An Effective Field Theory for One-dimensional Polarized Fermi Gases

We derive an effective field theory describing the long wavelength, low energy properties of one-dimensional (1D) attractive Fermi gases with spin imbalance. Our theory is based on the exact solution (Bethe ansatz) of the microscopic Hamiltonian, the Gaudin-Yang model. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a novel quantum fluid, a two-component Luttinger liquid with spin-charge mixing. Applying the theory, we obtain the correlation functions and the universal low temperature thermodynamics. Our theory can also predict the phase diagram of weakly coupled 1D gases, a quasi-1D system recently realized in experiments at Rice university.     

A comparative study of dielectric response function models for liquid water

Various methodologies that aim at an analytic representation of the dielectric response function (DRF) of liquid water with emphasis on the Bethe ridge region are compared. The use of optical data is a common feature to all models presented providing an empirical ground for modelling the valence energy losses where many-body (and phase) effects are expected to be most prevalent. The dispersion models used for describing the momentum dependence of the DRF are evaluated against the recent inelastic X-ray scattering (IXS) spectroscopy data. Recent developments along the lines of Ritchie's extended-Drude scheme for an improved representation of the experimental Bethe ridge are presented.     

Practical calculations of stopping powers for intermediate energy electrons in some elemental solids

This study presents calculation results of the stopping power (SP) of electrons of kinetic energy from 10 eV to 100 keV for some elemental solids. The method is based on utilization of the modified Bethe-Bloch SP expression and analytical expression for effective atomic electron number and effective mean excitation energies of target atoms, and for effective charge of incoming electrons, Sugiyama’s semi-empirical formula is embedded in the formula. An analytical expression for the practical SP calculations using Bethe approximation and Thomas-Fermi model of atom is taken from an pervious study and the calculated results of the SPs from this formula for electrons in some elemental solids, such as Al, Si, Cr, Ni, Cu, Ge, Pd, Ag, Pt, and Au, are calculated and rigorously compared with experimental data, Penelope code results and with results of other calculations such as the non-relativistic Bethe SP equation and the empirical modification of the Bethe equation by Joy and Luo. The results are found to be in good agreement for some targets but some limited agreement for some energies and targets is also observed.     

Exact Analysis of a One-Dimensional Weakly Repulsive Bose-Fermi Mixture

We study a one-dimensional system of Bose–Fermi mixture with repulsive $\delta $ -function interactions using the nested Bethe ansatz method. This system is integrable when the masses of bonsons and fermions are equal and the interactions between Bose–Bose and Bose–Fermi particles are equal. By use of the power series expansion method, the Surtherland integral equation, which describes the ground state properties, is solved analytically in the weak coupling regime. Physical quantities such as the ground state energy, the sound velocity, and the chemical potential are explicitly expressed in terms of a dimensionless interaction parameter $\gamma =c/D$ and boson fraction $\alpha =N_{b}/N$ , where $c$ is the interaction strength, $D$ is the number density, $N_{b}$ is the number of bosons, and N is the total number of particles.     

Electronic stopping power of liquid water for protons down to the Bragg peak

An improved dielectric response model that accurately represents the recent experimental data for liquid water over the whole Bethe surface is used to calculate the electronic stopping power of protons (of fixed-charge) in liquid water from several MeV down to the Bragg peak region. The results are by approximately 20% lower than the ICRU values and earlier studies. A shell-correction term with a contribution of 15-20% to Bethe's high-energy stopping number is obtained. The present work offers a first-principle approach for stopping power calculations that overcomes the well-known limitations of Bethe's stopping theory, namely, the need for separate determination of the mean excitation energy (the I-value) and the shell-corrections. In particular, all type of inner-shell effects are built into the model through the kinematically restricted integrals over the Bethe surface. The net contribution of higher-order corrections is found to be minimal over most of the present range. Thus, within the uncertainty of the dielectric model (few %) the present calculations are 'exact' down to approximately 100 keV.     

