有限温度下一维Gaudin-Yang模型的热力学性质

本文通过数值求解有限温度下一维均匀费米Gaudin-Yang模型的热力学Bethe-ansatz方程, 研究了此模型的基本性质,得到了在给定的温度或给定的相互作用下, 化学势、相互作用、粒子密度和熵的相互变化图像. 对结果分析发现, 在给定温度和相互作用下, 熵随着化学势的变化有一个量子临界区域.     

Gaussian Time-Dependent Variational Principle for Bosons

We investigate the Dirac time-dependent variational method for a system of non-ideal Bosons interacting through an arbitrary two body potential. The method produces a set of non-linear time dependent equations for the variational parameters. In particular we have considered small oscillations about equilibrium. We obtain generalized RPA equations that can be understood as interacting quasi-bosons, usually mentioned in the literature as having a gap. The result of this interaction provides us with scattering properties of these quasi-bosons including possible bound-states, which can include zero modes. In fact the zero mode bound state can be interpreted as a new quasi-boson with a gapless dispersion relation. Utilizing these results we discuss a straightforward scheme for introducing temperature.     

有限温度下一维Hubbard模型的化学势泛函理论研究

通过数值方法求解了有限温度下一维均匀Hubbard模型的热力学Bethe-ansatz方程组,得到了在给定温度和相互作用强度情况下,比热c、磁化率χ和压缩比κ随化学势μ的变化图像.基于有限温度下一维均匀Hubbard模型的精确解,利用化学势(μ)-泛函理论研究了一维谐振势下的非均匀Hubbard模型,给出了金属态和Mott绝缘态下不同温度情况时局域粒子密度n_i和局域压缩比_κi随格点的变化情况.     

On the critical dynamics of ferromagnets

The dynamic scaling functions for ferromagnets above and below the critical temperature are determined using mode coupling theory. Below the critical temperature we study isotropic ferromagnets taking into account the exchange interaction only and give the first numerical solution of the resulting mode coupling equations. In the paramagnetic phase we examine how the critical dynamics is modified by the addition of the dipoledipole interaction. On the basis of this theory we are able to explain in a unifying fashion the results of different experimental methods; i.e.: neutron scattering, hyperfine interaction and electron-spin resonance. Predictions for new experiments are made.     

Parameterized effective potential for molecules and its optimization in the single-determinant approximation

A parameterized effective potential for molecules is developed in which the Coulomb and exchange parts of the Hartree-Fock potential are expressed in terms of the electron-nucleus interaction potential. Within the framework of the single-determinant approximation, equations for determining the parameters of the effective potential and of the finite basis set are obtained. In contrast to the equations of the Hartree-Fock method, the solution procedure for the equations for the parameterized effective potential does not require self-matching of the orbital expansion coefficients in terms of the basis set functions. Using the calculation of the ground state energy of diatomic hydrides as an example, the dependence of the effective potential parameters on the number of particles in the system is analyzed in detail. Based on this analysis, a simple two-parameter model is proposed. The results of calculations in terms of this model deviate from those obtained by the precision Hartree-Fock method by 0.02–0.06%.     

The MAST FV/FE scheme for the simulation of two-dimensional thermohaline processes in variable-density saturated porous media

A novel methodology for the simulation of 2D thermohaline double diffusive processes, driven by heterogeneous temperature and concentration fields in variable-density saturated porous media, is presented. The stream function is used to describe the flow field and it is defined in terms of mass flux. The partial differential equations governing system is given by the mass conservation equation of the fluid phase written in terms of the mass-based stream function, as well as by the advection–diffusion transport equations of the contaminant concentration and of the heat. The unknown variables are the stream function, the contaminant concentration and the temperature. The governing equations system is solved using a fractional time step procedure, splitting the convective components from the diffusive ones. In the case of existing scalar potential of the flow field, the convective components are solved using a finite volume marching in space and time (MAST) procedure; this solves a sequence of small systems of ordinary differential equations, one for each computational cell, according to the decreasing value of the scalar potential. In the case of variable-density groundwater transport problem, where a scalar potential of the flow field does not exist, a second MAST procedure has to be applied to solve again the ODEs according to the increasing value of a new function, called approximated potential. The diffusive components are solved using a standard Galerkin finite element method. The numerical scheme is validated using literature tests.     

