Topological superfluid in a two-dimensional polarized Fermi gas with spin-orbit coupling and adiabatic rotation

We study the properties of superfluid in a two-dimensional(2 D) polarized Fermi gas with spin–orbit coupling and adiabatic rotation which are trapped in a harmonic potential. Due to the competition between polarization, spin–orbit coupling, and adiabatic rotation, the Fermi gas exhibits many intriguing phenomena. By using the Bardeen–Cooper–Schrieffer(BCS) mean-field method with local density approximation, we investigate the dependence of order parameter solution on the spin–orbit coupling strength and the rotation velocity. The energy spectra with different rotation velocities are studied in detail. Besides, the conditions for the zero-energy Majorana fermions in topological superfluid phase to be observed are obtained. By investigating distributions of number density, we find that the rotation has opposite effect on the distribution of number density with different spins, which leads to the enhancement of the polarization of Fermi gas. Here,we focus on the region of BCS pairing and ignore the Fulde–Ferrell–Larkin–Ovchinnikov state.     

BS分子α带系A~2Π→X~2Σ~+及γ带系C~2Π→X~2Σ~+法兰克-康登因子的计算

在双原子分子核运动的薛定谔方程中，计入分子的振转相互作用项，在Ｍｏｒｓｅ势近似下得出的波函数除与振动量子数有关外，还与转动量子数有关。本文用该波函数编程计算了ＢＳ分子α带系Ａ２Π→Ｘ２Σ＋及γ带系Ｃ２Π→Ｘ２Σ＋法兰克－康登（Ｆｒａｎｃｋ－Ｃｏｎｄｏｎ）因子（简称Ｆ－Ｃ因子）。计算中转动量子数的取值由Ｊ＝０至Ｊ＝２００，其结果适用于低温、高温和强激波条件。     

Beam-propagation method for analysis of z -dependent structures that uses a local oblique coordinate system

In the most current beam-propagation method (BPM), the coupling between the transverse and the longitudinal fields in z -dependent structures is ignored under the staircase approximation, which results in violation of power conservation. We propose a novel BPM that is derived in a local oblique coordinate system to analyze z -dependent structures accurately and efficiently without taking the staircase approximation. The coupling between the transverse and the longitudinal fields is automatically included in the local oblique coordinate system, and power is thus conserved if the reflection is neglected.     

八级形变系统的集体运动

利用一组内部坐标和三个欧拉角描述八极形变系统的集体运动,动能被分解成三部分:体坐标系下的形变振动,体坐标系围绕实验室系的转动以及振动和转动的耦合.量子化的动能算符被导出,一些特殊八极形变下的集体谱被讨论.     

旋转内接悬臂梁的刚柔耦合动力学特性分析

对固结于旋转刚环上内接柔性梁的刚柔耦合动力学特性进行了研究. 在精确描述柔性梁非线性变形基础上, 利用Hamilton变分原理和假设模态法, 在计入柔性梁由于横向变形而引起的轴向变形二阶耦合量的条件下, 推导出一次近似耦合模型. 忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量, 对简化模型做无量纲化处理. 首先分析在非惯性系下内接悬臂梁的动力学响应, 并与外接悬臂梁进行比较; 其次研究内接悬臂梁的稳定性;最后分析内接悬臂梁失稳临界转速的收敛性. 研究发现, 与外接悬臂梁存在动力刚化效应不同,内接悬臂梁存在着动力柔化效应; 给出了内接悬臂梁无条件稳定的临界径长比以及失稳的临界转速的计算方法; 若第一阶固有频率随转速增大而减小,则该内接悬臂梁处于有条件稳定; 随着模态截断数的增加,内接悬臂梁失稳的临界转速减小且有收敛值. 关键词： 内接悬臂梁 一次近似简化模型 动力柔化 临界转速     

Vibrational relaxation of a molecule in a dense medium

In this paper we consider some features of vibrational relaxation of a guest molecule in a host matrix. The model system involves a harmonic molecule interacting with a harmonic medium. The molecule-medium coupling was handled by the rotating wave approximation considering linear terms in the intramolecular displacements and high terms in the medium displacements. Three specific models for the molecule-medium coupling were considered, which involve single phonon decay, vibron-phonon decay and multiphonon decay. Within the framework of the random phase approximation the Heisenberg equations of motion for the system could be expressed in terms of a unified scheme which is valid for both single phonon and multiphonon processes. Explicit solutions were derived utilizing the Wigner-Weisskopf approximation. This generalized formalism was applied for the study of the time evolution of the distribution, the cooling and the heating processes of the oscillator by a thermal field and for the coupling between vibrational relaxation and infra-red emission.     