The hierarchically graded multilevel finite element method

 Using higher p-order ansatz functions in the finite element method achieves already with a rather small number of elements good approximations of the smooth part of the solution. For covering this part the p-method is more efficient than the h-method. Otherwise is a high p-order too expensive according to computational effort to use it on a large number of elements which might be necessary to approximate the solution in disturbed areas of a structure. We present an ansatz space which balances the good approximation quality of higher p-ansatz with their computational cost by assigning each level of an hierarchical sequence of meshes an own adequate ansatz space. Received 30 November 2000     

Improved Variational Approach to the Two-Site Bose-Hubbard Model

An improved variational ansatz is proposed to capture the most striking properties of the ground state of a slightly biased attractive two-site Bose-Hubbard Hamiltonian. Our ansatz, albeit its simplicity, is found to capture well the exact properties of the ground state for a wide variety of model parameters, in particular the fragmentation occurring before the formation of cat-like states and also the formation of strongly correlated cat-like states.     

On the Reentrant Transitions and Magnetization Plateaus in the Spin-1/2 Ising–Heisenberg Model on Diamond-Like Decorated Bethe Lattices

A critical behavior and magnetization process of the frustrated spin-1/2 Ising–Heisenberg model on diamond-like decorated Bethe lattices is examined within the framework of the decoration–iteration transformation and exact recursion relations. It is demonstrated that the investigated spin model with a sufficiently high coordination number of the Bethe lattice may exhibit reentrant phase transitions. Three different magnetization scenarios with up to two consecutive fractional plateaus can be detected in the low-temperature magnetization curve, whereas the intermediate magnetization plateau either corresponds to the classical ferrimagnetic spin alignment and/or the more striking quantum monomer–dimer spin arrangement.     

Zernike-Galerkin method: efficient computational tool for elastically deformable optics

We present the Zernike-Galerkin method, a tool for the discretization of partial differential equations (PDEs) on thin membranes in polar coordinates. The use of a truncated Zernike series as ansatz yields a semianalytical compact and parametric solution of the PDE. We demonstrate its use for the solution of the Poisson equation in polar coordinates, which is the equation of governing a thin strained membrane's deformation, or the flow of heat, both of which are important influences for the deformable membrane design. The obtained solution is directly expressed in terms of the components of the wavefront error, which highly facilitates the formulation of design questions. The method is computational highly efficient due to the sparsity and recursivity of the ansatz, is applicable to other PDEs, and can be efficiently combined with geometric optical and optimization methods. Its application to model a pressure-driven adaptive lens membrane is demonstrated.     

Cross section calculations in condensed media: charged particles in liquid water

Ionisation cross sections for charged particles are deduced within the framework of the relativistic plane wave first Born approximation and the classical electromagnetic theory. The macroscopic dielectric response function is related to the atomic generalised oscillator strength. Interaction cross sections for proton impact on liquid water are presented and discussed. A semi-empirical model for the angular distribution of secondary electrons produced by proton impact on liquid water, which is based on the Bethe approach, is presented.     

Quantifying Fluctuations from the Tunnelling Differential Conductance

Dynes ansatz (Dynes et al. in Phys. Rev. Lett. 53:2437, 1984) is a broadly utilised procedure to extract the superconducting energy gap from the tunnelling differential conductance, a quantity that is measured by scanning tunnelling microscopy (STM) techniques. In this paper, we investigate the limit of applicability of this ansatz in nanoscale superconductors and propose a generalisation that permits to study thermal and quantum fluctuations in STM experiments.     

Intrinsic Localized Modes in an Order-parameter-preserving Antiferromagnet

Intrinsic localized modes in an order-parameter-preserving antiferromagnet are investigated withemploying the Dyson-Maleev transformation and the coherent-state ansatz. These modes which be-low the magnon frequency band correspond to a local large-angle, low-frequency precessional mo-tion of spins, quantum states of which are characterized by the indefiniteness of the number of rele-vant magnons.     

