链间超交换相互作用下spin-Peierls梯子模型的基态行为

采用Lanczos数值计算方法研究了具有链间海森堡相互作用和链间Dzyaloshinskii-Moriya(DM)相互作用spin-Peierls梯子模型的基态行为.分析了链间海森堡相互作用和链间DM相互作用对系统二聚化的影响.结果发现，这两种链间作用都不利于系统的二聚化，会造成系统基态二聚化的减小，这说明随着系统维度的增大，系统的各向相互作用会限制系统的二聚化，甚至会破坏系统的二聚化相. 关键词： spin-Peierls模型 海森堡相互作用 DM相互作用 二聚化     

Calculation of the thermodynamic potentials of changes in translational, rotational, and vibrational degrees of freedom in the dimerization of aromatic molecules

The work presents a method for calculating the thermodynamic potentials (free Gibbs energy, enthalpy, and entropy) and an analysis of the contributions of changes in translational, rotational, and vibrational degrees of freedom to the energy characteristics of the dimerization of aromatic compounds. On the whole, changes in the Gibbs energy caused by these contributions were shown to exceed the experimental energies of dimerization in solution in magnitude, which was evidence of the necessity of taking them into account for the aggregation of molecules. We determined changes in the Gibbs energy and entropy of translational, rotational, and vibrational (mechanical) degrees of freedom and the enthalpy of vibrations, which can be used to analyze the energy characteristics of dimerization reactions. These dimerization energy components should be calculated separately for each compound.     

Calculation of free-free Gaunt factors for 1 keV electrons in a 1 keV normal density Ce plasma

We compare numerical results for free-free Gaunt factors in a hot dense cesium plasma, obtained in the average atom approximation either with a simple approximate analytic potential or with the finite temperature Thomas-Fermi model. We obtain results (for the spectrum of radiation from a 1 keV electron incident on a cesium ion in a 1 keV plasma) from an exact numerical calculation in partial waves of the relativistic electron Bremsstrahlung cross section treated as a single electron transition within these potentials. Comparison shows that Born approximation results in the same potentials fail by large factors, especially at the soft photon end of the spectrum.     

硅纳米晶体薄膜热膨胀性质的分子动力学研究

基于Stillinger-Weber势对硅纳米晶体薄膜的热膨胀性质进行了分子动力学模拟。研究表明,硅纳米晶体薄膜表面层原子的二聚现象引起薄膜收缩,而原子之间的非和谐势能引起薄膜膨胀;在约400K以下的低温段,由于硅纳米晶体薄膜表面层原子发生二聚的原子数目随温度的升高而明显增多,而原子间非和谐势能很小,故此时二聚主导热膨胀性质,热膨胀系数为负;在高温段（约400K以上）,由于发生二聚的原子数目随温度升高不再显著地增加并渐趋于稳定,而原子间非和谐势能逐渐显著并主导热膨胀性质,故热膨胀系数为正。     

Quantum self-consistent approach to the charge gap of the quasi-one-dimensional organic conductors

We apply an extended quantum self-consistent method, in which quantum fluctuations are taken into account, to the bosonization Hamiltonian to investigate analytically the charge gap in the quasi-one-dimensional (1D) organic conductors at quarter-filling described by the 1D Hubbard model with dimerization and alternate potential on site. It is shown that either dimerization or alternate potential gives rise to the enhancement of the charge gap. Our results are compared with those of the numerical and the other analytical theories. Our results are also consistent with the experimental data of the actual organic materials when the effect of nearest-neighbor Coulomb interaction is taken into account.     

Exact and numerical results for a dimerized coupled spin- 1/2 chain

We establish exact results for coupled spin-1/2 chains for special values of the four-spin interaction V and dimerization parameter delta. The first exact result is at delta = 1/2 and V = -2. Because we find a very small but finite gap in this dimerized chain, this can serve as a very strong test case for numerical and approximate analytical techniques. The second result is for the homogeneous chain with V = -4 and gives evidence that the system has a spontaneously dimerized ground state. Numerical diagonalization and bosonization techniques indicate that the interplay between dimerization and interaction could result in gapless phases in the regime 0相似文献   

Numerical experiment of anharmonic oscillators by using the symplectic scheme-shooting method

Symplectic scheme-shooting method (SSSM) is applied to solve the energy eigenvalues of anharmonic oscillators characterized by the potentials V(x)=λx4 and V(x)=(1/2)x2+λx2α with α=2,3,4 and doubly anharmonic oscillators characterized by the potentials V(x)=(1/2)x2+λ1x4+λ2x6, and a high order symplectic scheme tailored to the "time"-dependent Hamiltonian function is presented. The numerical results illustrate that the energy eigenvalues of anharmonic oscillators with the symplectic scheme-shooting method are in good agreement with the numerical accurate ones obtained from the non-perturbative method by using an appropriately scaled basis for the expansion of each eigenfunction; and the energy eigenvalues of doubly anharmonic oscillators with the sympolectic scheme-shooting method are in good agreement with the exact ones and are better than the results obtained from the four-term asymptotic series. Therefore, the symplectic scheme-shooting method, which is very simple and is easy to grasp, is a good numerical algorithm.     

