Comparison characteristics of surface acoustic waves propagating on LGT and quartz substrates

For comprehending the propagation characteristics of surface acoustic waves (SAW) on novel piezoelectric crystal Langatate (LGT), the numerical analysis of the most important propagation characteristics of surface acoustic waves (SAW) on LGT are presented and compared with that of quartz. The results are that the phase velocity on LGT is generally about 1000 m/s slower than that on quartz; there are zero temperature cuts and pure mode directions on LGT; the electromechanical coupling coefficient (K^2) of LGT is larger than that of quartz. The results show that LGT has lower propagation velocity, higher electromechanical coupling coefficient, good temperature stability and other good characteristic. The results also show that there are somewhat deviations with different material constants, especially, the temperature coefficient of frequency.     

Symmetry Analysis of （2＋1）—Dimensional Nonlinear Klein—Gordon Equations

We have obtained two types of two-dimensional similarity reductions for the (2 1)-dimensional Klain-Gordon system using the standard classical Lie group approach with computer algebra.The well-known one-dimension al reductions,radial and travelling reductions are equivalent to the two special cases of our general two-dimensional reductions.     

Conditional Similarity Solutions of （2＋1）—Dimensional General nonintegrable KdV Equation

The real physics models are usually quite complex with some arbitrary parameters which will lead to the nonintegrability of the model.To find some exact solutions of a nonintegrable model with some arbitrary parameters is much more difficult than to find the solutions of a model with some special parameters.In this paper,we make a modification for the usual direct method to find some conditional similarity solutions of a (2 1)-dimensional general nonintegrable KdV equation.     

Theoretical prediction of the optimal conditions for observing the stereodynamical vector properties of the C（3P）＋OH （X2∏）→CO（X1S＋）＋H（2S） reaction

The best optimal initial reactant state and collision energy for observing the stereodynamical vector properties of the title reaction in the ground electronic state X2A’ potential energy surface （PES）[Zanchet et al. 2006 J. Phys. Chem. A 110 12017] are theoretically predicted using the quasi-classical trajectory （QCT） method for the first time. The calculated results reveal that the smallest value of the rotational quantum number j, larger vibrational quantum number v, and the lower strength of collision energy should be selected for offering the most obvious picture about the stereodynamical vector properties. Polarization-dependent differential cross sections and the angular momentum alignment distribution, P（θr） and P（Φr） in the center-of-mass frame, are obtained to gain an insight into the alignment and orientation of the product molecules. The rotational angular momentum vector j’ of CO is aligned to be perpendicular to reagent relative velocity k. The product polarizations align along the y axis, pointing to the positive direction of the y axis. A new method is developed to investigate massive reactions with various initial states and to further study the vector properties of the fundamental reactions in detail.     

Multiple—Scattering of Near—Edge x—ray Absorption Fine Structure of Sulphur—Passivated InP（100） Surface

We use the multiple-scattering cluster method to calculated the sulphur 1s near-edge x-ray absorption fine structure (NEXAFS) of S-passivated InP(100) surface.The physical origins of the resonances in the NEXAFS have been unveiled.It is shown that the most important resonance is attributed to the photoelectron scattering between the central sulphur and the nearest indium atoms.The studies show that two S-S dimers with the bond lengths of 2.05A and 3.05A coexist in the surface,meanwhile the bridge and antibridge site adsorption of single S could not be ruled out.We support the scanning tunnelling microscopy result that the S-passivated InP(100) surface exhibits significant discorder.     

Microscopic—Theoretical Calculations of R—Line Thermal Shifts and Broadenings of MgO：V^2＋

A great improvement on a previous work (PHYS.Rev.B48 (1993) 14067) has been made.By taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of basic wavefunctions within d^3 electronic configuration,the values of all the parameters in the expressions of thermal shift(TS) and thermal broadening (TB) from EPI for the ground level,R level and R line of MgO:V^2 have microscopically been evaluated;and then,both the TS and TB of R line and various contributions to them have uniformly been calculated.The results are in very good agreement with the experimental data.It is found that all the three terms of TS from EPI are red shifts;the term of the contribution to TS from thermal expansion is blue shift.The Raman term is the largest,and the other terms are also important for TS.The R-line TS of MgO:V^2 comes from the first-order term of EPI.The elastic Raman scattering of acoustic phonons plays a dominant role in R-line TB of MgO:V^2 .For calculations of both the TS and TB,it is very important to take into account all the admixtures of wavefunctions.     