Exploring the thermodynamics of a two-dimensional Bose gas

Using in situ measurements on a quasi-two-dimensional, harmonically trapped (87)Rb gas, we infer various equations of state for the equivalent homogeneous fluid. From the dependence of the total atom number and the central density of our clouds with chemical potential and temperature, we obtain the equations of state for the pressure and the phase-space density. Then, using the approximate scale invariance of this 2D system, we determine the entropy per particle and find very low values (below 0.1k(B)) in the strongly degenerate regime. This shows that this gas can constitute an efficient coolant for other quantum fluids. We also explain how to disentangle the various contributions (kinetic, potential, interaction) to the energy of the trapped gas using a time-of-flight method, from which we infer the reduction of density fluctuations in a nonfully coherent cloud.     

Faddeev equations and the method of hyperspherical harmonics in the problem of three-nucleon continuum

A method for solving the Faddeev equations in configuration space is developed for a three-nucleon system in the continuum by using the decomposition over a hyperspherical basis. The wave functions of Nd-system, phase shifts, and cross sections of Nd-scattering at subthreshold energies are calculated. Also, within the framework of this method, one-dimensional integral equations are formulated for the problem of infinite motion of all three strongly interacting particles, and the Faddeev equations for a system of three hadrons with Coulomb interaction in the continuum are modified. Similar methods of investigation of three-particle systems are reviewed.     

The kinetic energy partition method applied to a confined quantum harmonic oscillator in a one-dimensional box

A new, physically motivated, basis set expansion method for solving quantum eigenvalue problems with competing interaction potentials is presented. In contrast to the usual dissection of the potential energy into unperturbed and perturbing terms, we divide the kinetic energy into partial terms by modifying the mass factor. The partition scheme results in partial kinetic energies with their effective mass factors. By distributing each partial kinetic energy to a respective potential energy to form a subsystem, the total Hamiltonian is written as the sum of subsystem Hamiltonians. Using a linear combination of the subsystem wave-functions to represent the system wave-function we obtain a set of coupled equations for the expansion coefficients, by solving these energies and wave-functions can be obtained. We demonstrate the solution scheme with a standard model system: a confined harmonic oscillator in a one-dimensional box. With only a few (less than ten) basis functions from each subsystem, we can reproduce the exact solutions very accurately, thus showing the applicability of this method.     

On solving nonhomogeneous Bethe-Salpeter equations

A new method for solving nonhomogeneous Bethe-Salpeter equations is developed on the basis of employing expansions of interaction amplitudes and kernels in the basis of four-dimensional spherical harmonics. The method, which is applicable to both scalar and spinor equations, is expounded for the case of the nonhomogeneous Bethe-Salpeter equation for scalar particles in the ladder approximation. The model phase shifts calculated by this method are in good agreement with results published previously.     

Dynamics of solidification in binary melts during rapid cooling II. Analysis of basic equations

In the first part of our paper we have derived a set of stochastic differential equations which describe the solidification of binary melts. The equations have been derived within the framework of the model in which the mass and heat transport and the kinetics of the phase transition is considered. In the second part of our paper we present the analysis of the set of general equations. On the basis of this analysis it will be obvious which approximations can be used for the solution of the basic equations in a particular regime of solidification. The adiabatic approximation is one of them. Another situation occurs when the thermodynamic conditions of the phase transformation change fast with time. The system not only moves away from thermodynamic equilibrium but also we can observe inertia of the system, which results in a delay of the evolution of the system respecting the steady-state regime (e.g. the nucleation processes) and the adiabatic approximation cannot be assumed. Concluding this paper, the method used in paper [13] to describe the nucleation in binary systems is presented as an example of the solution of the set of general equations in the case where the adiabatic approximation cannot be adopted.     

Six-Bodies Calculations Using the Hyperspherical Harmonics Method

In this work we show results for light nuclear systems and small clusters of helium atoms using the hyperspherical harmonics basis. We use the basis without previous symmetrization or antisymmetrization of the state. After the diagonalization of the Hamiltonian matrix, the eigenvectors have well defined symmetry under particle permutation and the identification of the physical states is possible. We show results for systems composed up to six particles. As an example of a fermionic system, we consider a nucleon system interacting through the Volkov potential, used many times in the literature. For the case of bosons, we consider helium atoms interacting through a potential model which does not present a strong repulsion at short distances. We have used an attractive gaussian potential to reproduce the values of the dimer binding energy, the atom-atom scattering length, and the effective range obtained with one of the most widely used He–He interaction, the LM2M2 potential. In addition, we include a repulsive hypercentral three-body force to reproduce the trimer binding energy.     

Two-particle scattering on the lattice: Phase shifts,spin-orbit coupling,and mixing angles

We determine two-particle scattering phase shifts and mixing angles for quantum theories defined with lattice regularization. The method is suitable for any non-relativistic effective theory of point particles on the lattice. In the center-of-mass frame of the two-particle system we impose a hard spherical wall at some fixed large radius. For channels without partial-wave mixing the partial-wave phase shifts are determined from the energies of the nearly spherical standing waves. For channels with partial-wave mixing further information is extracted by decomposing the standing wave at the wall boundary into spherical harmonics, and we solve coupled-channels equations to extract the phase shifts and mixing angles. The method is illustrated and tested by computing phase shifts and mixing angles on the lattice for spin-1/2 particles with an attractive Gaussian potential containing both central and tensor force parts.     

