Exact Solution for a Multiphoton Generalized Jaynes-Cummings Model with Inverse Operators

A new exactly solvable multiphoton generalized Jaynes-Cummings model is presented, whose Hamiltonian is related to the inverse of field mode creation and annihilation operators. Then we use supersymmetric unitary operators to diagonalize the Hamiltonian above and obtain their energy spectra and eigenstates. In addition, its pseudo-invariant eigen-operator is found as well, directly leading to the corresponding energy-level gap.     

Non-Relativistic Treatment of a Generalized Inverse Quadratic Yukawa Potential

A bound state solution is a quantum state solution of a particle subjected to a potential such that the particle's energy is less than the potential at both negative and positive infinity. The particle's energy may also be negative as the potential approaches zero at infinity. It is characterized by the discretized eigenvalues and eigenfunctions,which contain all the necessary information regarding the quantum systems under consideration. The bound state problems need to be extended using a more precise method and approximation scheme. This study focuses on the non-relativistic bound state solutions to the generalized inverse quadratic Yukawa potential. The expression for the non-relativistic energy eigenvalues and radial eigenfunctions are derived using proper quantization rule and formula method, respectively. The results reveal that both the ground and first excited energy eigenvalues depend largely on the angular momentum numbers, screening parameters, reduced mass, and the potential depth. The energy eigenvalues,angular momentum numbers,screening parameters,reduced mass,and the potential depth or potential coupling strength determine the nature of bound state of quantum particles. The explored model is also suitable for explaining both the bound and continuum states of quantum systems.     

Generalized Inverse Mean Curvature Flows in Spacetime

Motivated by the conjectured Penrose inequality and by the work of Hawking, Geroch, Huisken and Ilmanen in the null and the Riemannian case, we examine necessary conditions on flows of two-surfaces in spacetime under which the Hawking quasilocal mass is monotone. We focus on a subclass of such flows which we call uniformly expanding, which can be considered for null as well as for spacelike directions. In the null case, local existence of the flow is guaranteed. In the spacelike case, the uniformly expanding condition leaves a 1-parameter freedom, but for the whole family, the embedding functions satisfy a forward-backward parabolic system for which local existence does not hold in general. Nevertheless, we have obtained a generalization of the weak (distributional) formulation of this class of flows, generalizing the corresponding step of Huisken and Ilmanen’s proof of the Riemannian Penrose inequality.     

BRST Invariant Theory of a Generalized 1 + 1 Dimensional Nonlinear Sigma Model with Topological Term

We give a generalized Lagrangian density of 1 + 1 Dimensional O(3) nonlinear σ model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear σ model, give the example of not introducing the lost constraint = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter β originating from the freedom degree of BRST transformation in a general O(3) nonlinear sigma model, and we gain the general commutation relations of ghost field. PACS numbers: 11.10.Lm; 11.30.Ly     

Inverse of Radiation Field Operators and the Generalized Jaynes-Cummings Model

We generalize the standard Jaynes-Cummings model (JCM) to a model Hamiltonian with the radiation field operators being the inverse of a harmonic oscillator's creation and annihilation operators. Some new commutative relations about the inverse operators are derived and the generalized JCM Hamiltonian's eigenstates are derived.     

Features of the Solution of Direct and Inverse Scattering Problems for Inhomogeneities with a Small Wave Size

Doklady Physics - An acoustic field scattered by a single inhomogeneity consists of components of different orders of multipolarity. For symmetric or weak-contrast inhomogeneities of a small wave...     

Solution of a Generalized Inverse Spectral Problem for Weakly Resolved Spectra Using a Coefficient of Correlation

We consider in a new statement the inverse problem of the theory of vibrational spectra of molecules, in which a theoretical spectral curve directly gets closer to the experimental one. A coefficient of correlation between the curves is used as a criterion of the closeness of the curves and as a functional of the inverse problem. The procedure developed for solving the inverse problem makes it possible to dispense with the preliminary referencing of frequencies in an experimental spectrum and with its expansion into elementary absorption bands.     