Theoretical study of stereodynamics for the O（3P） ＋ H2 → OH ＋ H reaction

This paper employs the quasi-classical trajectory calculations to study the influence of collision energy on the title reaction on the potential energy surface of the ground ³A' triplet state developed by Rogers et al. (J. Phys. Chem. A 2000 104 2308). It calculates the product angular distribution of P(θ_r), P(φ_r) and P(θ_r, φ_r) which reflects vector correlation. The distribution P(θ_r) shows that product rotational angular momentum vectors j' of the products are strongly aligned along the relative velocity direction k. The distribution of P(φ_r) implies a preference for left-handed product rotation in planes parallel to the scattering plane. Four different polarisation-dependent cross-sections are also presented in the centre-of-mass frame. Results indicate that OH is sensitively affected by collision energies of H₂.     

Variable Separation Solutions for the （2＋1）—Dimensional Burgers Equation

Considering that the multi-linear variable separation approach has been proved to be very useful to solve many (2 1)- dimensional intergrable systems,we obtain the variable separation solutions of the Burgers eqation with arbitrary number of variable separated functions.The Y-shaped soliton fusion phenomenon is revealed.     

Exotic Localized Coherent Structures of New（2＋1）－Dimensional Soliton Equation

The variable separation approach is used to obtain localized coherent structures of the new(2 1)-dimensional nonlinear partial differential equation.Applying the Baecklund transformation and introducing the arbitrary functions of the seed solutions,the abundance of the localized structures of this model are derived.Some special types of solutions solitoff,dromions,dromion lattice,breathers and instantons are discussed by selecting the arbitrary functions appropriately .The breathers may breath in their amplititudes,shapes,distances among the peaks and even the number of the peaks.     

Structures of（ΩΩ）0＋and（[1]Ω）1＋in Extended Chiral SU（3） Quark Model

The structures of (ΩΩ)0 and ([1]Ω)1 are studied in the extended chiral SU(3) quark model in which vector meson exchanges are included. The effect from the vector meson fields is very similar to that from the one-gluon exchange (OGE) interaction. Both in the chiral SU(3) quark model and in the extended chiral SU(3) quark model,di-omega (ΩΩ)0 is always deeply bound, with over one hundred MeV binding energy, and ([1]Ω)1 ‘s binding energy is around 20 MeV. An analysis shows that the quark exchange effect plays a very important role for making di-omega (ΩΩ)0 deeply bound.     

On the stochastic confinement in SU(2) lattice gauge theory

We extend the Olesen approach to confinement, originally proposed for SU(∞) gauge theory, to the SU(2) group. We perform Monte Carlo calculations of the spectral density, which describes the distribution of eigenvalues of the Wilson loop in the SU(2) lattice gauge theory (LGT), for square loops up to size 4 × 4. Our results indicate the onset of disorder in the 4-dimensional LGT so that at weak coupling confinement is due to non-abelian fluctuations of the gauge field. We describe the Monte Carlo data by formulae of the 2-dimensional LGT with some effective coupling constant. We formulate how this effective coupling constant should depend on the size of the loop in order that the Olesen hypothesis about the dimensional reduction (i.e. approximate reduction of the 4-dimensional LGT to the effective 2-dimensional LGT in the confinement region) would be held. Using the strong-coupling expansion where the Olesen hypothesis holds in fourteen orders, we perform quantitative estimates. The density of simple vortices up to size 4 × 4 is calculated. A connection between the definitions of spectral densities for the SU(∞) and SU(2) groups is considered. Explicit formulae for the spectral density in the 2-dimensional SU(2) LGT are derived.     

钽酸镓镧与石英声表面波传播特性对比研究

钽酸镓镧(LGT)是近年研制出的新型压电材料。计算了这种材料在不同切向和传播方向的声表面波传播特性,并和石英晶体上相应切向和传播方向的声表面波传播特性进行了对比分析。计算结果表明这种材料的声表面波传播速度一般比石英低1000 m/s左右,和石英一样,具有零温度切向和纯模方向,但它的机电耦合系数K²却远高于石英。还对目前报道的LGT的不同材料常数进行了对比计算,计算结果表明不同材料常数的声表面波传播特性有明显的差异,其中以频率温度系数差异最大。     

ANALYTIC STUDY OF su(3) LATTICE GAUGE THEORY

The variational-cumulant expansion method has been extended to the case of lattice SU(3) Wilson model.The plaquette energy as an order parameter has calculated to the 2nd order expansion.No 1st order phase transition in the d=4 case is found which is in agreement with the monte Carlo results,and the 1st order phase transition in the d=5 case is clearly seen.The method can be used in the study of problems is LGT with SU(3) gauge group.     

