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

We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Dynamics of dark energy

Coherent preparation by laser light of quantum states of atoms and molecules can lead to quantum interference in the amplitudes of optical transitions. In this way the optical properties of a medium can be dramatically modified, leading to electromagnetically induced transparency and related effects, which have placed gas-phase systems at the center of recent advances in the development of media with radically new optical properties. This article reviews these advances and the new possibilities they offer for nonlinear optics and quantum information science. As a basis for the theory of electromagnetically induced transparency the authors consider the atomic dynamics and the optical response of the medium to a continuous-wave laser. They then discuss pulse propagation and the adiabatic evolution of field-coupled states and show how coherently prepared media can be used to improve frequency conversion in nonlinear optical mixing experiments. The extension of these concepts to very weak optical fields in the few-photon limit is then examined. The review concludes with a discussion of future prospects and potential new applications.

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Electromagnetically induced transparency : Optics in coherent media

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Table Of Integrals Series And Products

Modified Gravity and Cosmology

Quaternions have an (over a century-old) extensive and quite complicated interaction with special relativity. Since quaternions are intrinsically 4-dimensional, and do such a good job of handling 3-dimensional rotations, the hope has always been that the use of quaternions would simplify some of the algebra of the Lorentz transformations. Herein we report a relatively nice result for the relativistic combination of non-collinear 3-velocities. If we work with the relativistic half-velocities $w$ defined by $v={2w\over1+w^2}$, and promote them to quaternions using $\mathbf{w} = w \; \mathbf{\hat n}$, where $\mathbf{\hat n}$ is a unit quaternion, then we shall show \[ \mathbf{w}_{1\oplus2} = \mathbf{w}_1 \oplus \mathbf{w}_2 =(1-\mathbf{w}_1\mathbf{w}_2)^{-1} (\mathbf{w}_1 +\mathbf{w}_2) = (\mathbf{w}_1 +\mathbf{w}_2)(1-\mathbf{w}_2\mathbf{w}_1)^{-1}. \] All of the complicated angular dependence for relativistic combination of non-collinear 3-velocities is now encoded in the quaternion multiplication of $\mathbf{w}_1$ with $\mathbf{w}_2$. This result can furthermore be extended to obtain an elegant and compact formula for the associated Wigner angle: \[ \mathrm{e}^{\mathbf{\Omega}} = \mathrm{e}^{\Omega \; \mathbf{\hat\Omega} } = (1-\mathbf{w}_1\mathbf{w}_2)^{-1} (1-\mathbf{w}_2\mathbf{w}_1), \] in terms of which \[ {\mathbf{\hat{n}}}_{1\oplus2} = \mathrm{e}^{\mathbf{\Omega}/2} \;\; {\mathbf{w}_1+\mathbf{w}_2\over |\mathbf{w}_1+\mathbf{w}_2|}; \qquad\qquad {\mathbf{\hat{n}}}_{2\oplus1} = \mathrm{e}^{-\mathbf{\Omega}/2} \;\; {\mathbf{w}_1+\mathbf{w}_2\over |\mathbf{w}_1+\mathbf{w}_2|}. \] Thus, we would argue, many key results that are ultimately due to the non-commutativity of non-collinear boosts can be easily rephrased in terms of the algebra of quaternions.

Relativistic combination of non-collinear 3-velocities using quaternions

We explore signature-changing emergent geometries in a BEC; specifically analogues of signature change from Euclidean to Lorentzian regions. In our BEC-based analogue model, signature change is achieved via a change in atomic interactions from repulsive to attractive. The particle production resulting from a finite-duration Euclidean-signature event is calculated firstly in the hydrodynamic limit. A combination of trans-Planckian physics and signature change results from the inclusion of ultraviolet modes, modifying the expected particle production. We also propose using analogue signature changing events as an amplifier for analogue ``cosmological particle production” and investigate the experimental applicability of this in future BEC experiments. Article not available.

Signature-Change Events, Trans-Planckian Physics and Quasi-Particle Amplification in Bose-Einstein Condensates

Mass, energy, and momentum are fundamental concepts in Newtonian physics. In Einstein's theory of general relativity, however, spacetime is itself a dynamic object, so how does one choose the fundamental quantities? In his Perspective, Visser discusses a new approach to defining one such quantity--angular momentum--recently published by Rizzi in Physical Review Letters .

A New Twist

Reply to ‘Comment on ‘Elementary analysis of the special relativistic combination of velocities, Wigner rotation and Thomas precession”

Dimensional analysis shows that the speed of light and Newton's constant of gravitation can be combined to define a quantity $F_* = {c^4\over G_N}$ with the dimensions of force (equivalently, tension). Then in any physical situation we must have $F_{physical} = f \; F_*$, where the quantity $f$ is some dimensionless function of dimensionless parameters. In many physical situations explicit calculation yields $f= O(1)$, and quite often $f \leq {1\over4}$. This has lead multiple authors to suggest a (weak or strong) maximum force/maximum tension conjecture. Working within the framework of standard general relativity, we will instead focus on counter-examples to this conjecture, paying particular attention to the extent to which the counter-examples are physically reasonable. The various counter-examples we shall explore strongly suggest that one should not put too much credence into any universal maximum force/maximum tension conjecture. Specifically, fluid spheres on the verge of gravitational collapse will generically violate the weak (and strong) maximum force conjectures. If one wishes to retain any general notion of "maximum force" then one will have to very carefully specify precisely which forces are to be allowed within the domain of discourse.

Matt Visser

Papers

Relativistic combination of non-collinear 3-velocities using quaternions

Signature-Change Events, Trans-Planckian Physics and Quasi-Particle Amplification in Bose-Einstein Condensates

A New Twist

Reply to ‘Comment on ‘Elementary analysis of the special relativistic combination of velocities, Wigner rotation and Thomas precession”

Counterexamples to the maximum force conjecture