Tail resonances of Fermi-Pasta-Ulam q-breathers and their impact on the pathway to equipartition

Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time, resonant anomalies (peaks) are observed in its weakly excited tail for long times preceding equipartition. We observe a similar resonant tail structure also for exact time-periodic Lyapunov orbits, coined q-breathers due to their exponential localization in modal space. We give a simple explanation for this structure in terms of superharmonic resonances. The resonance analysis agrees very well with numerical results and has predictive power. We extend a previously developed perturbation method, based essentially on a Poincare-Lindstedt scheme, in order to account for these resonances, and in order to treat more general model cases, including truncated Toda potentials. Our results give a qualitative and semiquantitative account for the superharmonic resonances of q-breathers and natural packets.     

Three-Body Systems with Square-Well Potentials in L = 0 States

The angular part of the Faddeev equations is solved analytically for s-states in case of two-body square-well potentials. The results are, still analytically, generalized to arbitrary short-range potentials for both small and large distances. We consider systems with three identical bosons, three non-identical particles, and two identical spin- fermions plus a third particle with arbitrary spin. The angular wave functions are in general linear combinations of trigonometric and exponential functions. The Efimov conditions are obtained at large distances. General properties and applications to short-range potentials are discussed. Gaussian potentials are used for illustrations. The results are useful for numerical calculations, where, for example, large distances can be treated analytically and matched to the numerical solutions at smaller distances. The saving in computational efforts could be substantial. Received May 20, 1996; revised January 24, 1997; accepted for publication January 27, 1997     

Dynamical energy equipartition of the Toda model with additional on-site potentials

We study the dynamical energy equipartition properties in the integrable Toda model with additional uniform or disordered on-site energies by extensive numerical simulations. The total energy is initially equidistributed among some of the lowest frequency linear modes. For the Toda model with uniform on-site potentials, the energy spectrum keeps its profile nearly unchanged in a relatively short time scale. On a much longer time scale, the energies of tail modes increase slowly with time. Energy equipartition is far away from being attached in our studied time scale. For the Toda model with disordered on-site potentials, the energy transfers continuously to the high frequency modes and eventually towards energy equipartition. We further perform a systematic study of the equipartition time teq depending on the energy density εand the nonlinear parameter α in the thermodynamic limit for the Toda model with disordered on-site potentials. We find teq∝(1/ε)~a(1/α)~b, where b ≈ 2 a. The values of a and b are increased when increasing the strengths of disordered on-site potentials or decreasing the number of initially excited modes.     

Time-dependent i-DFT exchange-correlation potentials with memory: applications to the out-of-equilibrium Anderson model

We have recently put forward a steady-state density functional theory (i-DFT) to calculate the transport coefficients of quantum junctions. Within i-DFT it is possible to obtain the steady density on and the steady current through an interacting junction using a fictitious noninteracting junction subject to an effective gate and bias potential. In this work we extend i-DFT to the time domain for the single-impurity Anderson model. By a reverse engineering procedure we extract the exchange-correlation (xc) potential and xc bias at temperatures above the Kondo temperature T_K. The derivation is based on a generalization of a recent paper by Dittmann et al. [N. Dittmann et al., Phys. Rev. Lett. 120, 157701 (2018)]. Interestingly the time-dependent (TD) i-DFT potentials depend on the system’s history only through the first time-derivative of the density. We perform numerical simulations of the early transient current and investigate the role of the history dependence. We also empirically extend the history-dependent TD i-DFT potentials to temperatures below T_K. For this purpose we use a recently proposed parametrization of the i-DFT potentials which yields highly accurate results in the steady state.     

具有对称和反对称超交换相互作用的一维spin-Peierls系统的基态行为

采用Lanczos数值计算方法研究了具有Dzyaloshinskii-Moriya（DM）相互作用和Kaplan-She khtman-Entin-Wohlman-Aharony（KSEA）相互作用的一维spin-Peierls（s-P）系统的基态 行为.计算结果发现KSEA相互作用总是不利于系统二聚化，并且它还影响DM相互作用对系统 二聚化的贡献，甚至可以抵消其作用；在某些特定条件下, KSEA和DM的共同作用可以破坏系 统的二聚化基态而转化为均匀基态. 关键词： DM相互作用 KSEA相互作用 二聚化     

