Variational methods, multisymplectic geometry and continuum mechanics

This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order multisymplectic field theories with constraints, such as the incompressibility constraint. The results obtained in this paper set the stage for multisymplectic reduction and for the further development of Veselov-type multisymplectic discretizations and numerical algorithms. The latter will be the subject of a companion paper.     

Entropy squeezing for three-level atom interacting with a single-mode field

The entropy squeezing for a three-level atom interacting with a single-model field is studied. A general definition of entropy squeezing for three-level atom is given according to entropic uncertainty relation of three-level system, and the calculation formalism of entropy is derived for a cascade three-level atom. By using numerical calculation, the entropy squeezing properties of a cascade three-level atom are examined. Our results show that, three-level atom can generate obvious entropy squeezing effect via choosing appropriate superposition state of three-level atom. Our results are meaningful for preparing three-level system information resources with ultra-low quantum noise.     

Structure function scaling in compressible super-Alfvénic MHD turbulence

Supersonic turbulent flows of magnetized gas are believed to play an important role in the dynamics of star-forming clouds in galaxies. Understanding statistical properties of such flows is crucial for developing a theory of star formation. In this Letter we propose a unified approach for obtaining the velocity scaling in compressible and super-Alfvénic turbulence, valid for the arbitrary sonic Mach number, M(S). We demonstrate with numerical simulations that the scaling can be described with the She-Lévêque formalism, where only one parameter, interpreted as the Hausdorff dimension of the most intense dissipative structures, needs to be varied as a function of M(S). Our results thus provide a method for obtaining the velocity scaling in interstellar clouds once their Mach numbers have been inferred from observations.     

Covariant Hamiltonian for the electromagnetic two-body problem

We give a Hamiltonian formalism for the delay equations of motion of the electromagnetic two-body problem with arbitrary masses and with either repulsive or attractive interaction. This dynamical system based on action-at-a-distance electrodynamics appeared 100 years ago and it was popularized in the 1940s by the Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. As an application, the Hamiltonian formalism is used to construct a semiclassical canonical quantization based on the numerical trajectories of the attractive problem.     

Some results on the evolution of microstructure for pulsed beam irradiation

Studies relating to the development of microstructure using pulsed electron and cyclotron beams are very useful in understanding damage effects in pulsed fusion reactors. In this paper we give some exact results to link the evolution of micro-structure during pulsing with that during continuous irradiation, since the effects in the latter case are relatively well understood. Two pulsing time regimes are considered: pulsing times (a) smaller and (b) larger. than microstructural evolution time constants. In both these cases the adiabatic approximation can be used to decouple the point defect variables from the microstructural variables. In case (a) for pulsed electron irradiation and for relatively small pulsing times in cyclotron irradiation the evolution of the microstructure can be exactly simulated by continuous irradiation using an appropriately determined dose rate. A similar analysis is made for case (b) and several effects encountered in continuous irradiation are shown to manifest themselves in pulsed irradiation. A general formalism is developed to determine the equivalent continuous irradiation parameters like dosc rate which will simulate the microstructural development under pulsing. Our treatment is semiquantitative and is based on the analysis of the trajectories in the phase space. The results presented provide a simple practical approach for interpreting and understanding experimental observations.     

A simple and efficient numerical scheme to integrate non-local potentials

As nuclear wave functions have to obey the Pauli principle, potentials issued from reaction theory or Hartree-Fock formalism using finite-range interactions contain a non-local part. Written in coordinate space representation, the Schrödinger equation becomes integro-differential, which is difficult to solve, contrary to the case of local potentials, where it is an ordinary differential equation. A simple and powerful method was proposed several years ago, with the trivially equivalent potential method, where the non-local potential is replaced by an equivalent local potential, which is state dependent and has to be determined iteratively. Its main disadvantage, however, is the appearance of divergences in potentials if the wave functions have nodes, which is generally the case. We will show that divergences can be removed by a slight modification of the trivially equivalent potential method, leading to a very simple, stable and precise numerical technique to deal with non-local potentials. Examples will be provided with the calculation of the Hartree-Fock potential and associated wave functions of ¹⁶O using the finite-range N³LO realistic interaction.     

