Quantum dynamics in sine-square deformed conformal field theory: Quench from uniform to non-uniform CFTs

In this work, motivated by the sine-square deformation (SSD) for (1+1)-dimensional quantum critical systems, we study the non-equilibrium quantum dynamics of a conformal field theory (CFT) with SSD, which was recently proposed to have continuous energy spectrum and continuous Virasoro algebra. In particular, we study the time evolution of entanglement entropy after a quantum quench from a uniform CFT, which is defined on a finite space of length $L$, to a sine-square deformed CFT. We find there is a crossover time $t^{\ast}$ that divides the entanglement evolution into two interesting regions. For $t\ll t^{\ast}$, the entanglement entropy does not evolve in time; for $t\gg t^{\ast}$, the entanglement entropy grows as $S_A(t)\simeq \frac{c}{3}\log t$, which is independent of the lengths of the subsystem and the total system. This $\log t$ growth with no revival indicates that a sine-square deformed CFT effectively has an infinite length, in agreement with previous studies based on the energy spectrum analysis. Furthermore, we study the quench dynamics for a CFT with M$\ddot{\text{o}}$bius deformation, which interpolates between a uniform CFT and a sine-square deformed CFT. The entanglement entropy oscillates in time with period $L_{\text{eff}}=L\cosh(2\theta)$, with $\theta=0$ corresponding to the uniform case and $\theta\to \infty$ corresponding to the SSD limit. Our field theory calculation is confirmed by a numerical study on a (1+1)-d critical fermion chain.Comment: are welcome; 10 pages, 4 figures; v2: refs added; v3: refs added; A physical interpretation of t* is added; v4: published version (selected as Editors' Suggestion

Belgian Economy characteristics and its experiences

Belgium ranks middle in EU countries with highly specified economy, clear property system, efficient and healthy legal as well as financial institutions. It encourages thrifty and diligence which have been a representative sample of high efficiency economy since 12th century. Its success has provided beneficial experiences for China’s economy transformation. Key words: high efficiency economy, thrifty and diligence, high-tech and small companies Résumé: La Belgique se figure parmi les pays d’UE avec son économie bien spécifique, le système de propriété clair, les institutions légales et financières efficaces et saines. Elle encourage l’économie & diligence qui était un échantillon représentatif de l’économie de haute efficacité depuis le 12e siècle. Son succès a offert des expériences bénéfiques pour la transformation économique de la Chine. Mots-Clés: économie de haute efficacité, économie & diligence, haute technologie & petites entreprise

Reflection on the Experiences of US and European Automobile Industry to Hubei’s Future Development

Surpassing the US in car sales in 2009. China has, since the world financial crisis, been showing big potential while US automobiles industry under complete depression. Green car, which has long been popular in European countries such as Belgium, has therefore become a key for the revival of the world car industry. As one of the three major automobile bases in China, how can Hubei benefit from the current challenge and development opportunity in the pro-crisis era?Key words: Saving and new energy vehicles; US automobile; decay; European “green” plastics; Hubei; developmen

Bright 22 μ\mum Excess Candidates from WISE All-Sky Catalog and Hipparcos Main Catalog

In this paper we present a catalog which includes 141 bright candidates ($\leq10.27$ mag, V band) showing the infrared (IR) excess at 22 $\mu$m. Of which, 38 stars are known IR excess stars or disk, 23 stars are double or multiple stars and 4 are Be stars. While the remaining more than 70 stars are identified as the 22 $\mu$m excess candidates in our work. The criterion of selecting candidates is $K_s-[22]_{\mu m}$. All these candidates are selected from \emph{WISE} All-sky data cross-correlated with \emph{Hipparcos} Main Catalog and the likelihood-ratio technique is employed. Considering the effect of background, we introduce the \emph{IRAS} 100 $\mu$m level to exclude the high background. We also estimated the coincidence probability of these sources. In addition, we presented the optical to mid-infrared SEDs and optical images of all the candidates, and gave the observed optical spectra of 6 stars with NAOC's 2.16-m telescope. To measure for the dust amount around each star, the fractional luminosity is also provided. We also test whether our method of selecting IR excess stars can be used to search for extra-solar planets, we cross-matched our catalog with known IR-excess stars having planets but none is matched. Finally, we give the fraction of stars showing IR-excess for different spectral type of main-sequence stars.Comment: 45 pages, 16 figures, 4 tables. Accepted for publication in ApJ