Global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on bipartite lattices

In this paper the global symmetry of the Hubbard model on a bipartite lattice is found to be larger than SO(4). The model is one of the most studied many-particle quantum problems, yet except in one dimension it has no exact solution, so that there remain many open questions about its properties. Symmetry plays an important role in physics and often can be used to extract useful information on unsolved non-perturbative quantum problems. Specifically, here it is found that for on-site interaction U ≠ 0 the local SU(2) × SU(2) × U(1) gauge symmetry of the Hubbard model on a bipartite lattice with N_a^D sites and vanishing transfer integral t = 0 can be lifted to a global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with t > 0. (Examples of a bipartite lattice are the D-dimensional cubic lattices of lattice constant a and edge length L = N_aa for which D = 1, 2, 3,... in the number N_a^D of sites.) The generator of the new found hidden independent charge global U(1) symmetry, which is not related to the ordinary U(1) gauge subgroup of electromagnetism, is one half the rotated-electron number of singly occupied sites operator. Although addition of chemical-potential and magnetic-field operator terms to the model Hamiltonian lowers its symmetry, such terms commute with it. Therefore, its 4^N_aD energy eigenstates refer to representations of the new found global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry. Consistently, we find that for the Hubbard model on a bipartite lattice the number of independent representations of the group SO(3) × SO(3) × U(1) equals the Hilbert-space dimension 4^N_aD. It is confirmed elsewhere that the new found symmetry has important physical consequences.     

Application of large deviation theory to the mean-field $\boldsymbol{\varphi}^\mathsf{4}$-model

A large deviation technique is used to calculate the microcanonical entropy function s(v,m) of the mean-field ϕ⁴-model as a function of the potential energy v and the magnetization m. As in the canonical ensemble, a continuous phase transition is found. An analytical expression is obtained for the critical energy v_c(J) as a function of the coupling parameter J.     

A Higher Dimensional Inflationary Universe in General Relativity

A five dimensional Kaluza-Klein inflationary universe is investigated in the presence of massless scalar field with a flat potential. To get an inflationary universe a flat region in which potential V is constant is considered. Some physical and kinematical properties of the universe are also discussed.     

Creation of fundamental particles in Wesson’s IMT

Fundamental particles, regarded as possible constituents of quarks and leptons, are described classically in the framework of the Weyl-Dirac version of Wesson’s Induced Matter Theory (IMT). There are neutral particles and particles having charge \(\pm \frac{1}{3}e\). The particles appear on the 4D brane, our universe, and are filled with an induced by the 5D bulk substance. This substance is taken to have mass density, pressure, and (if charged) charge density, and is characterized by the equation of state ρ + P = 0. The interior is separated from the surrounding vacuum by a spherical boundary surface where the components of the 4D metric tensor h ₀₀ = 1/h ₁₁ = 0. Outside of the boundary holds the Schwarzschild, or the Reissner–Nordstrøm metric, while the particles are characterized by Mass, Radius, Charge.     

高反射率Mo/B4C多层膜设计及制备

 运用遗传算法优化设计了Mo/B₄C多层膜结构。入射光入射角度取10°时,设计的理想多层膜膜对数为150,周期为3.59 nm,Gamma值（Mo膜厚与周期的比值）为0.41,峰值反射率为33.29%。采用恒功率模式直流磁控溅射方法制作Mo/B₄C多层膜。通过在Mo/B4C多层膜与基底之间增加15 nm厚的Cr粘附层,提高多层膜与基底的粘附力。另外,还采用调整多层膜Gamma值的方法减小其内应力,调整后多层膜结构周期为3.59 nm, Mo膜厚1.97 nm, B4C膜厚1.62 nm,峰值反射率26.34％。制备了膜对数为150的Mo/B₄C膜并测量了其反射率,在波长7.03 nm处,Mo/B₄C多层膜的近正入射反射率为21.0％。最后对测量结果进行了拟合,拟合得到Mo/B₄C多层膜的周期为3.60 nm,Gamma值0.60,界面粗糙度为0.30 nm。     

通用ATS实现技术研究

我国武器装备通用ATS(自动测试系统)经历了从引进、仿制到自行研制的过程,但是目前通用ATS总的局面是通用ATS不通用,这种局面主要是由于国内对通用ATS实现技术缺乏统一认识造成的。基于此,本文研究了与开发通用ATS密切相关的标准／规范、硬件配置技术、接口技术、集成测试软件开发环境技术。本文的研究结果适用于所有开发通用ATS的项目。     

Level-dynamic approach to the excited spectra of the Jahn-Teller model – kink-train lattice and ‘glassy’ quantum phase

The dynamics of excited phonon spectra of the E⊗e Jahn-Teller (hereafter, JT) model mapped onto the generalized Calogero-Moser (gCM) gas of pseudoparticles implies a complex interplay between nonlinearity and fluctuations of quasiparticle trajectories. A broad crossover appears in a pseudotime (interaction strength) between the initial oscillator region and the nonlinear region of the kink-train lattice as a superlattice of the kink-antikink gCM trajectories. The local nonlinear fluctuations, nuclei (droplets) of the growing kink phase arise at the crossover, forming a new intermediate droplet “glassy” phase as a precursor of the kink phase. The “glassy” phase is related to a broad maximum in the entropy of the probability distributions of pseudoparticle accelerations, or level curvatures. The kink-train lattice phase with multiple kink-antikink collisions is stabilised by long-range correlations when approaching a semiclassical limit. A series of bifurcations of nearest-level spacings were recognised as signatures of pre-chaotic behaviour at the quantum level in the kink phase. Statistical characteristics can be seen to confirm the coexistence within all of the spectra of both regularity and chaoticity to a varying extent (nonuniversality). Regions are observed within which one of the phases is dominant.     

Acoustic radiation force on an air bubble and soft fluid spheres in ideal liquids: Example of a high-order Bessel beam of quasi-standing waves

The partial wave series for the scattering of a high-order Bessel beam (HOBB) of acoustic quasi-standing waves by an air bubble and fluid spheres immersed in water and centered on the axis of the beam is applied to the calculation of the acoustic radiation force. A HOBB refers to a type of beam having an axial amplitude null and an azimuthal phase gradient. Radiation force examples obtained through numerical evaluation of the radiation force function are computed for an air bubble, a hexane, a red blood and mercury fluid spheres in water. The examples were selected to illustrate conditions having progressive, standing and quasi-standing waves with appropriate selection of the waves’ amplitude ratio. An especially noteworthy result is the lack of a specific vibrational mode contribution to the radiation force determined by appropriate selection of the HOBB parameters.     

Dynamical and thermodynamical stability of two-dimensional flows: variational principles and relaxation equations

We review and connect different variational principles that have been proposed to settle the dynamical and thermodynamical stability of two-dimensional incompressible and inviscid flows governed by the 2D Euler equation. These variational principles involve functionals of a very wide class that go beyond the usual Boltzmann functional. We provide relaxation equations that can be used as numerical algorithms to solve these optimization problems. These relaxation equations have the form of nonlinear mean field Fokker-Planck equations associated with generalized “entropic” functionals [P.H. Chavanis, Eur. Phys. J. B 62, 179 (2008)].