a nanomechanical resonator with a radiation pressure force5,6,7, and provide an experimental demonstration and an analytical description of how a signal input to a microwave cavity induces coherent stimulated emission and, consequently, signal amplification This generic scheme, which is based on two linear oscillators, has the advantage of being conceptually and practically simpler than the Josephson junction devices In our device, we achieve signal amplification of 25 decibels with the addition of 20 quanta of noise, which is consistent with the expected amount of added noise The generality of the model allows for realization in other physical systems as well, and we anticipate that near-quantum-limited mechanical microwave amplification will soon be feasible in various applications involving integrated electrical circuits

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Microwave amplification with nanomechanical resonators

We calculate the heat transfer between electrons to acoustic and optical phonons in monolayer and bilayer graphene (MLG and BLG) within the quasiequilibrium approximation. For acoustic phonons, we show how the temperature-power laws of the electron-phonon heat current for BLG differ from those previously derived for MLG and note that the high-temperature (neutral-regime) power laws for MLG and BLG are also different, with a weaker dependence on the electronic temperature in the latter. In the general case we evaluate the heat current numerically. We suggest that a measurement of the heat current could be used for an experimental determination of the electron-acoustic-phonon coupling constants, which are not accurately known. However, in a typical experiment heat dissipation by electrons at very low temperatures is dominated by diffusion and we estimate the crossover temperature at which acoustic-phonon coupling takes over in a sample with Joule heating. At even higher temperatures optical phonons begin to dominate. We study some examples of potentially relevant types of optical modes, including, in particular, the intrinsic in-plane modes and additionally the remote surface phonons of a possible dielectric substrate.

Tero T. Heikkilä

Papers

Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications

High-temperature surface superconductivity in topological flat-band systems

Flat bands in topological media

Microwave amplification with nanomechanical resonators

Electron-phonon heat transfer in monolayer and bilayer graphene