Unitary representations of the Virasoro and super-Virasoro algebras

It is shown that a method previously given for constructing representations of the Virasoro algebra out of representations of affine Kac-Moody algebras yields the full discrete series of highest weight irreducible representations of the Virasoro algebra. The corresponding method for the super-Virasoro algebras (i.e. the Neveu-Schwarz and Ramond algebras) is described in detail and shown to yield the full discrete series of irreducible highest weight representations.     

Set logics and their representations

We examine a set logic by means of all its representations as a concrete logic together with the automorphism groups of the representations. The most important are the minimal representations, i.e., the ones defined by minimal full collections of two-valued states. From this point of view we also investigate some Greechie diagrams.     

Representations of hypergraph states with neural networks

The quantum many-body problem(QMBP) has become a hot topic in high-energy physics and condensed-matter physics. With an exponential increase in the dimensions of Hilbert space, it becomes very challenging to solve the QMBP, even with the most powerful computers. With the rapid development of machine learning, artificial neural networks provide a powerful tool that can represent or approximate quantum many-body states. In this paper, we aim to explicitly construct the neural network representations of hypergraph states. We construct the neural network representations for any k-uniform hypergraph state and any hypergraph state,respectively, without stochastic optimization of the network parameters. Our method constructively shows that all hypergraph states can be represented precisely by the appropriate neural networks introduced in [Science 355(2017) 602] and formulated in [Sci. China-Phys.Mech. Astron. 63(2020) 210312].     

Lie algebras and representations of continuous groups

It is shown that every finitely generated continuous group has a subgroup generated by its infinitesimal transformations. This subgroup has a group algebra which is the Lie algebra of the group. By obtaining complete systems in the Lie algebra and complete rectangular arrays, it is shown that these can yield matrix representations of the continuous group. Illustrative examples are given for the rotation groups and for the full linear groups. It would seem that all the finite motion representations can be obtained by these methods, including spin representations of rotation groups. But the completeness of the method is not here demonstrated.     

Learning Numerosity Representations with Transformers: Number Generation Tasks and Out-of-Distribution Generalization

One of the most rapidly advancing areas of deep learning research aims at creating models that learn to disentangle the latent factors of variation from a data distribution. However, modeling joint probability mass functions is usually prohibitive, which motivates the use of conditional models assuming that some information is given as input. In the domain of numerical cognition, deep learning architectures have successfully demonstrated that approximate numerosity representations can emerge in multi-layer networks that build latent representations of a set of images with a varying number of items. However, existing models have focused on tasks requiring to conditionally estimate numerosity information from a given image. Here, we focus on a set of much more challenging tasks, which require to conditionally generate synthetic images containing a given number of items. We show that attention-based architectures operating at the pixel level can learn to produce well-formed images approximately containing a specific number of items, even when the target numerosity was not present in the training distribution.     

States on Clifford algebras

We study states on Clifford algebras from the point of view of C*-algebras. A criterium is given under which the odd-point functions vanish. A particular set of states, called quasi-free states is extensively studied and explicit representations are given; as an application we give an approximate calculation of the ground state of a Fermion system.On leave from Matematisk Institut, University of Aarhus, Denmark.Aangesteld navorser van het Belgisch N. F. W. O. On leave from University of Louvain, Belgium.     

On a method of constructing irreducible multiplier representations

A systematic method is presented for constructing the irreducible multiplier representations (ray representations) of a class of finite groups corresponding to a given factor system. The method consists in first identifying a normal subgroup of prime index, classifying its irreducible multiplier representations into orbits and then inducing the required representations from these orbits. The proposed technique finds useful application in solid state physics where irreducible multiplier representations of the point group underlying the group of the wave vector are frequently required.     

The Spectra of Quantum States and the Kronecker Coefficients of the Symmetric Group

Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can associate a representation of the symmetric group defined by a Young diagram whose normalised row lengths approximate the spectrum. We show that, for allowed spectra, the representation of the composite system is contained in the tensor product of the representations of the two subsystems. This gives a new physical meaning to representations of the symmetric group. It also introduces a new way of using the machinery of group theory in quantum informational problems, which we illustrate by two simple examples.     

