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.     

Perturbation expansion in phase-ordering kinetics. II. N-vector model

The perturbation theory expansion presented earlier to describe the phase-ordering kinetics in the case of a nonconserved scalar order parameter is generalized to the case of the n-vector model. At lowest order in this expansion, as in the scalar case, one obtains the theory due to Ohta, Jasnow, and Kawasaki (OJK). The second-order corrections for the nonequilibrium exponents are worked out explicitly in d dimensions and as a function of the number of components n of the order parameter. In the formulation developed here the corrections to the OJK results are found to go to zero in the large n and d limits. Indeed, the large-d convergence is exponential.     

Magnetic properties of a nearly classical one-component plasma in three or two dimensions

The magnetic properties of the one-component plasma, in three and two dimensions, are studied in the nearly classical case. Since magnetism is an essentially quantum effect, Planck's constant ? can be used as a small parameter. A generalized Wigner-Kirkwood expansion in powers of ?² is derived. This expansion is used for computing the induced magnetization. The displacement of the liquid-solid phase transition of the model, when a magnetic field is applied, is discussed. The model is applicable to electrons deposited at the surface of liquid helium.     

A vertical eigenfunction expansion for the propagation of sound in a downward-refracting atmosphere over a complex impedance plane

The propagation of sound in a stratified downward-refracting atmosphere over a complex impedance plane is studied. The problem is solved by separating the wave equation into vertical and horizontal parts. The vertical part has non-self-adjoint boundary conditions, so that the well-known expansion in orthonormal eigenfunctions cannot be used. Instead, a less widely known eigenfunction expansion for non-self-adjoint ordinary differential operators is employed. As in the self-adjoint case, this expansion separates the acoustic field into a ducted part, expressed as a sum over modes which decrease exponentially with height, and an upwardly propagating part, expressed as an integral over modes which are asymptotically (with height) plane waves. The eigenvalues associated with the modes in this eigenfunction expansion are, in general, complex valued. A technique is introduced which expresses the non-self-adjoint problem as a perturbation of a self-adjoint one, allowing one to efficiently find the complex eigenvalues without having to resort to searches in the complex plane. Finally, an application is made to a model for the nighttime boundary layer.     

Correlation effects on charge exchange in the time-dependent Newns-Anderson model

The electron correlation effect on the charge exchange problem in the time-dependent Newns-Anderson model with U→∞ is discussed in the approach of the expanded wavefunction in terms of electron-hole pair excitation. Only a limited case is analyzed rigorously on the expansion terms up to the eighth order of the admixture coupling constant to conclude that the same expression holds for the non-adiabatic exchange of the total charge as in the non-interacting case. This conclusion is conjectured to hold somewhat generally.     

Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice

The frequency-moment expansion method is developed to analyze the validity of the Luttinger sum rule within the Mott-Hubbard insulator, as represented by the generalized Hubbard model at half filling and large U. For the particular case of the Hubbard model with nearest-neighbor hopping on a triangular lattice lacking the particle-hole symmetry results reveal substantial violation of the sum rule.     

Bohmian and quantum phase space distribution expansions and approximations

Dias and Patra derived an expansion of the Wigner distribution and related it to the de Broglie–Bohm model. We show that the coefficients of the expansion are related to the conditional central moments and cumulants of the Wigner distribution. The even order cumulants depend only on the amplitude of the wave function and the odd order cumulants depend only on the phase. In addition, we give a different expansion of the Wigner distribution from which their expansion can be derived as a special case. Our expansion allows for different approximations for higher order terms. We also give expansions for the momentum representation. We show how the results are applicable to pulse propagation in a dispersive medium.     

Comments on the use of the Landau theory in some order-order transitions

The application of the Landau theory of phase transitions to a two-sublattice magnet results in a broad range of magnetic transitions. The use of a two-component order parameter enables one to describe both order-disorder and order-order transitions. In particular, the metamagnetic transitions exhibit the thermal hysteresis. It is shown that the Kittel model is a special case of the Landau expansion. Finally, an alternative one-component order parameter expansion is discussed.     

Self-consistent RPA based on a many-body vacuum

Self-Consistent RPA is extended in a way so that it is compatible with a variational ansatz for the ground-state wave function as a fermionic many-body vacuum. Employing the usual equation-of-motion technique, we arrive at extended RPA equations of the Self-Consistent RPA structure. In principle the Pauli principle is, therefore, fully respected. However, the correlation functions entering the RPA matrix can only be obtained from a systematic expansion in powers of some combinations of RPA amplitudes. We demonstrate for a model case that this expansion may converge rapidly.     

Einstein-Cartan gravity with scalar-fermion interactions

In this paper, we have considered the g-essence and its particular cases, k-essence and f-essence, within the framework of the Einstein-Cartan theory. We have shown that a single fermionic field can give rise to the accelerated expansion within the Einstein-Cartan theory. The exact analytical solution of the Einstein-Cartan-Dirac equations is found. This solution describes the accelerated expansion of the Universe with the equation of state parameter w = −1 as in the case of ΛCDM model.     