计及级联内缺陷空间关联的团簇动力学模拟

团簇动力学（CD）是一种快速模拟材料辐照损伤长时间动力学演化方法.基于平均场速率理论的CD不考虑级联内的缺陷空间关联效应.而实体动力学蒙特卡罗（OKMC）模型虽然考虑空间关联效应,但受到时间尺度和辐照剂量的限制.将模拟粒子初级辐照级联缺陷分布的Monte Carlo模型（IM3D）与OKMC基于常数时间退火方法进行耦合,有效计及级联内的缺陷空间关联性,作为CD模型的有效辐照产生项,建立计及空间关联效应的团簇动力学模型（CD-SC）.结果表明：CD-SC模拟的辐照损伤结果与长时间OKMC结果吻合.有助于提高典型辐照条件下核材料长时间辐照损伤的多尺度模型的准确度和效率.     

Reflection in a Translation Invariant Surface

We prove that the focal set generated by the reflection of a point source off a translation invariant surface consists of two sets: a curve and a surface. The focal curve lies in the plane orthogonal to the symmetry direction containing the source, while the focal surface is translation invariant. In addition, we show that the focal curve is not physically visible. This is done by constructing explicitly the focal set of the reflected line congruence (2-parameter family of oriented lines in ) with the aid of the natural complex structure on the space of all oriented affine lines.      

Invariant polygons in systems with grazing-sliding

The paper investigates generic three-dimensional nonsmooth systems with a periodic orbit near grazing-sliding. We assume that the periodic orbit is unstable with complex multipliers so that two dominant frequencies are present in the system. Because grazing-sliding induces a dimension loss and the instability drives every trajectory into sliding, the system has an attractor that consists of forward sliding orbits. We analyze this attractor in a suitably chosen Poincare section using a three-parameter generalized map that can be viewed as a normal form. We show that in this normal form the attractor must be contained in a finite number of lines that intersect in the vertices of a polygon. However the attractor is typically larger than the associated polygon. We classify the number of lines involved in forming the attractor as a function of the parameters. Furthermore, for fixed values of parameters we investigate the one-dimensional dynamics on the attractor.     

Cascades with coupled map lattices in preferential attachment community networks

In this paper, cascading failure is studied by coupled map lattice （CML） methods in preferential attachment community networks. It is found that external perturbation R is increasing with modularity Q growing by simulation. In particular, the large modularity Q can hold off the cascading failure dynamic process in community networks. Furthermore, different attack strategies also greatly affect the cascading failure dynamic process. It is particularly significant to control cascading failure process in real community networks.     

Invariant Tori in Hamiltonian Systems with Impacts

It is shown that a large class of solutions in two-degree-of-freedom Hamiltonian systems of billiard type can be described by slowly varying one-degree-of-freedom Hamiltonian systems. Under some non-degeneracy conditions such systems are found to possess a large set of quasiperiodic solutions filling out two dimensional tori, which correspond to caustics in the classical billiard. This provides a unified proof of existence of quasiperiodic solutions in convex billiards and other systems with impacts including classical billiard in electric and magnetic fields, dual billiard, and Fermi–Ulam systems. Received: 8 September 1999 / Accepted: 16 November 1999     

Invariant surfaces of a three-dimensional manifold with constant Gauss curvature

We give a reduction procedure to determine (locally) the surfaces with constant Gauss curvature in a three-dimensional manifold which are invariant under the action of a one-parameter subgroup of the isometry group of the ambient space. We apply this procedure to describe the invariant surfaces with constant Gauss curvature in $H^2\times R$ and in $H_3$.     

Inverse scattering equation with a coulombic reference potential

The relation of Marchenko's inverse scattering integral equation for charged and non charged particles is derived. Analytic properties of scattering functions and Jost solutions for both situations are of central importance. Limiting situations fork → 0, and implications for practical applications are discussed.     

The Parametrization Invariant and Gauge Invariant Effective Actions in Quantum Field Theory

The review of formulation and methods of calculation of the parametrization and gauge invariant effective actions in quantum field theory is given. As an example the Vilkovisky-De Witt Effective action (EA) is studied (this EA is a natural representative of gauge and parametrization invariant EA's). The examples where the use of the standard EA leads to the ambiguity are demonstrated. This happens as the result of dependence of the standard EA upon the choice of gauge condition. These examples are as follows: Coleman-Weinberg potential in the finite theories and symmetry breaking, EA in quantum gravity with matter and d = 5 gauged supergravity, the possibility of spontaneous supersymmetry breaking in N = 1 supergravity and the spontaneous compactification in the multidimensional R²-gravity. In all these cases the one-loop Vilkovisky-De Witt EA is found and therefore the problem of gauge dependence of EA is solved. The dependence of standard EA of composite fields upon the gauge is studied for the general gauge theories. The class of gauge and parametrization invariant EA's of the composite fields is offered.