THE TWO-BOSON SCATTERING PHASE SHIFTS IN THE GENERAL φ6 THEORY WITH THE GAUSSIAN WAVE-FUNCTIONAL APPROACH

The two-particle scattering phase shifts with a λφ⁴ +ξφ⁶ interaction are com-puted in (1 + 1) and (2 + 1) dimensions using the Gaussian wave-functional approach.Through numerical analysis, we give the phase-shift curves with respect to the scat-tering energy for most cases of this theory. In (1 + 1) and (2 + 1 ) dimensions, for the symmetry vacuum the phase shifts are positive or negative depending on the signs of the renormalized parameter, while for the asymmetric vacuum the phase shifts are negative.     

High accuracy calculation of the hydrogen negative ion in strong magnetic fields

Using a full configuration-interaction method with Hylleraas-Gaussian basis function, this paper investigates the 1¹0⁺, 1¹(–1)⁺ and 1¹(–2)⁺ states of the hydrogen negative ion in strong magnetic fields. The total energies, electron detachment energies and derivatives of the total energy with respect to the magnetic field are presented as functions of magnetic field over a wide range of field strengths. Compared with the available theoretical data, the accuracy for the energies is enhanced significantly. The field regimes 3 < γ < 4 and 0.02 < γ < 0.05, in which the 1¹(–1)⁺ and 1¹(–2)⁺ states start to become bound, respectively, are also determined based on the calculated electron detachment energies.     

OPTICAL-OPTICAL DOUBLE-RESONANCE EXCITATION SPECTRA OF THE (6d)1Πg, (7d)1Πg HIGH-LYING RYDBERG STATES IN Na2

Two ¹Π_g states of Na₂ for v≤13 have been observed by using optical-optical double resonance (OODR) fluorescence excitation spectroscopy. The intermediate levels in B¹Π_u state are identified by the numerical calculations with the molec-ular constants for B¹Π_u←X¹Σ_g⁺ transitions and confirmed by the complemen-tary A¹Σ_g⁺←X¹Σ_g⁺ polarization spectra. Absolute vibrational numberings of the (6d)¹Π_g and (7d)¹Π_g states are determined by comparing the experimental OODR excitation intensities with the simulated Franck-Condon factors. The Dnnham coef-ficients and the Rydberg-Klein-Rees (RKR) potential energy curves of the (6d)¹Π_g, (7d)¹Π_g states are reported.     

Stacking fault energy of cryogenic austenitic steels

Stacking fault energy and stacking fault nucleation energy are defined in terms of the physical nature of stacking faults and stacking fault energy, and the measuring basis for stacking fault energy. Large quantities of experimental results are processed with the aid of a computer and an expression for calculating stacking fault energy has been obtained as γ³⁰⁰_SF(mJ·m^-2)=γ⁰_SF+1.59Ni-1.34Mn+0.06Mn²-1.75Cr+0.01Cr²+15.21Mo-5.59Si-60.69(C+1.2N)^1/2 + 26.27(C+1.2N)(Cr+Mn+Mo)^1/2+0.61[Ni·(Cr+Mn)]^1/2.     

Spectroscopic parameters and molecular constants of HI(X~1Σ~+),DI(X~1Σ~+) and TI(X~1Σ~+) isotope molecules

The potential energy curve (PEC) of HI(X¹Σ⁺) molecule is studied using the complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration interaction approach at the correlation-consistent basis sets, aug-cc-pV6Z for H and aug-cc-pV5Z-pp for I atom. Using the PEC of HI(X¹Σ⁺), the spectroscopic parameters of three isotopes, HI(X¹Σ⁺), DI(X¹Σ⁺) and TI(X¹Σ⁺), are determined in the present work. For the HI(X¹Σ⁺), the values of D₀, D_e, R_e, ω_e, ω_eχ_e, α_e and B_e are 3.1551 eV, 3.2958 eV, 0.16183 nm, 2290.60 cm^-1, 40.0703 cm^-1, 0.1699 cm^-1 and 6.4373 cm^-1, respectively; for the DI (X¹Σ⁺), the values of D₀, D_e, R_e, ω_e, ω_eχ_e, α_e and B_e are 3.1965 eV, 3.2967 eV, 0.16183 nm, 1626.8 cm^-1, 20.8581 cm^-1, 0.0611 cm^-1 and 3.2468 cm^-1, respectively; for the TI (X¹Σ⁺), the values of D₀, D_e, R_e, ω_e, ω_eχ_e, α_e and B_e are of 3.2144 eV, 3.2967 eV, 0.16183 nm, 1334.43 cm^-1, 14.0765 cm^-1, 0.0338 cm^-1 and 2.1850 cm^-1, respectively. These results accord well with the available experimental results. With the PEC of HI(X¹Σ⁺) molecule obtained at present, a total of 19 vibrational states are predicted for the HI, 26 for the DI, and 32 for the TI, when the rotational quantum number J is equal to zero (J = 0). For each vibrational state, vibrational level G(?), inertial rotation constant B_? and centrifugal distortion constant D_? are determined when J = 0 for the first time, which are in excellent agreement with the experimental results.     

