Quantenfeldtheorie wechselwirkender Vielteilchensysteme zur semiklassischen Beschreibung von kollektiver Bewegung mit großen Amplituden

By using path integral methods a collective quantum field theory of interacting many-body systems is developed, the classical limit of which is given by the time-dependent mean-field approximation. In this way the mean-field approximation is embedded into the full quantum mechanics and the quantum corrections to the “classical” mean-field approximation can be systematically evaluated. By including the dominant quantum corrections to the mean-field approximation a semiclassical theory of large amplitude collective motions in many-body-systems, which show a highly nonlinear dynamic and are not accessible to perturbation theoretical methods, is derived. The semiclassical theory is developed explicitly for bound states and decay processes like nuclear fission. In the case of bound states this leads to the quantization of the time-dependent Hartree-Fock-Theory, which is demonstrated for a uniform nuclear rotation.     

严格耦合波理论和Kogelnik耦合波理论近似比较

将严格耦合波理论与Kogelnik近似理论比较,研究了Kogelnik理论的近似条件。以两种理论的衍射效率特性曲线的相关或衍射效率计算差别作为判断标准,分析Kogelnik耦合波理论的近似条件。分析结论表明,体全息的Kogelnik理论近似条件与条纹密度、折射率调制度和介质厚度相关,其中反射体全息的近似条件还与条纹面倾角相关。     

Adiabatic Approximation in Interaction Between Two-Level Atom in an External Potential V(χ) and Optical Field

In discussion about the detection of the BoseEinstein condensation, the adiabatic approximation method was taken. According to the perturbation theory, this approximation is studied in detail by a single atom model in this paper.     

Scattering amplitude of absorbing and nonabsorbing spheroidal particles in the WKB approximation

This work is devoted to a theoretical study of scattering of light by absorbing and nonabsorbing oriented spheroidal particles in the Wentzel-Kramers-Brillouin (WKB) approximation. Within the framework of the scattering theory, we investigate the form factor and the scattering amplitude for this approximation. The Rayleigh-Gans-Debye theory (RGD), the diffraction approximation (DA), and the anomalous diffraction (AD) are treated as particular cases for nonabsorbing spheroids. To illustrate our formalism, we analyze some numerical examples.     

Tilt-invariant theory of rough-surface scattering: I

The small-slope approximation (SSA) in rough-surface scattering theory uses the surface slope as a small parameter of expansion. But, from the physical point of view, the slope may not be a restrictive parameter because we can change the slope of a surface simply by tilting the coordinate system. We present the theory of rough-surface scattering in a coordinate-invariant form. The new method, tilt-invariant approximation (TIA), leads to a different expansion that does not require that the slope of a surface be small. For a small Rayleigh parameter this approximate solution provides the correct perturbation theory, for a large Rayleigh parameter it provides the Kirchhoff approximation with several correcting terms.     

Second-order Percus-Yevick theory for a confined hard-sphere fluid

A fluid of hard spheres confined between two hard walls and in equilibrium with a bulk hard-sphere fluid is studied using a second-order Percus-Yevick approximation. We refer to this approximation as second-order because the correlations that are calculated depend upon the position of two hard spheres in the confined fluid. However, because the correlation functions depend upon the positions of four particles (two hard spheres and two walls treated as giant hard spheres), this is the most demanding application of the second-order theory that has been attempted. When the two walls are far apart, this calculation reduces to our earlier second-order approximation calculations of the properties of hard spheres near a single hard wall. Our earlier calculations showed this approach to be accurate for the single-wall case. In this work we calculate the density profiles and the pressure of the hard-sphere fluid on the walls. We find, by comparison with grand canonical Monte Carlo results, that the second-order approximation is very accurate, even when the two walls have a small separation. We compare with a singlet approximation (in the sense that correlation functions that depend on the position of only one hard sphere are considered). The singlet approach is fairly satisfactory when the two walls are far apart but becomes unsatisfactory when the two walls have a small separation. We also examine a simple theory of the pressure of the confined hard spheres, based on the usual Percus-Yevick theory of hard-sphere mixtures. Given the simplicity of the latter approach the results of this simple (and explicit) theory are surprisingly good.     

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum, it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantum theory.     

Eikonal Approximation to 5D Wave Equations and the 4D Space-Time Metric

We apply a method analogous to the eikonal approximation to the Maxwell wave equations in an inhomogeneous anisotropic medium and geodesic motion in a three dimensional Riemannian manifold, using a method which identifies the symplectic structure of the corresponding mechanics, to the five dimensional generalization of Maxwell theory required by the gauge invariance of Stueckelberg's covariant classical and quantum dynamics. In this way, we demonstrate, in the eikonal approximation, the existence of geodesic motion for the flow of mass in a four dimensional pseudo-Riemannian manifold. These results provide a foundation for the geometrical optics of the five dimensional radiation theory and establish a model in which there is mass flow along geodesics. We then discuss the interesting case of relativistic quantum theory in an anisotropic medium as well. In this case the eikonal approximation to the relativistic quantum mechanical current coincides with the geodesic flow governed by the pseudo-Riemannian metric obtained from the eikonal approximation to solutions of the Stueckelberg–Schrödinger equation. The locally symplectic structure which emerges is that of a generally covariant form of Stueckelberg's mechanics on this manifold.     

