N=2 6-dimensional supersymmetric E6 breaking

We study the N=2 supersymmetric E₆ models on the 6-dimensional space–time where the supersymmetry and gauge symmetry can be broken by the discrete symmetry. On the space–time M⁴×S¹/(Z₂×Z₂′)×S¹/(Z₂×Z₂′), for the zero modes, we obtain the 4-dimensional N=1 supersymmetric models with gauge groups SU(3)×SU(2)×SU(2)×U(1)², SU(4)×SU(2)×SU(2)×U(1), and SU(3)×SU(2)×U(1)³ with one extra pair of Higgs doublets from the vector multiplet. In addition, considering that the extra space manifold is the annulus A² and disc D², we list all the constraints on constructing the 4-dimensional N=1 supersymmetric SU(3)×SU(2)×U(1)³ models for the zero modes, and give the simplest model with Z₉ symmetry. We also comment on the extra gauge symmetry breaking and its generalization.     

基于对偶混合变分原理的Signorini问题的数值模拟

基于Signorini问题的对偶混合变分形式,提出了一种非协调有限元逼近格式,证明了离散的B-B条件,获得了Raviart-Thomas(k=0)有限元逼近的误差界O(h^3/4),并且Uzawa型算法对协调与非协调有限元逼近格式进行了数值求解.根据数值结果的分析和比较,表明应用非协调有限元逼近格式求解更有效.     

Universal quantum control based on parametric modulation in superconducting circuits

As superconducting quantum circuits are scaling up rapidly towards the noisy intermediate-scale quantum(NISQ)era, the demand for electronic control equipment has increased significantly. To fully control a quantum chip of N qubits,the common method based on up-conversion technology costs at least 2 × N digital-to-analog converters(DACs) and N IQ mixers. The expenses and complicate mixer calibration have become a hinderance for intermediate-scale quantum control.Here we propose a universal control scheme for superconducting circuits, fully based on parametric modulation. To control N qubits on a chip, our scheme only requires N DACs and no IQ mixer, which significantly reduces the expenses. One key idea in the control scheme is to introduce a global pump signal for single-qubit gates. We theoretically explain how the universal gates are constructed using parametric modulation. The fidelity analysis shows that parametric single-qubit(two-qubit) gates in the proposed scheme can achieve low error rates of 10~(4), with a gate time of about 60 ns(100 ns).     

若干高精度恒稳的半显式差分格式

本文构造了解色散方程u₁=au_xxx的若干三层恒稳的半显式差分格式。第Ⅰ、Ⅱ类格式的局部截断误差的阶为O(τ²+h²+(τ²)/(h³));而第Ⅲ、Ⅳ类格式的局部截断误差的阶为O(τ²+h⁴+((τ)/(h))²+τh)。用判别稳定性的Von Neumann准则可证明:第Ⅰ、Ⅱ类格式及当参数α≤1时的第Ⅲ、Ⅳ类格式都是无条件稳定的,并且当必须的边界条件给定时它们可以显式地进行计算。     

Branes, geometry and N = 1 duality with product gauge groups of SO and Sp

We study N = 1 dualities in four-dimensional supersymmetric gauge theories as the world volume theory of D4 branes with one compact direction in type IIA string theory. We generalize the previous work for SO(N_c1) × Sp(N_c2) with the superpotential W = TrX⁴ to the case of W = TrX^4(k+1) in terms of brane configuration. We conjecture that the new dualities for the product gauge groups of SO(N_c1) × Sp(N_c2) × SO(N_c3), SO(N_c1) × Sp(N_c2) × SO(N_c3) × Sp(N_c4) and higher multiple product gauge groups can be obtained by reversing the ordering of NS5 branes and D6 branes while preserving the linking numbers. We also describe the above dualities in terms of wrapping D6 branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. The theory with adjoint matter can be regarded as taking multiple copies of NS5 brane in the configuration of brane or geometric approaches.     

M-theory on AdS4 × M: the complete Osp(2|4) × SU(3) × SU(2) spectrum from harmonic analysis

We reconsider the Kaluza-Klein compactifications of D = 11 supergravity on AdS₄ × (G/H)₇ manifolds that were classified in the eighties, in the modern perspective of AdS₄/CFT₃ correspondence. We focus on one of the three N = 2 cases: (G/H)₇ = M¹¹¹ = SU(3) × SU(2) × U(1) /SU(2) × U(1)′ × U(1)′'. Relying on the systematic use of the harmonic analysis techniques developed in the eighties by one of us (P. Fré) with R. D'Auria, we derive the complete spectrum of long, short and massless Osp(2|4) × SU(3) × SU(2) unitary irreducible representations obtained in this compactification. Our result also provides a general scheme for the other N = 2 compactifications. Furthermore, it is a necessary comparison term in the AdS₄/CFT₃ correspondence: the complete AdS/CFT match of the spectra that we obtain will provide a much more stringent proof of the ACS/CFT correspondence than in the S⁷ case, since the structure of the superconformal field theory on the M2-brane world volume must be such as to reproduce, at the level of composite operators, the flavor group representations, the conformal dimensions and the hyperchanges that we obtain in the present article. The investigation of this match is left to future publications. Here we provide an exhaustive construction of the Kaluza-Klein side of our spectroscopy.     