Singular solitons in optical metamaterials by ansatz method and simplest equation approach

This paper derives singular 1-soliton solution for optical metamaterials. There are two integration approaches that obtains the solution. These are the ansatz approach and the simplest equation approach. The second method also leads to an additional set of solutions that emerge as a by-product. These are topological soliton, rational solution and singular periodic solution. The constraint conditions for the existence of these solutions are also exhibited. The numerical simulation of a topological 1-soliton solution is also exhibited.     

Combined optical solitons with parabolic law nonlinearity and spatio-temporal dispersion

In this work, combined optical solitons are constructed in a weakly nonlocal nonlinear medium. The spatio-temporal dispersion (STD), parabolic law nonlinearity, detuning, nonlinear dispersion as well as inter-modal dispersion are taken into account. The integration tool that is applied is the complex envelope function ansatz. The influences of different parameters on dynamical behavior of combined optical solitons are discussed. The results are useful in describing the propagation of combined optical solitons with STD and parabolic law nonlinearity.     

Bright,dark and dark-singular soliton solutions of nonlinear Schrödinger's equation with spatio-temporal dispersion

This article presents an analytical study of the propagation of solitons through optical fibres. We consider a nonlinear Schrödinger equation with spatio-temporal dispersion and quadratic–cubic nonlinearity. Jacobi elliptic functions are used as an ansatz to extract optical dark and bright solitons as well as Jacobi elliptic solutions. The extended direct algebraic method gives dark and dark-singular soliton solutions. The constraint conditions which guarantee the existence of soliton solutions are listed.     

Optical properties of alkali-earth atoms and Na2 calculated by GW and Bethe–Salpeter equations

Starting from the GW approximation (GWA) beyond density functional theory and solving the eigenvalue problem associated with the Bethe–Salpeter equation which accounts for the excitonic effect, I have determined optical properties of isolated Be, Mg and Ca atoms and Na₂. In the representation of single electron wave functions, I have used the all-electron mixed basis approach in which both plane waves and atomic orbitals are used as a basis set. The resulting quasiparticle energies and optical absorption spectra are compared with available experimental data.     

Incoherent intensities of electromagnetic waves in a random medium layer and radiative transfer theory

Abstract

Equations for incoherent intensities are obtained for electromagnetic waves in a random medium layer with plane parallel boundaries. These are based on the Bethe–Salpeter equation under the ladder approximation. These equations are then compared with the radiative transfer equations for this problem. Differences between these two approaches are pointed out and discussed. The Müller matrix is derived based on a first-order approximation to the equations for incoherent intensities which is then used to highlight the significance of the above-mentioned differences in radar cross-section computations.     

Vortex fluctuations in two-dimensional superconductors above and below the Berezinskii-Kosterlitz-Thouless temperature

The vortex-unbinding transition in two-dimensional superconductors is revisited. The approach presented here is based on a Thomas-Fermi-type ansatz and allows to calculate the vortex density and the screened interaction below and above the transition temperature within a unified formalism.     

(2+1)维非线性演化方程的形式新解

主要从两个方面讨论(1)将非线性演化方程的形式级数解进行对称延拓;(2)利用"秩"的概念,对非线性演化方程进行分类.即如果方程各项中"秩"的取值全为奇数或偶数,则可借助椭圆方程的方法解之;若方程各项中"秩"的取值奇偶性不一致,则给出一形式幂级数解.并以两个(2+1)维非线性演化方程为例,说明改进的方法能较好地求得非线性演化方程的更多形式新解.     

Optical solitons to the nonlinear Shrödinger’s equation with spatio-temporal dispersion using complex amplitude ansatz

In this work, we investigate the optical solitons to the non-linear Shrödinger’s equation with spatio-temporal dispersion. There are two types of non-linear media studied in this paper. They are Kerr law and parabolic law. By adopting a complex amplitude ansatz method composed of the addition of bright and dark optical solitons, we present the exact dark, bright and dark-bright or combined optical solitons to the model. Numerical results and discussions are also presented.