Electron transport near the Mott transition in n-GaAs and n-GaN

In this paper, we study the temperature dependence of the conductivity and the Hall coefficient near the metal–insulator phase transition. A theoretical investigation is performed within the effective mass approximation. The variational method is used to calculate the eigenvalues and eigenfunctions of the impurity states. Unlike previous studies, we have included nonlinear corrections to the screened impurity potential, because the Thomas–Fermi approximation is incorrect for the insulator phase. It is also shown that near the phase transition the exchange interaction is essential. The obtained temperature dependencies explain several experimental measurements in gallium arsenide (GaAs) and gallium nitride (GaN).     

Studying pion effects on the chiral phase transition

We investigate the chiral phase transition at finite temperatures and zero chemical potential with Dyson-Schwinger equations. Our truncation for the quark-gluon interaction includes mesonic degrees of freedom, which allows us to study the impact of the pions on the nature of the phase transition. Within the present scheme we find a 5% change of the critical temperature due to the pion backreaction whereas the mean field character of the transition is not changed.     

TTF-TCNQ的Peierls相变研究

根据建立在电子-声子相互作用基础上的Peierls相变理论，利用形变势模型和半经验晶体轨道方法计算的能带结构数据，对一维有机导体TTF-TCNQ的Peierls相变温度进行了计算，结果表明,TTF链的相变温度低于TCNQ链的相变温度，从而说明前者的电子-声子耦合相互作用比后者要弱,TTF-TCNQ在54K的金属-绝缘体相变主要发生在TCNQ链上. 关键词： 一维有机导体 Peierls相变温度 电子-声子相互作用     

A minimal relativistic model of gravitation within standard restrictions of the Classical Theory of Fields

The minimal relativistic model of gravitation on the basis of the gauge-invariant theory of the linear scalar massless field is suggested. The principle of the multiplicative inclusion of gravitational interaction, the requirements being that the simplicity and invariance of the theory under the allowed (gauge) transformation of potential Ф → Ф′ = Ф + const as the basis of the approach, is used. A system of gauge-invariant gravitational field and matter equations is obtained and an energy-momentum tensor with a positively defined density of the field energy is constructed. The exact solutions to equations for the central static field and for fields of spherically symmetric and plane gravitational waves in the free space and in the material media are obtained.     

Effective Potential for the Reaction-Diffusion-Decay System

In previous work we have developed a general method for casting stochastic partial differential equations (SPDEs) into a functional integral formalism, and have derived the one-loop effective potential for these systems. In this paper we apply the same formalism to a specific field theory of considerable interest, the reaction-diffusion-decay system. When this field theory is subject to white noise we can calculate the one-loop effective potential (for arbitrary polynomial reaction kinetics) and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions. For specific choices of interaction terms the one-loop renormalizability can be extended to higher dimensions. We also show how to include the effects of fluctuations in the study of pattern formation away from equilibrium, and conclude that noise affects the stability of the system in a way which is calculable.     

Solving the differential Yakubovsky equations for p 3He scattering by the cluster-reduction method

The cluster-reduction method has been used to solve numerically the differential equations for the s-wave Yakubovsky components in the nppp system. Proton scattering on a ³He nucleus has been considered for energies below the three-body threshold in the singlet and triplet spin states of the system. Nucleon-nucleon interaction has been simulated by the MT I–III potential, and the Coulomb interaction between the protons has been taken into account. Effective equations that describe the relative motion of clusters have been derived. The low-energy behavior of phase shifts has been analyzed. The values of ¹ A=8.2 fm and ³ A=7.7 fm have been obtained for, respectively, the singlet and triplet scattering lengths. The calculated phase shifts agree well with experimental data.     

Stability and Chaos of Two Coupled Bose-Einstein Condensates with Three-Body Interaction

We study the dynamics of two Bose-Einstein condensates (BECs) tunnel-coupled by a double-well potential.A real three-body interaction term is considered and a two-mode approximation is used to derive two coupled equations,which describe the relative population and relative phase. By solving the equations and analyzing the stability of the system, we find the stable stationary solutions for a constant atomic scattering length. When a periodically time-varying scattering length is applied, Melnikov analysis and numerical calculation demonstrate the existence of chaotic behavior and the dependence of chaos on the three-body interaction parameters.