The eikonal approximation revisited

Summary Certain problems in optical scattering are best understood when the more complicated exact scattering theory is replaced by an approximation. The Fraunhofer approximation is a well-known example. In the past ten years a considerable amount of work has been done in various disciplines towards assessing the usefulness of a new approximation referred to in the literature either as the eikonal approximation or as the high-energy approximation. The purpose of this paper is to provide a much needed review of this work and in addition to examine the historical evolution of this approximation which essentially started in optics when Bruns introduced the term eikonal in 1895. Part of this work was done when SKS was at Saha Institute of Nuclear Physics, Calcutta, and at Institute of Wetland Management and Ecological Design, Calcutta, India.     

Tilt-invariant theory of rough-surface scattering: I

Abstract

The small-slope approximation (SSA) in rough-surface scattering theory uses the surface slope as a small parameter of expansion. But, from the physical point of view, the slope may not be a restrictive parameter because we can change the slope of a surface simply by tilting the coordinate system. We present the theory of rough-surface scattering in a coordinate-invariant form. The new method, tilt-invariant approximation (TIA), leads to a different expansion that does not require that the slope of a surface be small. For a small Rayleigh parameter this approximate solution provides the correct perturbation theory, for a large Rayleigh parameter it provides the Kirchhoff approximation with several correcting terms.     

On the calculation of second order properties: An equation of motion approach

In the light of the equation of motion method a general expression for polarisability calculation has been derived. From this general expression, different approximation methods can be deduced for different choices of ground state and excitation manifold. Among these the coupled Hartree-Fock theory is the most extensively used one for polarisability calculations. It has also been shown that this theory has a simple relationship with random phase approximation.     

关于复合场论和束缚态的一个讨论

本文探讨了现有量子场论和量子化复合场论之间的内在联系。发现在梯形近似下,它们是自洽并有内在联系的;但在更一般的非梯形近似的情况下,这种内在联系并未找到。 关键词：     

One-Particle Distribution Functions and Thermodynamics of Crystals with Many-Body Forces. III. Perturbation Theory

The theory of crystalline state described in preceding papers is considered as a zeroth-order approximation. Statistical perturbation theory is used for the purpose of improving this approximation. The second-order corrections to the Helmholtz free energy and thermodynamic properties of strongly anharmonic crystals are derived. The properties of solid Ar, Kr, and Xe are calculated using various pair-potential functions in conjunction with the AXILROD -TELLER -MUTO three-body potential. The first quantum corrections are taken into account in the quasi-classical approximation. The result of computations are compared with the experimental data.     

Hadronic density of states from string theory

We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nù?ez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of a Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM theory, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.     

Technique to manage polarization aberrations

Optimizing the polarization characteristics of an optical system is generally a complicated problem, unlike the case of optimizing scalar characteristics such as pupil function. Here, we will propose a linear approximation approach to solve this problem systematically and define the conditions to be satisfied to make the approximation accurate. This approximation scheme is constructed by naturally extending a concept of the scalar imaging theory.     

Interpretation of the d-parameters,occurring in the Mayants-Averbukh theory of infrared intensity,in terms of the bond dipole moment concept: Equivalence with the valence-optical theory in the zeroth approximation for linear and planar molecules

From a comparison with the valence-optical theory of infrared intensity in the zeroth approximation, it is suggested that the d-parameters (elements of the effective charge tensor D_n⁰ of a bond) occurring in the Mayants-Averbukh theory can be expressed in terms of bond dipole moment components and their derivatives with respect to components of the Cartesian bond displacement vector. With this interpretation, which may be suitable for practical application, the Mayants-Averbukh theory formally appears as a combination of the “special” and the generalized valence-optical theory. In particular, it is found that for linear molecules the Mayants-Averbukh theory is equivalent to the “special” valence-optical theory in the zeroth approximation. For planar molecules the Mayants-Averbukh theory is equivalent to the generalized valence-optical theory (zeroth approximation) for in-plane modes and to the “special” valence-optical theory for out-of-plane modes.     

Renormalizable Quantum Gauge Theory of Gravity

The quantum gravity is formulated based on the principle of local gauge invariance. The model discussedin this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton‘s theory of gravity. In the first-order approximation and for vacuum,it gives out Einstein‘s general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantumtheory.     

Steady-State Analysis of Two Single-Mode Dye Laser Models with Multiplicative Colored Model

In this paper, a unified expansion theory that can be simultaneously applied to both large and small correlation times developed by Gang HU is established and applied to the systems driven by multiplicative colored noise. The stationary intensity probabilities are calculated for colored gain-noise and colored-loss-noise models. Comparing with the predictions of the best Fokker-Planck equation and the unified colored-noise approximation for the stationary intensity probability of the two models, it is found that the results of the unified expansion theory are in better agreement with simulations and experimental results than those of the best Fokker-Planck equation approximation and the unified colored-noise approximation.     

Gaseous ion mobility and diffusion in electric fields of arbitrary strength

In a previous paper we presented the first kinetic theory of gaseous ion mobility which is valid for electric fields of arbitrary strength and for arbitrary ion-neutral interaction potentials and mass ratios. In this paper we extend this theory to gaseous ion diffusion and systematize it so as to greatly decrease the effort involved in computing high approximations to the transport coefficients. Analytical results in low approximation are discussed, as are scaling rules for ion mobilities and diffusion coefficients. An extensive study of the convergence of the successive approximations of this theory is given for model systems, from which it is concluded that the theory is accurate, particularly in third and higher approximation, when applied to ion mobility and mean kinetic energy. When applied to diffusion, the theory is less successful in some circumstances, but it is still the best general theory currently available.     

Dual boson approach to collective excitations in correlated fermionic systems

We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in the so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to an extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to “bare” RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.