Mean field approximation for noisy delay coupled excitable neurons

Mean field approximation of a large collection of FitzHugh-Nagumo excitable neurons with noise and all-to-all coupling with explicit time-delays, modelled by N?1 stochastic delay-differential equations is derived. The resulting approximation contains only two deterministic delay-differential equations but provides excellent predictions concerning the stability and bifurcations of the averaged global variables of the exact large system.     

Critical dynamics of a localized moment system coupled to conduction electrons

We discuss the critical dynamics of a system of localized spins interacting with conduction electrons via an isotropic exchange coupling between the respective spin densities. It is shown that the elimination of the conduction electrons by an adiabatic approximation is not allowed for small wave vectors. The quantum mechanical Fokker-Planck equation derived in a previous paper is used to investigate the renormalization of the kinetic coefficients due to nonlinear mode coupling contributions.     

Gitterdynamik der Ionenkristalle mit einer quantenmechanischen Behandlung der Ionendeformation

The problem of the electron-phonon coupling is selfconsistently solved by means of a Hartree-Fock approximation and a tight binding approximation for the wave functions. From this we derive a general system of equations of motion which involves both a polarization and a radial and axial deformation of the electronic shell of an ion. Moreover, it is shown under what restrictions the “breathing shell” model of Schröder can be derived.     

简谐+四次势中自旋轨道耦合旋转玻色-爱因斯坦凝聚体的基态结构

研究了囚禁于简谐+四次势中具有自旋轨道耦合相互作用的旋转玻色-爱因斯坦凝聚体的基态结构; 考虑了自旋轨道耦合相互作用和旋转对基态结构的影响; 结果发现在自旋轨道耦合相互作用与旋转共同作用下, 系统呈现出丰富且新奇的基态结构, 如条形、双排和蛇皮花斑状等.     

Equal-time kinetic equations in a rotational field

We investigate quantum kinetic theory for a massive fermion system under a rotational field. From the Dirac equation in rotating frame we derive the complete set of kinetic equations for the spin components of the 8- and 7-dimensional Wigner functions. While the particles are no longer on a mass shell in the general case due to the rotation–spin coupling, there are always only two independent components, which can be taken as the number and spin densities. With help from the off-shell constraint we obtain the closed transport equations for the two independent components in the classical limit and at the quantum level. The classical rotation–orbital coupling controls the dynamical evolution of the number density, but the quantum rotation–spin coupling explicitly changes the spin density.     

Higher order effects in the master equation for coupled systems

The usual derivations of the master equation for coupled systems such as the laser make an assumption of weak coupling both for the coupling of the components to their heat baths and for the internal coupling between the components. It is this second condition that we wish to relax. In the usual derivation of the irreversible part of the master equation the approximation is made that the density operator for the coupled system factorizes into a product of the density operators for the two components. However when strong coupling is present, such as in high intensity lasers this approximation is no longer valid. To illustrate how the irreversible part of the master equation may be derived without making the factorization ansatz we consider the case of two coupled boson fields. Our derivation leads to additional terms in the usual master equation arising from correlations between the heat baths introduced by the coupling. This modified master equation yields the correct stationary solution for the density operator of the coupled system, whereas the usual master equation leads to a stationary solution for the density operator correct for the free components only.     

Spin-orbit coupled Bose-Einstein condensate under rotation

We examine the combined effects of Rashba spin-orbit (SO) coupling and rotation on trapped spinor Bose-Einstein condensates. The nature of single particle states is thoroughly examined in the Landau level basis and is shown to support the formation of a half-quantum vortex. In the presence of weak s-wave interactions, the ground state at strong SO coupling develops ringlike structures with domains whose number shows step behavior with increasing rotation. For the fast rotation case, the vortex pattern favors a triangular lattice, accompanied by density depletion in the central region and a weakened Skyrmionic character as the SO coupling is enhanced. Giant vortex formation is facilitated when SO coupling and rotation are both strong.     