Double-heavy tetraquark states with heavy diquark-antiquark symmetry

We calculate the masses of the QQqq(Q=c,b:q=u,d,s)tetraquark states with the aid of heavy diquark-antiquark symmetry(HDAS)and the chromomagnetic interaction(CMI)model.The masses of the highestspin(J=2)tetraquarks that have only the(QQ)(3):(qq)₃.color structure are related with those of conventional hadrons using HDAS.Thereafter,the masses of their partner states are determined with the mass splittings in the CMI model.Our numerical results reveal that(i)the lightest ccnn(n=u,d)is an I(J^P)=0(1⁺)state around 3929 MeV(53 MeV above the DD^* threshold),and none of the double-charm tetraquarks are stable;(ii)the stable double-bottom tetraquarks are the lowest 0(1⁺)bbin around 10488 MeV(≈116 MeV below the BB^*threshold)and the lowest 1/2(1⁺)bbns around 10671 MeV(≈20 MeV below the BB_s^*/B_sB^*threshold);and(iii)the two lowest bcnn tetraquarks,namely the lowest 0(0⁺)around 7167 MeV and the lowest 0(1)around 7223 MeV,are in the nearthreshold states.Moreover,we discuss the constraints on the masses of double-heavy hadrons.Specifically,for the lowest nonstrange tetraquarks,we obtain T_cc<3965 MeV,T_bb<10627 MeV,and T_bc<7199 MeV.     

Hawking-Page phase transitions of charged AdS black holes surrounded by quintessence

Hawking-Page phase transitions between the thermal anti-de Sitter vacuum and charged black holes surrounded by quintessence are studied in the extended phase space.The quintessence field,with the state parameter-1相似文献   

Phase transition and pitting corrosion behaviour for Mo—implanted aluminium

Molybdenum ions are implanted into aluminium with high ion flux and high dose at elevated temperatures of 200℃, 400℃ and 500℃. Due to the high temperature and high flux of vacancies and interstitial atoms, the atom diffusion and chemical effects are enhanced during the ion implantation. The effects increase with increasing ion flux and dose, so that new phase formation and phase transition emerge noticeably. X-ray diffraction analysis shows that when the aluminium is implanted with Mo ions at a low ion flux (25μA/cm²), the Al₅Mo alloy is formed. The atomic ratio of Mo/Al of the Al₅Mo phase is close to 20%. When the aluminium is implanted with Mo ions at a high ion flux (50μA/cm²), the phase transition from Al₅Mo to Al₁₂Mo appears, and the latter is dominant, which is determined to be the final phase. The ratio of Mo/Al in Al₁₂Mo is 7.7%. Rutherford backscattering spectroscopy indicates also that the Mo/Al atom ratio is ～7% to ～8% in Mo-implanted aluminium. The atomic ratios of the constituents in Al₅Mo and Al₁₂Mo are of stoichiometric composition for these alloys. The thicknesses of the Al₁₂Mo alloy layers for Mo-implanted Al with ion doses of 3×10¹⁷/cm² and 1×10¹⁸/cm² are 550nm and 2000nm, respectively. The pitting corrosion potential V_p increases obviously. It is clear that due to the formation of Al₁₂Mo alloy layer, the pitting corrosion resistance is enhanced.     

