Superradiance Lattice

We show that the timed Dicke states of a collection of three-level atoms can form a tight-binding lattice in momentum space. This lattice, coined the superradiance lattice (SL), can be constructed based on electromagnetically induced transparency (EIT). For a one-dimensional SL, we need the coupling field of the EIT system to be a standing wave. The detuning between the two components of the standing wave introduces an effective uniform force in momentum space. The quantum lattice dynamics, such as Bloch oscillations, Wannier-Stark ladders, Bloch band collapsing and dynamic localization can be observed in the SL. The two-dimensional SL provides a flexible platform for Dirac physics in graphene. The SL can be extended to three and higher dimensions where no analogous real space lattices exist with new physics waiting to be explored.Comment: 6pages, 4 figure

Fermions on Thick Branes in the Background of Sine-Gordon Kinks

A class of thick branes in the background of sine-Gordon kinks with a scalar potential $V(\phi)=p(1+\cos\frac{2\phi}{q})$ was constructed by R. Koley and S. Kar [Classical Quantum Gravity \textbf{22}, 753 (2005)]. In this paper, in the background of the warped geometry, we investigate the issue of localization of spin half fermions on these branes in the presence of two types of scalar-fermion couplings: $\eta\bar{\Psi}\phi\Psi$ and $\eta\bar{\Psi}\sin\phi \Psi$. By presenting the mass-independent potentials in the corresponding Schr\"{o}dinger equations, we obtain the lowest Kaluza--Klein (KK) modes and a continuous gapless spectrum of KK states with $m^2>0$ for both types of couplings. For the Yukawa coupling $\eta\bar{\Psi}\phi\Psi$, the effective potential of the right chiral fermions for positive $q$ and $\eta$ is always positive, hence only the effective potential of the left chiral fermions could trap the corresponding zero mode. This is a well-known conclusion which had been discussed extensively in the literature. However, for the coupling $\eta\bar{\Psi}\sin\phi \Psi$, the effective potential of the right chiral fermions for positive $q$ and $\eta$ is no longer always positive. Although the value of the potential at the location of the brane is still positive, it has a series of wells and barriers on each side, which ensures that the right chiral fermion zero mode could be trapped. Thus we may draw the remarkable conclusion: for positive $\eta$ and $q$, the potentials of both the left and right chiral fermions could trap the corresponding zero modes under certain restrictions.Comment: 22 pages, 21 figures, published version to appear in Phys. Rev.

Solutions to integrable space-time shifted nonlocal equations

In this paper we present a reduction technique based on bilinearization and double Wronskians (or double Casoratians) to obtain explicit multi-soliton solutions for the integrable space-time shifted nonlocal equations introduced very recently by Ablowitz and Musslimani in [Phys. Lett. A, 2021]. Examples include the space-time shifted nonlocal nonlinear Schr\"odinger and modified Korteweg-de Vries hierarchies and the semi-discrete nonlinear Schr\"odinger equation. It is shown that these nonlocal integrable equations with or without space-time shift(s) reduction share same distributions of eigenvalues but the space-time shift(s) brings new constraints to phase terms in solutions.Comment: 16 page

The solutions of classical and nonlocal nonlinear Schr\"{o}dinger equations with nonzero backgrounds: Bilinearisation and reduction approach

In this paper we develop a bilinearisation-reduction approach to derive solutions to the classical and nonlocal nonlinear Schr\"{o}dinger (NLS) equations with nonzero backgrounds. We start from the second order Ablowitz-Kaup-Newell-Segur coupled equations as an unreduced system. With a pair of solutions $(q_0,r_0)$ we bilinearize the unreduced system and obtain solutions in terms of quasi double Wronskians. Then we implement reductions by introducing constraints on the column vectors of the Wronskians and finally obtain solutions to the reduced equations, including the classical NLS equation and the nonlocal NLS equations with reverse-space, reverse-time and reverse-space-time, respectively. With a set of plane wave solution $(q_0,r_0)$ as a background solution, we present explicit formulae for these column vectors. As examples, we analyze and illustrate solutions to the focusing NLS equation and the reverse-space nonlocal NLS equation. In particular, we present formulae for the rouge waves of arbitrary order for the focusing NLS equation.Comment: 44 pages, 11 figure

12导联动态心电图与冠状动脉造影结果的对比分析

Objective:To discuss the value of the 12-lead dynamic electrocardiogram (DCG) in diagnosis of coronary heart disease(CHD) by comparing and analyzing the results between 12-lead DCG and coronary angiography. Methods: 105 patients with suspected CHD undergoing both 12-lead DCG and coronary angiography were analyzed. Results: 105 patients with positive coronary angiography of 46 cases, 59 cases were negative, of which 12 lead DCG showed ischemic ST segment depression in 32 patients, no ST-segment depression in 14 cases, normal coronary angiography in 59 cases of 12-lead DCG showed ischemic ST segment depression in 23 patients, no ST-segment depression in 36 cases. Conclusion:12-lead DCG is one of ideal non-invasive methods in the diagnosis of CHD of ischemic ST segment depression with typical chest pain.It is simple,economic and practical.目的  通过比较分析12导联动态心电图（DCG）与冠状动脉造影结果，探讨12导联DCG对冠心病的临床诊断价值。方法  将105例可疑冠心病患者24h同步12导联DCG与冠状动脉造影结果进行对比分析。结果  105例患者经冠状动脉造影阳性46例，其中32例12导联DCG显示缺血性ST段压低，无ST段压低改变14例；冠状动脉造影正常的59例中12导联DCG显示缺血性ST段压低23例，无ST段压低改变36例。结论  12导联DCG是临床诊断缺血性ST段压低伴典型胸痛的冠心病较为理想的无创性检查方法之一，而且操作简单，价廉、实用