Single-site theory for the random Hubbard alloy

A new theory for the random system with electron correlation is presented, which is an extension of the Hubbard's theory for the random system and also an extension of the CPA for the interacting electron system. The equation of motion for the Green function is solved by the same decoupling method used by Hubbard. The self-consistent relations for the Green function, the self-energy and the effective occupation number are derived. It is predicted in the binary alloy system that tails or satellites of the state density are produced by the combined effect of the randomness and electron correlation. The origin of the tail is the inelastic scattering of the electron byA — B atomic pairs, whose electronic configuration is changed during the scattering. Numerical calculations are reported for a simple model.     

Multi-level quantum electrodynamic calculation of spontaneous emission and small signal gain in high voltage free electron lasers

Abstract

Using the Weisskopf-Wigner technique, a self consistent quantum electrodynamic (SCQED) theory of spontaneous emission of radiation and single photon small signal gain is developed for high voltage free electron lasers (FEL). Excellent agreement is obtained simultaneously to our knowledge for the first time between the predictions and the experimental observations for lineshift, linewidth and gain. The SCQED theory predicts lineshift and broadening due to quantum mechanical effects for linear, helical and tapered undulator FELs which are not predicted by the classical/conventional FEL theories, but which have been observed ^{4,5,18,22,23,45,46}. Excellent agreement is obtained between the SCQED theory predicted spontaneous emission spectra and the 1980–81 ACO FEL^4,18, ACO Optical Klystron FEL^45,46, Stanford 10.6 μm FEL²² and Stanford 3.4 μm FEL²³ experimental spectra. This agreement is much better than the prediction from the classical/conventional FEL theory which gives errors of many tens of percent. We show that the spontaneous emission spectrum obtained from classical/conventional FEL theories is valid only in the limit of a short undulator containing a small number of periods. The small signal gain derived from the SCQED theory is shown to reduce to Colson's gain formula^12,34 in the classical limit. However, the SCQED theory predicts significant reductions in the small signal gain which agree well with the ACO gain data⁵, and are not predicted well by Colson's formula. Due to the non-neglible finite electron state lifetime, it is discovered that a fundamental physical gain limit exists which is universal to all types of FELs within the limits of the single photon transition scheme considered (i.e. if multiphoton effects are ignored). Finally, the implications of the theoretically obtained results are discussed for practical conditions of experimental interest. It is shown that under practical experimental conditions quantum effects can be quite important in the FEL.     

Kohn’s theorem, Larmor’s equivalence principle and the Newton–Hooke group

We consider non-relativistic electrons, each of the same charge to mass ratio, moving in an external magnetic field with an interaction potential depending only on the mutual separations, possibly confined by a harmonic trapping potential. We show that the system admits a “relativity group” which is a one-parameter family of deformations of the standard Galilei group to the Newton–Hooke group which is a Wigner–?nönü contraction of the de Sitter group. This allows a group-theoretic interpretation of Kohn’s theorem and related results. Larmor’s theorem is used to show that the one-parameter family of deformations are all isomorphic. We study the “Eisenhart” or “lightlike” lift of the system, exhibiting it as a pp-wave. In the planar case, the Eisenhart lift is the Brdi?ka–Eardley–Nappi–Witten pp-wave solution of Einstein–Maxwell theory, which may also be regarded as a bi-invariant metric on the Cangemi–Jackiw group.     

Interaction of radiation and a relativistic electron in motion in a constant magnetic field

This paper examines the effect of multiple photon emission on the quantum mechanical state of an electron emitting synchrotron radiation and on the intensity of that radiation. Calculations are done with a variant of perturbation theory based on the use of extended coherent states. A general formula is derived for the number of emitted photons, which allows taking into account their mutual interaction. A model problem is used to demonstrate the absence of the infrared catastrophe in the modified perturbation theory. Finally, the electron density matrix is calculated, and the analysis of this matrix makes it possible to conclude that the degree of the electron’s spatial localization increases with the passage of time if the electron is being accelerated. Zh. éksp. Teor. Fiz. 113, 841–864 (March 1998)     

Non-commutative geometry and measurements of polarized two photon coincidence counts

Employing Maxwell’s equations as the field theory of the photon, quantum mechanical operators for spin, chirality, helicity, velocity, momentum, energy, and position are derived. The photon “Zitterbewegung” along helical paths is explored. The resulting non-commutative geometry of photon position and the quantum version of the Pythagorean theorem is discussed. The distance between two photons in a polarized beam of given helicity is shown to have a discrete spectrum. Such a spectrum should become manifest in measurements of two photon coincidence counts. The proposed experiment is briefly described.     

Electron Anomalous Magnetic Moment in Basis Light-Front Quantization Approach

We apply the Basis Light-Front Quantization approach to the Hamiltonian field theory of Quantum Electrodynamics in free space. We solve for the mass eigenstates corresponding to an electron interacting with a single photon in light-front gauge. Based on the resulting non-perturbative ground state light-front amplitude we evaluate the electron anomalous magnetic moment. The numerical results from extrapolating to the infinite basis limit reproduce the perturbative Schwinger result with relative deviation less than 0.6%. We report significant improvements over previous works including the development of analytic methods for evaluating the vertex matrix elements of QED.     