Post-Newtonian equations for the metric perturbation generated by a rotating elastic earth

By using Synge's approximation method to describe the unperturbed problem, we obtain the equations for the gravitational field perturbation and the Lagrangian displacement that occur when an isolated and initially self-gravitating spherical and static elastic earth gets into steady rotation. These equations are explicitly derived in an order of approximation for the initial problem where both rotation and elastic structure manifest themselves in the perturbed state.     

直拉法晶体生长过程非稳态流体热流耦合

为了改善复杂对流形态下的晶体生长品质, 提出了一种改进的格子Boltzmann方法研究非稳态熔体流动和传热的耦合性质. 该方法基于不可压缩轴对称D2Q9模型, 构建了包含旋转惯性力和热浮力等外力项的演化关系, 实现了对轴对称旋转流体的速度、温度和旋转角速度的计算与分析. 结果表明, 非稳态熔体中的流、热耦合性质与格拉斯霍夫数和雷诺数的相互作用有关; 通过调节高雷诺数, 可有效抑制熔体中的自然对流, 改善温度分布, 有助于提高单晶的品质. 数值计算结果与实际硅单晶生长试验均证明了所提方法的正确性及有效性.     

The computation of Karplus equation coefficients and their components using self-consistent field and second-order polarization propagator methods

The Karplus equation has been investigated by ab initio computation of the spin-spin coupling constants for a series of rotated ethane geometries. The couplings have been calculated at the self-consistent field (SCF) level as well as using the second-order polarization propagator approximation (SOPPA) and the second-order polarization propagator approximation with coupled cluster singles and doubles amplitudes (SOPPA(CCSD)) and have been compared with results of previous calculations. The four principal components of the coupling constants rather than just the Fermi-contact have been calculated, and the common supposition that the Fermi-contact term is totally dominant has been confirmed. The derivatives of the orbital paramagnetic and orbital diamagnetic terms are significant but opposite in sign for the case of this rotation in ethane. It is found that the coefficients in the Karplus equation are largely overestimated at the SCF level, whereas the SOPPA(CCSD) results are in good agreement with coefficients derived from experimental coupling constant data or the results of multi-configurational self-consistent field (MCSCF) calculations. It is further observed that extending the Fourier series in the Karplus equation to include cos(3θ) and cos(4θ) terms neither significantly improves the quality of the fit nor significantly changes the values of the other coefficients. In order to simulate the Abraham and Pachler equation, calculations varying the nuclear charge on hydrogen have been performed. These will allow an abstract but flexible prediction of the effect of electronegative substituents.     

多声子无辐射弛豫速率的理论研究

本文应用量子力学生成函数法,在等效耦合模条件下导出多声子弛豫速率的普适表达式,及在高级近似条件下的解析表达式。指出Fong等人在弱耦合条件下用统计方法、Miyakawa等人在弱耦合和低温近似条件下所得多声子弛豫速率表达式的局限性。文中还计算了多声子弛豫速率对温度、声子能量、能隙以及位移参数的依赖关系。     

Transitions in a Logistic Growth Model Induced by Noise Coupling and Noise Color

With unified colored noise approximation, the logistic growth model is used to analyze cancer cell population when colored noise is included. It is found that both the coupling between noise terms and the noise color can induce continuous first-order-like and re-entrance-like phase transitions in the system. The coupling and the noise color can also increase tumor cell growth for small number of cell mass and repress tumor cell growth for large number of cell mass. It is shown that the approximate analytic expressions are consistent with the numerical simulations.     

Transitions in a Logistic Growth Model Induced by Noise Coupling and Noise Color

With unified colored noise approximation, the logistic growth model is used to analyze cancer cell population when colored noise is included. It is found that both the coupling between noise terms and the noise color can induce continuous first-order-like and re-entrance-like phase transitions in the system. The coupling and the noise color can also increase tumor cell growth for small number of cell mass and repress tumor cell growth for large number of cell mass. It is shown that the approximate analytic expressions are consistent with the numerical simulations.     

MAXIMAL EMITTED POWER OF HYPERRADIANCE FROM PERTURBED JOSEPHSON SYSTEMS

Consider two magnetically coupled and perturbed long Josephson junctions which operate in synchronized modes. Under first order approximation, the soliton solution of the system is derived by using a new perturbation technique. It is shown that the perturbing parameters limit the emitted power from the system, and the physically relevant coupling parameter leads to the increase of power. The formula of maximal emitted power is given for a particular power input. The results solve some important problems left over by previous analysis.