Measurement of the space–time interval in modified gravity theories in Palatini formalism

There are strong motivations that lead cosmologists to consider alternatives to Einstein’s theory of gravity in Palatini formalism. In addition, there are two distinguishable local frames in this formalism in which one of them is local inertial frame and the equivalence principle is satisfied. Different features of speed of light such as the causal structure constant, electromagnetic and gravitational wave velocities and Einstein velocity will not coincide in this local inertial frame for extended gravity theories in Palatini formalism. On the other hand, both the measurement of time and exchange of a signal between the distant points are required to determine spatial distances. In a particular situation where these aspects of the speed of light do not coincide, the distance determination will become more demanding because light will follow a time-like geodesic of the metric. In modified gravity theories in Palatini approach, theories involve a varying speed of photon. Therefore these kinds of theories must be based on some other technique of measuring spatial distances than radar or some terms should be corrected in the line element in the proposed model. We found out we should consider a coefficient which is proportional to energy density in each era, in the line element in order to be able to use radar for measuring distance in modified gravity theories in Palatini formalism. Analysis of some observational data will be affected by considering this coefficient in the line element.     

Time-dependent polarized radiation transfer in semi-infinite binary Markovian media

The problem of time-dependent radiation transfer in a semi-infinite plane-parallel random medium with Rayleigh scattering phase function including polarization is considered. The random medium is assumed to consist of two immiscible mixed materials with specular reflecting boundary. The mixing statistics of the two components of the medium is described by the two-state homogeneous Markovian statistics. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. Two different weight functions are used to obtain the numerical results for the ensemble-average for reflectivity, radiant energy, and net flux of the medium at any time.     

转移矩阵理论及其在Ⅲ/Ⅴ族半导体量子阱体系中的应用

应用转移矩阵方法求解三种不同量子阱体系中基于单带有效质量模型和包络函数近似下的一维定态薛定谔方程.首先,通过比较Ⅰ型单量子阱GaAlAs/GaAs/GaAlAs体系的解析解和数值解,该方法的精确性得到了验证.其次,与Ⅱ型断代量子阱AlSb/InAs/GaSb/AlSb系统的光致发光谱实验结果比较证实了该方法的适用性.最后,利用该方法推广计算了基于GaAs/GaAlAs材料的Ⅰ型耦合多量子阱体系的子带能级和波函数,说明了方法的通用性和实用性. 关键词： 量子阱 转移矩阵方法 光致发光     

Two-component Fermi systems: II. Superfluid coupled cluster theory

In this second paper of a series the coupled cluster method (CCM) or exp(S) formalism is applied to two-component Fermi superfluids using a Bardeen-Cooper-Schrieffer (BCS) ground state as a zeroth-order approximation. We concentrate on developing the formalism necessary for carrying out eventual numerical calculations on realistic superconducting systems. We do this by generalising the one-component formalism in an appropriate manner and by using the results in the first paper of this series, where we studied two-component Fermi fluids. We stress the previous successes of the CCM, both from the point of view of analytic and numerical results, and we further indicate its potential for studying superconductivity. We restrict ourselves here to a so-called ring plus single particle energy (RING+SPE) approximation for general potentials and show how it can be formulated as a set of four coupled, bilinear integral equations for the cluster-integrated amplitudes. These latter amplitudes are themselves derived from the four-point functions of the system which provide a measure of the two-particle/two-hole component in the true ground-state wavefunction with respect to the BCS model state. We indicate how to obtain possible analytic solutions.     

A class of collision processes with memory and application to simple chemical reactions in a solvent

We apply the general formalism of a class of non-Markovian processes which we have studied elsewhere to three simple models of chemical reactions: dissociation, isomerization, and diffusion in a double-well potential. Our method leads to explicitly solvable models and numerical computations. The results are in agreement with numerical simulation and stochastic dynamics studies of other authors.     

Disorder scattering in magnetic tunnel junctions: theory of nonequilibrium vertex correction

We report a first principles formalism and its numerical implementation for treating quantum transport properties of nanoelectronic devices with atomistic disorder. We develop a nonequilibrium vertex correction (NVC) theory to handle the configurational average of random disorder at the density matrix level so that disorder effects to nonlinear and nonequilibrium quantum transport can be calculated from atomic first principles in a self-consistent and efficient manner. We implement the NVC into a Keldysh nonequilibrium Green's function (NEGF) -based density functional theory (DFT) and apply the NEGF-DFT-NVC formalism to Fe/vacuum/Fe magnetic tunnel junctions with interface roughness disorder. Our results show that disorder has dramatic effects on the nonlinear spin injection and tunnel magnetoresistance ratio.     