Finite Temperature Phase Structure for SU(2) with a Mixed Action

The modified Migdal-Kadanoff (MK) renormalization transformation is applied to SU(2) lattice gauge theory (LGT) with a mixed action at finite temperature. The renormalization trajectory distributions and the phase structures in the whole coupling parameter space are obtained. Using the dependence of transition temperature on the coupling, the scaling behavior is found in the weak coupling region of β≥1.20. Numerical calculation gives the value of critical temperature T_c = 0.682A_mom. It is close to the data from the Monte Carlo simulation.     

Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics

Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.     

Generalized lattice gauge theory, spin foams and state sum invariants

We construct a generalization of pure lattice gauge theory (LGT) where the role of the gauge group is played by a tensor category. The type of tensor category admissible (spherical, ribbon, symmetric) depends on the dimension of the underlying manifold (≤3, ≤4, any). Ordinary LGT is recovered if the category is the (symmetric) category of representations of a compact Lie group. In the weak coupling limit we recover discretized BF-theory in terms of a coordinate-free version of the spin foam formulation. We work on general cellular decompositions of the underlying manifold.

In particular, we are able to formulate LGT as well as spin foam models of BF-type with quantum gauge group (in dimension ≤4) and with supersymmetric gauge group (in any dimension).

Technically, we express the partition function as a sum over diagrams denoting morphisms in the underlying category. On the LGT side this enables us to introduce a generalized notion of gauge fixing corresponding to a topological move between cellular decompositions of the underlying manifold. On the BF-theory side this allows a rather geometric understanding of the state sum invariants of Turaev/Viro, Barrett/Westbury and Crane/Yetter which we recover.

The construction is extended to include Wilson loop and spin network type observables as well as manifolds with boundaries. In the topological (weak coupling) case this leads to topological quantum field theories with or without embedded spin networks.     

VACUUM OF 2+1 DIMENSIONAL SU(2) LGT WITH FERMIONS AND SPONTANEOUS CHIRAL SYMMETRY BREAKING

By incorporating the exact ground state of pure gauge theory and the variational fermion vacuum state,the vacuum structure of 2+1 dimensional SU(2) LGT with fermions is studied.We calculate the fermion condensate <ψψ>,and obtain a good scaling behavior.

     

Fixed twist dynamics of SO(3) gauge theory

We perform a thorough study of 3+1-dimensional SO(3) LGT for fixed-twist background. We concentrate in particular on the physically significant trivial and 1-twist sectors. Introducing a ℤ₂ monopole chemical potential the 1st order bulk transition is moved down in the strong coupling region and weakened to 2nd order in the 4-dimensional Ising model universality class. In this extended phase diagram we gain access to a confined phase in every fixed-twist sector of the theory. The Pisa disorder operator is employed together with the Polyakov loop to study the confinement–deconfinement transition in each sector. Due to the specific properties of both operators, most results can be used to gain insight in the ergodic theory, where all twist sectors should be summed upon. An explicit mapping of each fixed-twist theory to effective positive plaquette models with fixed-twisted boundary conditions is applied to better establish their properties in the different phases.     

X-ray diffraction analysis of the surface acoustic wave propagation in langatate crystal

X-ray diffraction on a langatate crystal (La₃Ga_5.5Ta_0.5O₁₄, LGT) modulated by a Λ=12 μm Rayleigh surface acoustic wave (SAW) was studied in a double axis X-ray diffractometer scheme at the BESSY synchrotron radiation source. SAW propagation in the crystal causes sinusoidal modulation of the crystal lattice and the appearance of diffraction satellites on the rocking curves, with their number, angular positions, and intensities depending on the wavelength and amplitude of acoustic vibrations of the crystal lattice. Strong absorption of X-ray radiation in LGT enables the observation of the diffraction spectra extinction at certain SAW amplitudes. X-ray diffraction spectra analysis makes it possible to determine SAW amplitudes and wavelengths, to measure the power flow angles, and investigate the diffraction divergence in acoustic beam in LGT.     

THE FOKKER-PLANCK EQUATiON AND THE SCHWI NGER-DYSON EQUATION IN LATTICE GAUGE THEORY

The stochastic quantization in Lattice Gauge Theory (LGT) is discussed by using Langevin equations and Fokker-Planck equations. It is shown that the evolution equation in stochastic process reduces to Schwinger-Dyson equation when lattice system reaches equilibrium.