利用虚光子理论对轴沟道辐射的分析

 考虑电子的反冲的影响,利用虚光子与相对论电子的康普顿散射理论对轴沟道辐射进行了研究。在与电子纵向运动静止的坐标系中,把晶格场等效为虚光子。当虚光子与作沟道运动的电子发生康普顿散射时,虚光子就会转化为实光子辐射出去。根据该理论,得到了含有康普顿波长项的轴沟道辐射的精确波长表达式,其近似式就是经典理论推导的公式;同时得到了单电子轴沟道辐射的光子产额和辐射功率的公式,结果也与经典理论公式一致。     

Dimensional regularization of massless quantum electrodynamics in spherical spacetime

The quantization and renormalization of massless electrodynamics in a spacetime of constant curvature are discused. A formalism is presented which is valid in an arbitrary number of dimensions and therefore allows the use of dimensional regularization. In the discussion of the photon propagator it is found that anomalous mass terms dependent on the curvature arise, although these vanish in four dimensions. Further, the gauge-fixing term in the Lagrangian has the unconventional feature of not being a perfect square. The renormalizability of the theory is then demonstrated to one loop order, and the renormalization constants are shown to retain their flat spacetime values. Finally, expansions for the renormalized electron and photon propagators in terms of appropriate spherical harmonics are derived.     

Fundamental theories of waves and particles formulated without classical mass

Quantum and classical mechanics are two conceptually and mathematically different theories of physics, and yet they do use the same concept of classical mass that was originally introduced by Newton in his formulation of the laws of dynamics. In this paper, physical consequences of using the classical mass by both theories are explored, and a novel approach that allows formulating fundamental (Galilean invariant) theories of waves and particles without formally introducing the classical mass is presented. In this new formulation, the theories depend only on one common parameter called ‘wave mass’, which is deduced from experiments for selected elementary particles and for the classical mass of one kilogram. It is shown that quantum theory with the wave mass is independent of the Planck constant and that higher accuracy of performing calculations can be attained by such theory. Natural units in connection with the presented approach are also discussed and justification beyond dimensional analysis is given for the particular choice of such units.     

A generalized Slavnov-invariant Abelian Higgs-Kibble model

The supersymmetric structure of the Becchi-Rouet-Stora invariance is used for investigating the Abelian Higgs-Kibble model. It allows for a symmetric photon mass M, in which case a massless scalar state corresponding to the Goldstone model belongs to the physical sector. If M = 0, i.e. the photon mass is generated by the Higgs mechanism, this state is decoupled from the physical sector, as usual. The BPHZ renormalization procedure is used.     

Energy trapping in high-frequency vibrations of piezoelectric plates with partial mass layers under lateral electric field excitation

We study coupled face-shear (FS) and thickness-twist (TT) motions of a piezoelectric plate of monoclinic crystals with mass layers on the central parts of the plate surfaces. The plate is driven by a lateral electric field. Mindlin’s first-order theory of piezoelectric plates is used. An analytical solution is obtained. Numerical results are presented for an AT-cut quartz plate, including the motional capacitance of the plate as a resonator and the vibration modes trapped under the mass layers in the central portion of the plate. The relationship between the dimension of the mass layers and the number of trapped modes is examined.     

QED in Krein Space Quantization

In this paper we consider the QED in Krein space quantization. We show that the theory is automatically regularized. The three primitive divergences integrals in usual QED are considered in Krein QED. The photon self energy, electron self energy and vertex function are calculated in this formalism. We show that these quantities are finite. The infrared and ultraviolet divergencies do not appear. We discuss that Krein space quantization is similar to Pauli-Villars regularization, so we have called it the “Krein regularization”.     

偏振光在多层散射介质中传输的蒙特卡罗模拟研究*

基于米氏散射理论,运用斯托克斯-穆勒形式,结合子午面法和拒绝法,提出了偏振光在多层散射介质中传输的蒙特卡罗模型,并首次分析了当菲涅耳公式失效时,多层介质界面处的全反射行为.同时用该模型研究了微粒直径和介质折射率对漫反射和漫透射的影响.结果表明：无论是折射率匹配介质还是非匹配介质,当粒子浓度一致时,漫反射率都随微粒直径的增加而增加,随介质折射率的增加而减小,而漫透射率则相反.研究结果为生物组织的偏振光散射研究提供了理论验证模型.     