Spinning solutions in general relativity with infinite central density

This paper presents general relativistic numerical simulations of uniformly rotating polytropes. Equations are developed using MSQI coordinates, but taking a logarithm of the radial coordinate. The result is relatively simple elliptical differential equations. Due to the logarithmic scale, we can resolve solutions with near-singular mass distributions near their center, while the solution domain extends many orders of magnitude larger than the radius of the distribution (to connect with flat space–time). Rotating solutions are found with very high central energy densities for a range of adiabatic exponents. Analytically, assuming the pressure is proportional to the energy density (which is true for polytropes in the limit of large energy density), we determine the small radius behavior of the metric potentials and energy density. This small radius behavior agrees well with the small radius behavior of large central density numerical results, lending confidence to our numerical approach. We compare results with rotating solutions available in the literature, which show good agreement. We study the stability of spherical solutions: instability sets in at the first maximum in mass versus central energy density; this is also consistent with results in the literature, and further lends confidence to the numerical approach.     

Remove Degeneracy in Relativistic Symmetries for Manning-Rosen Plus Quasi-Hellman Potentials by Tensor Interaction

The relativistic Dirac equation under spin and pseudo-spin symmetries is investigated for Manning-Rosen plus quasi-Hellman potentials with tensor interaction. For the first time we consider the Hulthen plus Yukawa for tensor interaction. The Formula method is used to obtain the energy eigen-values and wave functions. We also discuss about the energy eigen-values and the Dirac spinors for the Manning-Rosen plus quasi-Hellman potentials for the spin and pseudo-spin symmetry with Formula method. To show the accuracy of the present model, some numerical results are shown in both pseudo-spin and spin symmetry limits.     

Global invariants for variable-mass systems

We investigate the effect of mass loss on the invariants of single particle motion in potentials having translational or rotational symmetry. These systems are non-Hamiltonian in the physical momenta, but for non-velocity-dependent potentials can be made formally Hamiltonian by treating the velocities as canonical momenta. Applying Noether's theorem to the formal Hamiltonian then yields global invariants corresponding to its symmetries. For velocity-dependent potentials, an exact invariant is constructed from the (non-Hamiltonian) vector field. The results are applied to charged particle motion in a magnetic dipole and agree well with numerical calculations.     

Green function approximation and path integral numerical methods

We evaluate the short time Green function by a series expansion of the exponent. The resulting expression allows the computation of the energy eigenvalues and eigenvectors of a quantum system with a very high precision. As an example, we show the comparison between the numerical results and the analytical solutions for harmonic and multi-well potentials both in one and two dimensions. Received 1st March 1999 and Received in final form 20 September 1999     

Response of an ideal gas in an external potential

We construct the exact solution for the time evolution of the local mass density in an ideal gas in which an external short-ranged separable potential is switched on at time t = 0. The redistribution of matter in strong potentials causing bound states or resonances is studied in great numerical detail.     

Approximate solution of Schr?dinger equation in D dimensions for inverted generalized hyperbolic potential

The Nikiforov?CUvarov method is used to investigate the bound state solutions of Schr?dinger equation with a generalized inverted hyperbolic potential in D-space. We obtain the energy spectrum and eigenfunction of this potential for arbitrary l-state in D dimensions. We show that the potential reduces to special cases such as Rosen?CMorse, Poschl?CTeller and Scarf potentials. The energy spectra and wave functions of these special cases are also discussed. The numerical results of these potentials are presented.     

The symmetric and antisymmetric superexchange interactions in spin-Peierls system

The influences of Dzyaloshinskii Moriya （DM） interaction and Kaplan-Shekhtman-Entinwohlman-Aharony （KSEA） interaction on the dimerization of a spin-Peierls system are investigated theoretically by using the Lanczos numerical method. The ground state of the spin-Peierls system is still dimerized phase when both of the DM and the KSEA interactions have the same value with Heisenberg interaction. It is found that the KSEA interaction and uniform DM interaction are always against systemic dimerization, but the staggered DM interaction acts in favour of dimerization. Furthermore, the influences of the DM and the KSEA interactions are also studied in terms of the ground state index rate and the energy gap index rate of the dimerized Heisenberg system. The results show that the DM interaction makes the index rates larger, while the KSEA interaction makes them smaller.     

Equipartition thresholds in chains of anharmonic oscillators

We perform a detailed numerical study of the transition to equipartition in the Fermi-Pasta-Ulam quartic model and in a class of potentials of given symmetry using the normalized spectral entropy as a probe. We show that the typical time scale for the equipartition of energy among Fourier modes grows linearly with system size: this is the time scale associated with the smallest frequency present in the system. We obtain two different scaling behaviors, either with energy or with energy density, depending on the scaling of the initial condition with system size. These different scaling behaviors can be understood by a simple argument, based on the Chirikov overlap criterion. Some aspects of the universality of this result are investigated: symmetric potentials show a similar transition, regulated by the same time scale.