弱非完整系统Mei对称性导致的新型精确和近似守恒量

研究弱非完整系统Lagrange方程的Mei对称性导致的一种结构方程和新型精确以及近似守恒量. 首先建立系统的Lagrange方程. 其次在群的无限小变换下, 给出了弱非完整系统及其一次近似系统Mei对称性的定义和判据, 然后得到了Mei对称性导致的新型结构方程、 新型精确和近似守恒量的表达式. 最后, 举例研究系统的精确新型守恒量和近似新型守恒量问题. 关键词： 弱非完整系统 Mei对称性 新型结构方程 新型守恒量     

Spectral representations for the memory kernel characterizing self-diffusion

Approximate spectral representations are developed for the memory kernel which characterizes self-diffusion. These spectral representations are based upon approximate eigenfunctions constructed via the Rayleigh variational principle. A heuristic model is developed first in an effort to provide physical insight into the nature of the approximations employed, and then a number of specific trial functions are examined. These trial functions include sums of identical one- and two-particle functions as well as linear combinations of hydrodynamical variables. The results from these spectral representations indicate that the long-time behavior of the memory kernel (and thereby of the momentum autocorrelation function) is sensitive to the long-range effects of the interparticle potential. In addition, the equivalence of most of these spectral representations to specific low-order perturbation approximations is demonstrated.     

折反式大视场星敏感器光学系统设计

讨论了由逆卡塞格林结构和补偿器构成的折反式星敏感器光学系统。该光学系统由一块球面反射镜、一块非球面反射镜以及由同种光学玻璃做成的两块球面透镜和一块非球面透镜组成。具有视场大、相对孔径大和易实现等优点。给出了该光学系统的设计指标和设计思想,并给出了由其初级像差公式确定初始结构参数的方法。经优化设计,得到了全视场为20°、入瞳直径为36.3mm、相对孔径为1∶1.2的光学系统。给出了它的成像质量评价。     

天光一号MOPA光学角多路系统的研制

 光学角多路系统是主振功放(MOPA)装置的重要组成部分。它不仅连接着主振荡器、预放大器及主放大器三个KrF激光系统，而且起着压缩激光脉宽的作用。光学角多路能使主振激光脉冲在能量上得到足够的放大，并使泵浦预放、主放激光腔的电子束能量及其脉宽得到充分的利用。介绍了天光一号装置上MOPA光学角多路系统的结构,并结合多年来运行的实践，提出了若干优化措施。     

天光一号MOPA光学角多路系统的研制

光学角多路系统是主振功放(MOPA)装置的重要组成部分。它不仅连接着主振荡器、预放大器及主放大器三个KrF激光系统,而且起着压缩激光脉宽的作用。光学角多路能使主振激光脉冲在能量上得到足够的放大,并使泵浦预放、主放激光腔的电子束能量及其脉宽得到充分的利用。介绍了天光一号装置上MOPA光学角多路系统的结构,并结合多年来运行的实践,提出了若干优化措施。     

Inequivalent Representations of Commutator or Anticommutator Rings of Field Operators and Their Applications

Hamiltonian of a system in quantum field theory can give rise to infinitely many partition functions which correspond to infinitely many inequivalent representations of the canonical commutator or anticommutator rings of field operators. This implies that the system can theoretically exist in infinitely many Gibbs states. The system resides in the Gibbs state which corresponds to its minimal Helmholtz free energy at a given range of the thermodynamic variables. Individual inequivalent representations are associated with different thermodynamic phases of the system. The BCS Hamiltonian of superconductivity is chosen to be an explicit example for the demonstration of the important role of inequivalent representations in practical applications. Its analysis from the inequivalent representations’ point of view has led to a recognition of a novel type of the superconducting phase transition. PACS: 03.70.+k, 05.30.−d, 11.10.−z, 74.20.Fg, 74.25.Bt, 74.78.Bz     