Compton scattering of an X-ray photon by an open-shell atom

A nonrelativistic quantum theory for the nonresonant Compton scattering of an X-ray photon by a free many-electron atom with an open shell in the ground state has been constructed in the single-configuration Hartree-Fock approximation outside the impulse approximation widely used in the literature. The transition to an atom with closed shells reproduces the results obtained previously in [6, 7]. The results of a test calculation for atoms with open (Ti, Fe) and closed (Zn) 3d core shells are presented. The effects of the radial relaxation of one-electron states in the field of core vacancies have been taken into account. The results of the calculation agree well with the experimental results [15, 16]. It has been established that the results of the impulse approximation in the investigated X-ray photon energy ranges disagree with those of our theory not only quantitatively but also qualitatively. In particular, the impulse approximation near the elastic (Thomson and Rayleigh) scattering line leads to a gross overestimation of the contributions from the deep atomic shells involved in the inelastic photon scattering only virtually to the scattering probability. The presented theory is general in character and its applicability to a particular element of the Mendeleev table with an open core shell or to a many-electron atomic ion is limited only by the requirement that the nonrelativistic Hartree-Fock approximation be properly used in describing the scattering-state wave functions.     

Evolution problems in spaces of probability measures

This is a short survey paper on the application of Monge’s theory of optimal mass transportation to evolution problems of a gradient type, in the case when the natural state space is the space of probability measures. This occurs for instance for Fokker-Planck equations, and optimal mass transportation methods provide, in this setting, very general existence and stability results.     

提高光子能量沉积计算效率的几种技巧

MCNP程序提供了计算光子沉积能的两种方法, 分别是F6和*F8。 当次级电子射程与网格尺度比较接近时, *F8的精度比F6高, 但计算效率比F6低很多。 分析比较了几种提高计算效率的技巧, 分别是: 网格大于10倍电子射程用F6; F6与*F8的联合使用; 改变电子能量子步数; 关掉δ电子; 次级电子自适应截断等。 数值模拟表明, F6与*F8的联合使用以及次级电子自适应截断这两种技巧对精度与效率兼顾得很好。 F6 and *F8 are two methods to calculate energy deposition of photon by MCNP program. If the dimension of grid is almost the same long as the range of secondary electron, the precision of *F8 is higher than that of F6, but the efficiency of F6 is greatly higher than that of *F8. This paper presents five techniques to increase the efficiency,namely: F6 is use to the model with grid dimension bigger than 10 ranges of secondary electron; combination of F6 and *F8; change the substeps of electron; turn off knock on electron; self adaption cutoff secondary electron. The two techniques, combination of F6 and *F8,self adaption cutoff secondary electron, can provide a good precision and efficiency.     

Towards a novel simulation approach for the transport of atomic states through polarized photons

A novel approach for transferring logic states from one quantum node to other is proposed. Logic states ‘0’ and ‘1’ are represented by two subspaces of the hyperfine states space of rubidium atom (⁸⁷Rb). The atom, placed at the center of a two-mode cavity, is excited by simultaneous application of two laser beams, one for each subspace. Based on the logic state of the atom, it makes a transition to a higher energy level within the corresponding subspace. When the atom relaxes back to a lower state within the subspace, a left- or right-circularly polarized photon is emitted depending on whether the initial state was logic ‘0’ or logic ‘1’. The polarized photon leaks out of the cavity, reaches the receive node and gets detected therein. Simulation results show the efficacy of the approach.     

Radiative return at NLO and the measurement of the hadronic cross-section in electron–positron annihilation

Electron–positron annihilation into hadrons plus an energetic photon from initial state radiation allows the hadronic cross-section to be measured over a wide range of energies. The full next-to-leading order QED corrections for the cross-section for annihilation into a real tagged photon and a virtual photon converting into hadrons are calculated where the tagged photon is radiated off the initial electron or positron. This includes virtual and soft photon corrections to the process and the emission of two real hard photons: . A Monte Carlo generator has been constructed, which incorporates these corrections and simulates the production of two charged pions or muons plus one or two photons. Predictions are presented for centre-of-mass energies between 1 and 10 GeV, corresponding to the energies of DANE, CLEO-C and B-meson factories. Received: 14 December 2001 / Published online: 5 April 2002     

Proof for Gauge Independence of the Energy-Momentum Tensor in Quantum Electrodynamics

Proof is given for gauge independence of the (Belinfante's) symmetric energy-momentum tensor in QED. Under the covariant LSZ-formalism it is shown that expectation values, supplemented with physical state conditions, of the energy-momentum tensor are gauge independent to all orders of the purturbation theory (the loop expansion). A study is also made, in terms of the gauge invariant operators of electron (known as the Dirac's or Steinmann's electron) and photon, in expectation of gauge invariant result without any restriction. It is, however, shown that singling out gauge invariant quantities is merely synonymous to fixing a gauge, then there needs again a use of the asymptotic condition to obtain gauge independent results.     

Spectrum calculations in the lattice Georgi-Glashow model

Numerical evidence is found for the appearance of a massless vector state, the “photon”, in the broken phase of the lattice Georgi-Glashow model. Data is also presented for the lowest-lying scalar mass in the theory. Our simulations indicate that the transition between symmetric and broken phases is weakly first order for a wide range of couplings.