NORMALLY ORDERED FORMS OF SHAPIRO-WAGNER PHASE OPERATORS AND THEIR APPLICATION

Based on the quantum mechanical representation |ξ〉=exp[\dfrac12|ξ|+ξ a⁺₁+ξ^* a⁺₂-a⁺₁a⁺₂]|00〉constructed by Fan Hong-yi and with the help of the technique of integration within an ordered product of operators, we derive the normally ordered expressions of the Shapiro-Wagner (SW) phase operators. They are in terms of the Bessel functions. As their application we discuss the minimal uncertain relation regarding the two-mode phase and number-difference operators.     

Electron-impact ionization cross section calculations for lithium-like ions

The electron-impact ionization of lithium-like ions C³⁺,N⁴⁺,O⁵⁺,Ne⁷⁺,and Fe2³⁺is studied using a combination of two-potential distorted-wave and R-matrix methods with a relativistic correction.Total cross sections are computed for incident energies from 1 to 10 times of ionization energy and better agreements with the experimental results are obtained in comparison with the theoretical data available.It is found that the indirect ionization processes become significant for the incident energy larger than about four times of the ionization energy.Contributions from the exchange effects along the isoelectronic sequence are also discussed and found to be important.The present method can be used to obtain systematic ionization cross sections for highly charged ions across a wide incident energy range.     

Scalar-Particle Self-Energy Amplitudes and Confinement in Minkowski Space

We analyze the analytic structure of the Covariant Spectator Theory (CST) contribution to the self-energy amplitude for a scalar particle in a ${\phi^2\chi}$ theory. To this end we derive dispersion relations in 1+1 and in 3+1 dimensional Minkowski space. The divergent loop integrals in 3+1 dimensions are regularized using dimensional regularization. We find that the CST dispersion relations exhibit, in addition to the usual right-hand branch cut, also a left-hand cut. The origin of this “spectator” left-hand cut can be understood in the context of scattering for a scalar ${\phi^2\chi^2}$ -type theory. If the interaction kernel contains a linear confining component, its contribution to the self-energy vanishes exactly.     

?4模型真空态间的转换算符

本工作在正则量子化的基础上,对$\phi^4$模型的哈密顿量采取正规序来正规化真空零点能,然后微扰计算了至次领头阶的真空态修正。同时首次得到可以在$\phi^4$模型的两个真空态之间转换的算符,我们相信这个算符也是适当极限条件下产生$\phi^4$扭结(kink)的算符的形式。最后简要说明了真空能的应用。     

Super-sensitivity measurement of tiny Doppler frequency shifts based on parametric amplification and squeezed vacuum state

The precision measurement of Doppler frequency shifts is of great significance for improving the precision of speed measurement. This paper proposes a precision measurement scheme of tiny Doppler shifts by a parametric amplification process and squeezed vacuum state. This scheme takes a parametric amplification process and squeezed vacuum state into a detection system, so that the measurement precision of tiny Doppler shifts can exceed the Cram′er–Rao bound of coherent light. Simultaneously, a simulation study is carried out on the theoretical basis, and the following results are obtained: for the signal light of Gaussian mode, when the amplification factor g = 1 and the squeezed factor r = 0.5, the measurement error of Doppler frequency shifts is 14.4% of the Cramer–Rao bound of the coherent light in our system. At the same time,when the local light mode and squeezed vacuum state mode are optimized, the measurement precision of this scheme can be further improved by ■ times, where n is the mode-order of the signal light.     

On the Geodesic Hypothesis in General Relativity

In this paper, we give a rigorous derivation of Einstein’s geodesic hypothesis in general relativity. We use small material bodies ${\phi^\epsilon}$ governed by the nonlinear Klein–Gordon equations to approximate the test particle. Given a vacuum spacetime ${([0, T]\times\mathbb{R}^3, h)}$ , we consider the initial value problem for the Einstein-scalar field system. For all sufficiently small ε and δ ≤ ε ^q , q > 1, where δ, ε are the amplitude and size of the particle, we show the existence of the solution ${([0, T]\times\mathbb{R}^3, g, \phi^\epsilon)}$ to the Einstein-scalar field system with the property that the energy of the particle ${\phi^\epsilon}$ is concentrated along a timelike geodesic. Moreover, the gravitational field produced by ${\phi^\epsilon}$ is negligibly small in C ¹, that is, the spacetime metric g is C ¹ close to the given vacuum metric h. These results generalize those obtained by Stuart in (Ann Sci École Norm Sup (4) 37(2):312–362, 2004, J Math Pures Appl (9) 83(5):541–587, 2004).     

