Comments on the scalar-tensor theory

Scalar-tensor theories are discussed as encompassing three classical long-range fields, including the electromagnetic field. In order to shed additional light on the restrictive assumptions made by Dicke concerning the coupling of the scalar field with matter, the ponderomotive laws of a scalar-tensor theory are constructed free of approximations in the form of integral laws. The integrals are extended over two- and three-dimensional domains that lie entirely in empty space but surround the regions containing matter; as for the latter, the vacuum field equations are not required to hold, but no further assumptions are made. It turns out that the gradient of the incident scalar field will contribute to the rate of change of the mass and linear momentum of a particle an amount proportional to that particle's scalar-field source strength, which in turn is an arbitrary function of time, unless Dicke's special restriction is imposed. To this extent the motion of a test particle is indeterminate, contrary to experience.A preliminary version of this paper was presented at the colloquium on relativistic fluids and fields under the auspices of the Centre National de la Recherche Scientifique in Paris in June 1967. Support by Aerospace Research Laboratories and by the Air Force Office of Scientific Research, both agencies of the United States Air Force, is gratefully acknowledged, as is a travel grant by the CNRS.     

Analytic theory of a tapered gyrotron resonator

An analytic theory has been derived for determining the eigenfrequencies, RF-field distribution and Q of the TE_mpq modes of a gyrotron resonator consisting of a circular cylinder joined to a slowly tapered section. Explicit results are obtained for a linear taper. The cavity modes are found to have an RF-field distribution which is useful for prebunching the electron beam and enhancing efficiency. For high Q cavities, the cavity Q depends on axial mode number q as q^–2, which is important for mode discrimination. Proper selection of taper length is found to reduce the Q of high q modes, also aiding in mode discrimination. The present approach may be applied to other forms of weakly irregular cavities, such as cavities with nonlinear tapers.Work supported by U.S.D.O.E. Contract DE-AC02-78ET-51013Supported by U.S. Department of Energy     

Comments on the theory of phase-conjugated waves

It is shown by a simple example that an argument frequently given in the literature, regarding the correction of distortions by phase conjugation is incorrect. The example does not imply that wave distortions cannot be corrected under usual circumstances. Rather, it indicates that there is a limit beyond which correction cannot be attained by this technique; and also that the underlying theory is more complicated than is generally realized.     

光子带隙谐振腔回旋管振荡器的自洽非线性理论

定义了光子带隙谐振腔(photonic-band-gap cavity, PBGC)的等效半径,论证了使用该半径将PBGC等效为具有模式选择性的金属圆柱谐振腔的有效性,揭示了其在PBGC设计过程中的指导性作用.基于等效半径的运用,建立起光子带隙谐振腔回旋管振荡器(PBG回旋管)的自洽非线性理论,并对工作于TE₃₂模的PBG回旋管作了理论分析和数值计算.目前的研究表明:高频电磁场沿角向呈行波或驻波的不同极化形式对PBG回旋管的注-波互作用过程具有较大的影响;较之电子回旋基波,该器件中二 关键词： 光子带隙谐振腔 等效半径 回旋管 自洽非线性理论     

Comments on molecular-field theory with correlations

An effective-field theory for the Ising model is derived from an identity given by Callen. The relation between this and Mattis' work is discussed.     

Numerical modeling of large orbit magnetron-type gyrotron throughself-consistent nonlinear theory

Self consistent nonlinear theory is applied to analyze the large orbit magnetron-type gyrotron in detail; many calculations are carried under different cavity dimensions and electron beam parameters. The influence of electron beam thickness and output structure is taken into consideration. Dimensions of a 16 slot, 35 GHz, 8th harmonic tube are given     

Comments on the equilibrium theory of the quantum hall effect

The relation between the thermal equilibrium Hall conductivity generated by minimal gauge transformation and the isolated Hall conductivity given by the Kubo formula is investigated. The contribution of the edge states and some general questions concerning the definition of the equilibrium Hall conductivity are discussed. It is shown that, in the case of an additive electron-impurity system, the two Hall conductivities coincide as long as the Fermi energy is situated in an energy gap.     

Comments on the variational modified-hypernetted-chain theory for simple fluids

The variational modified-hypernetted-chain (VMHNC) theory, based on the approximation of universality of the bridge functions, is reformulated. The new formulation includes recent calculations by Lado and by Lado, Foiles, and Ashcroft, as two stages in a systematic approach which is analyzed. A variational iterative procedure for solving the exact (diagrammatic) equations for the fluid structure which is formally identical to the VMHNC is described, featuring the theory of simple classical fluids as a one-iteration theory. An accurate method for calculating the pair structure for a given potential and for inverting structure factor data in order to obtain the potentialand the thermodynamic functions, follows from our analysis.     

特殊三反射镜太赫兹波段准光腔回旋管的动力学理论

基于回旋管线性理论,运用Laplace变换和留数定理的方法,在线性Vlasov-Maxwell方程组的框架下,研究了特殊三反射镜准光腔回旋管的动力学理论.导出了注-波互作用功率、频偏和起振电流公式,运用MATLAB进行了数值运算.结果表明,这种回旋管工作于高次谐波状况下能有较高的互作用功率,具有工作于太赫兹波段的潜力. 关键词： 三反射镜准光腔 太赫兹 回旋动力学理论     

Comments on the requirements for a general Stark broadening theory

An analysis is made of requirements for a general theory of Stark broadening applicable to both strong and weak collisions. It is pointed out in particular that inclusion of the static and weak interaction limits is not sufficient to obtain a generally valid theory. At least one other condition is necessary—a dynamic correction for strong, primarily static, collisions. The kangaroo process model microfield method is examined from this point of view, and it is shown that the model conditional probability leads to an incorrect functional form for the lowest order dynamic correction.     

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.     

Scattering theory of the linear Boltzmann operator

In time dependent scattering theory we know three important examples: the wave equation around an obstacle, the Schrödinger and the Dirac equation with a scattering potential. In this paper another example from time dependent linear transport theory is added and considered in full detail. First the linear Boltzmann operator in certain Banach spaces is rigorously defined, and then the existence of the Møller operators is proved by use of the theorem of Cook-Jauch-Kuroda, that is generalized to the case of a Banach space.     

Comments on Mielnik's generalized (non linear) quantum mechanics

We discuss a model of non linear quantum mechanics in which the wave equation satisfies the homogeneity condition (2.1). It is argued that in this model the set of (mixed) states is a simplex.Dedicated to Professor Günther Ludwig on the occasion of his sixtieth birthday     

About the exactness of the linear response theory

For quantum lattice systems with finite range potentials and integrable space clustering, we prove the linearity of the response theory when dealing with fluctuation observables.     

分布损耗加载回旋行波管多模稳态注波互作用理论与比较证实

基于目前国际上实验研究的均匀介质加载和周期介质加载结构,建立了一种分布式损耗加载回旋行波管(gyro-TWT)多模稳态注波互作用理论.利用这一理论,以TE01模式基波gyro-TWT注波互作用为例,将Ka和W波段的理论结果与实验和软件仿真进行比较,以证实理论的合理性.