一端附壁高分子链的Monte Carlo研究

采用简立方格点上的Monte Carlo模拟,研究一端被无限大不可穿透平面壁吸附的高分子链的均方末端距<R²>,以及高分子链的质量中心到平面吸附壁的平均距离<Z>,与链长N、参数u(u=e^-ε/kT,ε是链骨架原子间的相互作用能量,k是玻耳兹曼常数,T是热力学温度)的关系。结果表明:<R²>和<Z>都服从标度律,<R²>=αN^γ,<Z>=βN^η,其中,γ、η、α、β都是u的函数;u从1减小到0.5,则γ从1.01增大到1.19,η从0.51增大到0.60.     

πN scattering and electromagnetic corrections in the perturbative chiral quark model

We apply the perturbative chiral quark model to give predictions for the electromagnetic O(p²) low-energy couplings of the ChPT effective Lagrangian that define the electromagnetic mass shifts of nucleons and first-order (e²) radiative corrections to the πN scattering amplitude. We estimate the leading isospin-breaking correction to the strong energy shift of the π⁻p atom in the 1s state, which is relevant for the experiment “Pionic Hydrogen” at PSI.     

基于新的整数型分子图论指数M系统探索烷烃核磁共振碳谱(13C NMR)化学位移和CSS规律

系统研究了核磁共振碳谱与化学位移和规律,以及拓扑图论方法在定量结构波谱关系(QSSR)中的应用.本文基于路径长度矢量p=p1,p2,p3,…,pm)组合研究提出了一种新的整数型拓扑图论指数M=(p1+p2)+(p1-p3),并发现它与烷烃¹³C NMR化学位移和有良好线性相关性:回归方程及其统计参数为CSS=+14.329^* M-21.089;n=65,R=0.991,SD=7.684,F=3648.021,U=215381.656,Q=3719.563;交互校验CV结果为:R=0.990,R²(01)=0.981,SD(01)=8.086,F(01)=3288.113,U(01)=214982.172,Q(01)=4119.042.     

High energy factorization in electroweak processes

We propose to use high energy, k-dependent, factorization (HEF) in electroweak fusion processes in order to systematically improve the effective W approximation (EWA) at collider energies. Starting from the example of top production, we show that HEF provides correctly all quasi constant terms in the production cross section, i.e. not only the ones O(1/M_w²) which are typical of the EWA and are due to longitudinal polarizations of exchanged bosons, but also the ones O(1/M_w²) which are partly due to transverse polarizations. It turns out that latter contributions cannot be accounted for by collinear factorization only, but also come from longitudinal off-shell effects, typical of broken gauge theories, which are explicitly evaluated here.     

Universal enveloping algebra and differential calculi on inhomogeneous orthogonal q-groups

We review the construction of the multiparametric quantum group ISO_q,r(N) as a projection from SO_q,r (N + 2) and show that it is a bicovariant bimodule over SO_q,r(N). The universal enveloping algebra U_q,r(iso(N)), characterized as the Hopf algebra of regular functionals on ISO_q,r(N), is found as a Hopf subalgebra of U_q,r(so(N + 2)) and is shown to be a bicovariant bimodule over U_q,r(so(N)).

An R-matrix formulation of U_q,r(iso(N)) is given and we prove the pairing U_q,r(iso(N)) — ISO_q,r(N)). We analyze the subspaces of U_q,r(iso(N)) that define bicovariant differential calculi on ISO_q,r(N).     

Neumann边界条件的处理对差分解逼近精度的影响

本文以一维对流扩散方程为例,较系统地论证了Neumann边界的差分处理对差分解逼近精度的影响。并从数值上考察了Neumann边界的差分处理对二维Poisson方程差分解的影响。结果表明:O(h)格式可能导致一阶精度的差分解,也可能导致二阶精度的差分解;而O(h²)和O(h³)格式产生的差分解只有二阶精度。     

求解Burgers方程的一种交替分段隐式算法

首先提出一个新的求解Burgers方程的差分格式,然后在此差分格式的基础上构造了便于并行计算的交替分段隐格式,并作了线性化稳定性分析.数值结果表明,本方法具有较高的精度,尤适于扩散项系数较小时的计算,且有效避免了数值结果的非物理振荡.     

Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems

The clock operator U and shift operator V are higher-dimensional Pauli operators. Just recently, tighter uncertainty relations with respect to U and V were derived, and we apply them to study the electron localization properties in several typical one-dimensional nonuniform lattice systems. We find that uncertainties △ U² are less than, equal to, and greater than uncertainties △ V² for extended, critical, and localized states, respectively. The lower bound LB of the uncertainty relation is relatively large for extended states and small for localized states. Therefore, in combination with traditional quantities, for instance inverse participation ratio, these quantities can be as novel indexes to reflect Anderson localization.     

Granularity, microstructure, and flux creep in TlBa2Ca2Cu3O9+δ superconducting powder and silver-sheated tapes

Silver-sheathed TlBa₂Ca₂Cu₃O_9+δ (Tl-1223) tapes, with a transport critical current density, J_ct, of 6200 A/cm² at 75 K under zero magnetic field, were fabricated by the oxide-powder-in-tube (OPIT) method and characterized using an X-ray diffractometer (XRD), scanning electron microscope (SEM), transmission electron microscope (TEM), and superconducting quantum interference device (SQUID) magnetometer. The results of the magnetization and SEM study indicate that, in these tapes, individual grains are distributed randomly in orientation and weak links exist. However, strongly linked percolative current paths within the tape persisting in increasing fields, accompanied by strong intrinsic interplanar coupling, sustain a significant J_ct at high fields and lead to the plateau in the J_ct-H curve. Dislocation networks, which may act as effective pinning centers, are the common features observed in the tapes. To investigate the effects on flux pinning due to thermomechanical processing, magnetic relaxation at 1 and 2 T over 5–50 K was measured. The tape shows slightly lower normalized relaxation rates (S=-(1/M_o)dM/ dln t) than the cauliflower-like precursor powder. Analyses of the relaxation data obtained from the tape, after incorporating temperature dependence and field scaling, yield an expression for the effective pinning energy U_eff(J,T,H) = (U₁/H^0.54)[1-(T/ 72.5)²]⁴(J/J_i)^μ. This result was compared with the prediction of the collective flux-creep model, which suggests that Tl-1223 has a three-dimension-like (3D-like) vortex lattice. Presumably, a more plate-like powder morphology may result in improved texturing by the OPIT process. Tl_0.5Bi_0.5Sr₂CaCu₂O_7+δ ((Tl,Bi)-1212) powder with this morphology was therefore synthesized for comparison.     

Chiral symmetry for positive and negative parity nucleons

We investigate the role of chiral symmetry in the properties of positive and negative parity nucleons (N and N^*). When we consider two kinds of nucleons, two distinctive types of chiral assignment for N^* can be introduced. There are interesting differences between the two assignments in the properties of nucleons, which are studied using linear sigma models based on the two assignments. Behavior of N and N^* in the nuclear medium is also investigated using these linear models.     

GUT breaking on M×T/(Z2×Z2′)

We construct two SU(5) models on the space–time M⁴×T²/(Z₂×Z₂′) where the gauge and Higgs fields are in the bulk and the Standard Model fermions are on the brane at the fixed point or line. For the zero modes, the SU(5) gauge symmetry is broken down to SU(3)×SU(2)×U(1) due to non-trivial orbifold projection. In particular, if we put the Standard model fermions on the 3-brane at the fixed point in model II, we only have the zero modes and KK modes of the Standard Model gauge fields and two Higgs doublets on the observable 3-brane. So, we can have the low energy unification, and solve the triplet–doublet splitting problem, the gauge hierarchy problem, and the proton decay problem.     

Quantum metrology with coherent superposition of two different coded channels

We investigate the advantage of coherent superposition of two different coded channels in quantum metrology. In a continuous variable system, we show that the Heisenberg limit 1/N can be beaten by the coherent superposition without the help of indefinite causal order. And in parameter estimation, we demonstrate that the strategy with the coherent superposition can perform better than the strategy with quantum SWITCH which can generate indefinite causal order. We analytically obtain the general form of estimation precision in terms of the quantum Fisher information and further prove that the nonlinear Hamiltonian can improve the estimation precision and make the measurement uncertainty scale as 1/Nm for m ≥ 2. Our results can help to construct a high-precision measurement equipment, which can be applied to the detection of coupling strength and the test of time dilation and the modification of the canonical commutation relation.     

波动方程辛算法的迭代求解

对(∂²)/(∂x²)利用中心差商算子,对expt作对角Padé逼近,由波动偏微分方程可得到两类具有O(Δx²+Δt^2l)和O(Δx⁴+Δt^2l)精度的辛格式.对由此类辛格式产生的线性方程组构造了两种迭代解法,并对l=1,2,3,4给出了它们的收敛条件.并进行了数值实验.