Variational study of vacuum structure with fermions ind+1 dimensional Hamiltonian lattice gauge theory

The physical vacuum state and general expression for the Hamiltonian ofd+1 dimensional lattice gauge theory are given by incorporating the exact ground state of pure gauge theory and the variational fermion vacuum state. The applications toSU(2) andSU(3) gauge theories in 2+1 and 3+1 dimensions are demonstrated and the fermion condensates \(\left\langle {\bar \psi \psi } \right\rangle \) as functions of 1/g ² are calculated.     

Negative refraction in ferromagnetic materials under external magnetic field: a theoretical analysis

We present a detailed theoretical analysis on the possibilities and conditions for negative permeability and negative refraction occuring in the magnetic materials with both pronounced magnetic and dielectric responses to electromagnetic waves. The results indicate that the permeability is always positive for $\de=(2q+0.5)\pi$ ($\de$ is the initial phase difference of magnetic components $h_{x}$ and $h_{y }$ of incident electromagnetic wave, $q$ is integer), which means that it is difficult to realize negative refraction. However, for $\de=2q\pi, \de=(2q+1)\pi$, or $\de=(2q-0.5)\pi$, the negative permeability occurs at some range of free procession frequency, which means that the refraction can become negative under certain conditions. Further analysis reveals that for general positive permittivity there are various opportunities for realizing the negative refraction provided that some requirements are met. One concludes also that the refractive index for $\de=2q\pi$ case is similar to $\de=(2q+1)\pi$. The only difference between two cases of $\de=2q\pi$ and $\de=(2q+1)\pi$ is that the $x$-direction for $\de=2q\pi$ corresponds to the $y$-direction for $\de=(2q+1)\pi$, and the $y$-direction for $\de=2q\pi$ corresponds to the $x$-direction for $\de=(2q+1)\pi$. The results are valuable for designing and analysing the complex negative refraction of magnetic materials.     

TWO-PARTICLE BOUND STATES IN THE QUANTUM SINE-GORDON FIELD THEORY IN (D+1) DIMENSIONS

The two-particle states of the quantum sine-Gordon fields are studied variationally in (D+1) dimensions using the Gaussian wave functional approach. In both (1+1) and (2+1) dimensions, there exist two-particle bound states for certain ranges of coupling constant, where the vacuum states are stable. In the higher dimensions (D > 2), this approximation indicates that the two-particle states may be only the states consisting of two free particles, which is conformable to the triviality of the sine-Gordon field theory previously obtained in recent literatures.     

Interaction between two folded solitary waves for a modified Broer--Kaup system

By means of a Painlevé-Baicklund transformation and a multi-linear separation-of-variable approach, abundant localized coherent excitations of a modified Broer-Kaup system are derived. There appear possible phase shifts for the interactions of the （2＋1）-dimensional novel localized structures, which are discussed in this paper.     

Scalar Theories and Symmetry Breaking in the Light-Front Coupled-Cluster Method

We extend the light-front coupled-cluster (LFCC) method to include zero modes explicitly, in order to be able to compute vacuum structure in theories with symmetry breaking. Applications to \({\phi^3}\) and \({\phi^4}\) theories are discussed as illustrations and compared with variational coherent-state analyses.     

Phase and frequency shifts of two nonlinearly coupled oscillators

We analyze two nonlinearly phase coupled oscillators with eigenfrequencies ω₁and ω₂, where n\gw₁=m\gw₂+\gp, with integern andm. For \gh=0 there are up to four stable synchronized states which differ from each other only by the difference of the oscillators\rs phases. The number of different synchronized states depends on the coupling constants. If \gh does not vanish phase shifts and frequency shifts may occur givig rise to stable synchronized states which also differ from each other due to the frequencies. By means of the center manifold theorem we calculate these shifts explicitely. Different coupling constants are investigated: symmetrical, homogenously asymmetrical and arbitrary coupling constants. Our results point out the decisive influence of the symmetry of the coupling constants upon the frequency and phase shifts. Moreover the local stability of the unperturbed synchronized state (i.e. for \gh=0) determines the magnitude of the frequency and phase shifts.