Highly entangled ground States in tripartite qubit systems

We investigate the creation of highly entangled ground states in a system of three exchange-coupled qubits arranged in a ring geometry. Suitable magnetic field configurations yielding approximate Greenberger-Horne-Zeilinger and exact W ground states are identified. The entanglement in the system is studied at finite temperature in terms of the mixed-state tangle tau. By generalizing a conjugate gradient optimization algorithm originally developed to evaluate the entanglement of formation, we demonstrate that tau can be calculated efficiently and with high precision. We identify the parameter regime for which the equilibrium entanglement of the tripartite system reaches its maximum.     

Transfer matrix method for optimizing quasioptical EPR cavities

We present a convenient method for characterizing and optimizing the performance of quasioptical electron paramagnetic resonance (EPR) sample cavities. The formalism is based on the transfer matrix method used in transmission line analysis. Transfer matrix representations are defined for each of the essential components of an open resonator, and the method is demonstrated by application to selected practical examples. Emphasis is given to optimization of quasioptical EPR for aqueous biological samples.     

新型大面阵彩色CCD航测相机光学系统设计

介绍了一种有别于传统彩色航测相机的新型大面阵彩色CCD航测相机设计方案,该相机光学系统由Dalsa公司最新生产的6K×8K大面阵彩色CCD作为接收器.通过理论计算和ZEMAX光学设计软件的优化,给出了工作波长适应范围为0.46～0.70μm、焦距为360mm、视场角为10°、相对孔径为1∶4.3的设计实例.设计结果表明...     

FOI-PERFECT程序对电磁驱动高能量密度系统的三维弛豫磁流体力学模拟

提出一个完整的弛豫磁流体力学模型用于电磁驱动高能量密度系统的数值模拟, 它由弛豫电磁波动、弛豫热输运、P1/3近似辐射输运以及流体力学构成。电磁部分在真空区退化为电磁传播, 在等离子体物质区退化为磁扩散近似, 并且相速和群速是有上界的。这意味着弛豫磁流体力学能退化到传统的电阻性磁流体力学, 并且能用显式方法数值求解, 便于大规模高效并行化。基于此弛豫磁流体力学模型开发了三维辐射磁流体力学程序FOI-PERFECT, 指出了所采用的关键数值技术, 并给出了一些应用例子。     

Minimal curvature trajectories: Riemannian geometry concepts for slow manifold computation in chemical kinetics

In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale separation into fast and slow modes. The aim is to approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones via computation of a slow attracting manifold. We present a novel method for computing approximations of such manifolds using trajectory-based optimization. We discuss Riemannian geometry concepts as a basis for suitable optimization criteria characterizing trajectories near slow attracting manifolds and thus provide insight into fundamental geometric properties of multiple time scale chemical kinetics. The optimization criteria correspond to a suitable mathematical formulation of “minimal relaxation” of chemical forces along reaction trajectories under given constraints. We present various geometrically motivated criteria and the results of their application to four test case reaction mechanisms serving as examples. We demonstrate that accurate numerical approximations of slow invariant manifolds can be obtained.     

用于电磁驱动真空-等离子体系统数值模拟的弛豫磁流体力学模型

提出了一个弛豫磁流体力学模型,特别适合电磁驱动真空-等离子体系统的数值模拟。该模型和Seyler采用的弛豫模型有相似之处,即采用全电磁模型,不同的是采用忽略电子惯性项的广义欧姆定律直接作为本构来封闭麦克斯韦方程,减少了独立变量,是适合此类问题的最简模型。分析了磁流体力学模型电磁部分的色散关系,从而论证了其在真空区退化为电磁传播,在等离子体物质区退化为磁扩散近似,并且相速和群速是有上界的。改进了Seyler采用的时间离散方式,从而将时间精度从1阶提高到3阶,时间步长不受刚性源项约束,只受系统最大的特征速度确定的柯朗-弗里德里奇-列维(CFL)条件约束,便于显式计算和大规模并行化。