The Hopf bifurcation of twodimensional systems under the influence of one external noise source

The behaviour of the Hopf bifurcation under the influence of external noise is investigated by means of a twodimensional model which uses Gaussian white noise as input. The model includes the case of multiplicative and/or additive noise. Applying the Birkhoff transformation the model is transformed to the coordinates normally used to discuss the deterministic Hopf bifurcation. Then the stationary solution of the model is calculated as an expansion for weak noise: The Hopf bifurcation under the influence of noise exhibits a bifurcation interval with width and position depending on the noise power. Moreover, a class of the systems described by the model can perform noise driven bifurcations.     

Elastic properties of nanocrystalline forsterite under high pressure and high temperature

A simple theoretical model is developed to study the pressure–volume–temperature relationship and applied for nanocrystalline forsterite in the temperature range 300–1573 K and pressure range 0–9.6 GPa. The results obtained with the present model are in quite close agreement to the experimental values. The model is therefore extended to study the variation of bulk modulus and the coefficient of volume thermal expansion under high pressure and high temperature. The present study also reveals that the quasi-harmonic approximation, i.e., the product of bulk modulus and the coefficient of volume thermal expansion as constant, is valid at least up to the temperature 1573 K and pressure 9.6 GPa in case of nanocrystalline forsterite.     

Nonlinear wave propagation in constrained solids subjected to thermal loads

The classical mathematical treatment governing nonlinear wave propagation in solids relies on finite strain theory. In this scenario, a system of nonlinear partial differential equations can be derived to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such “residual” energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. These results suggest the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather.     

Turbulent flame and the darrieus–landau instability in a three-dimensional flow

The velocity of a weakly turbulent flame influenced by the Darrieus–Landau (DL) instability in a three-dimensional geometry is investigated on the basis of a model nonlinear equation. The equation takes into account realistically large thermal expansion of burning matter, external turbulence and thermal conduction related to small, but finite flame thickness. An external turbulent flow is imitated by a model obeying the Kolmogorov law. The effects of the DL instability and external turbulence are studied, first separately and then as they influence the flame dynamics together for different values of the turbulent intensity, different thermal expansion of the burning matter and different length scales of the hydrodynamic motion controlled by the width of a hypothetic tube with ideally adiabatic walls. The velocity increase obtained is in a good agreement with experimental results in the case of relatively weak turbulent intensity.     

Experimental study of the role of atomic interactions on quantum transport

We report an experimental study of quantum transport for atoms confined in a periodic potential and compare between thermal and Bose-Einstein condensation (BEC) initial conditions. We observe ballistic transport for all values of well depth and initial conditions, and the measured expansion velocity for thermal atoms is in excellent agreement with a single-particle model. For weak wells, the expansion of the BEC is also in excellent agreement with single-particle theory, using an effective temperature. We observe a crossover to a new regime for the BEC case as the well depth is increased, indicating the importance of interactions on quantum transport.     

A statistical model for evaluation and prediction of the noise exposure in a construction equipment area

A statistical model for evaluating and predicting the equivalent noise level and the noise exposure at a working area was made. The method is based on the statistical theory of regression analysis. The results are expressed as a functional expansion and the stochastic models that give the solution to the problem are confidence zones and prediction zones of noise, which are valid in every similar case.     

First order phase transition of expanding matter and its fragmentation

Based on an expanding matter model using Lennard-Jones potential, the instability of the system is examined. The instantaneous pressure, temperature and density fluctuation are calculated as a function of the density. The system undergoes the first order phase transition when the expanding velocity is slow. Although the system behaves dynamically for faster expansion, a kind of criticality seems to play an important role even in this case.     

The many-body problem within the Lee model

The structure of a field theoretical many-body problem is studied within the (non-static) Lee model. The explicit solvability of the renormalization problem allows the investigation of renormalization corrections in many-particle systems. Herefore, the renormalized equations are worked out for the N-V scattering and for the binding-energy problem of “N-V matter” — these cases taken in analogy to nucleon-nucleon scattering and nuclear matter. The N-V matter equations are obtained from a cluster expansion suitably defined for the field theoretical case. The ansatz for the correlated wave functions is chosen in such a way as to generate a two-hole-line expansion of the binding energy. The renormalized form of this field theoretical extension of Brueckner theory is discussed in detail revealing the medium effects on renormalization.     

Thermal wave scattering by two overlapping and parallel cylinders

In this paper an analytical solution of the temperature of an opaque material containing two overlapping and parallel subsurface cylinders, illuminated by a modulated light beam, is presented. The method is based on the expansion of plane and cylindrical thermal waves in series of Bessel and Hankel functions. This model is addressed to the study of heat propagation in composite materials with interconnection between inclusions, as is the case of inverse opals and fiber reinforced composites. Measurements on calibrated samples using lock-in infrared thermography confirm the validity of the model.     

非简谐振动对SiC的热膨胀系数数和介电性能的影响

利用抛物型电子能谱模型,考虑到原子的非简谐振动,求出了SiC中原子振动的简谐系数与非简谐系数,用固体物理理论和方法,得到了SiC的热膨胀系数和格林乃森参量以及介电常数随温度变化的解析式,探讨了原子非简谐振动对的影响。结果表明：的格林乃森参量和热膨胀系数均随温度升高而非线性增大,而介电常数随温度升高而非线性减小;原子振动的非简谐项（特别是第二非简谐项）对的热膨胀等热学性质和介电性能有重要影响,温度愈高,非简谐振动项的影响愈大。