Single crystal with a gradient in the lattice spacing

The triply-degenerate local mode of theU-center is coupled to non-degenerate, doubly-degenerate, and triply-degenerate lattice vibrations. Because of the coupling to degenerate lattice vibrations an optical Jahn-Teller-Effect is to be expected which influences the structural form of the side-band. To investigate this influence the absorption band belonging to the triply-degenerate lattice vibrations has been calculated. A response formalism employing double-time thermodynamic Green's functions has been used. The numerical calculation is done for KBr. Our result exhibits a considerable deviation of the structural form from the one in which the dynamical mixing due to the Jahn-Teller-effect has been neglected.     

Electron transfer controlled by conformational variations of a strongly dissipative system

In this paper, there is given a formulation of electron transfer in the system where the conformational transitions are present. The conformation changes were described as classical telegraphic noise. In the work it was assumed that electron transfer reaction can be completely interrupted by the fluctuation of the electronic coupling. A functional-integral formalism to the dynamics of a two-state system was used. The results have been derived within the noninteracting blip approximation with respect to the quantum fluctuations of the heat bath.     

上转换对Er3+，Yb3+共掺磷酸盐玻璃激光器输出的影响

研究了激光二极管抽运的Er^３＋，Yb^３＋共掺磷酸盐玻璃激光器中共协上转换(cooperative upconversion)和累积能量转移(cumulative energy transfer)对激光输出的影响.通过对速率方程的数值模拟，定量计算并分析了共协上转换和累积能量转移对激光输出的影响，发现共协上转换对阈值抽运功率的影响可达到22%之多，实验结果和理论曲线相当符合.这有助于对Er^３＋，Yb^３＋共掺磷酸盐玻璃激光器进行优化. 关键词： 共协上转换 累积能量转移 ３＋')" href="#">Er^３＋ ３＋共掺磷酸盐玻璃激光器')" href="#">Yb^３＋共掺磷酸盐玻璃激光器 数值分析     

On the dynamical properties of a Fermi accelerator model

In this paper we use discrete dynamical systems formalism to carefully investigate the effect of a time-dependent perturbation on a classical mechanical model. We present a study of a one-dimensional Fermi accelerator model and its parametric dependence on the amplitude of the movement of the wall. We focus on the low-energy region, in which the system may present chaotic behavior illustrated by orbits with stochastic behavior and sensitive dependence on initial conditions. Through numerical analysis, this behavior is quantitatively characterized by a positive Lyapunov exponent and by the position of the boundary of the observed ergodic component. Our results will be analyzed by comparing this model to a simplified version and to the Standard Map. These results indicate that the dynamics of the model is, in a certain sense, very weakly dependent of the parameter.     

The motion of a classical spinning particle in a Riemann-Cartan space-time

A consistent set of equations of motion for classical charged particles with spin and magnetic dipole moment in a Riemann-Cartan space-time is generated from a constrained Lagrangian formalism. The equations avoid the spurious free helicoidal solutions and at the same time conserve the canonical condition of normalization of the 4-velocity. The 4-velocity and the mechanical moment are parallel in this theory, where the condition of orthogonality between spin and 4-velocity is treated as a nonholonomic constraint. A generalized BMT precession equation is obtained as one of the results of the formalism.     

Spin-orbit forces in knockout reactions

The spin-orbit final-state interaction for the one-nucleon knockout reaction is studied in perpendicular kinematics using an eikonal formalism to investigate experimentally observed cross- section asymmetries. Our results elucidate previous numerical calculations indicating sensitivity of these asymmetries (as a function of the nuclear recoil momentum) to the imaginary part of the spin-orbit potential.     

A novel method to test particle ordering and final state alignment in helicity formalism

In this study,the non-trival effect of the selection of reference particles for decay angle definitions is demonstrated when constructing the partial-wave amplitude of multi-body decays using helicity formalism.This issue is often ignored in the standard use case of helicity formalism.A new technique is proposed to test the selection of the particle ordering,and it can also be used as a generalized method to calculate the rotation operators that are used for the final-state alignment between different decay chains.Moreover,numerical validations are performed to support the arguments and to verify the effectiveness of the proposed technique.