The stability of Bose--Einstein condensates in a two-dimensional shallow trap

The stability of Bose--Einstein condensates (BECs) loaded into a two-dimensional shallow harmonic potential well is studied. By using the variational method, the ground state properties for interacting BECs in the shallow trap are discussed. It is shown that the possible stable bound state can exist. The depth of the shallow well plays an important role in stabilizing the BECs. The stability of BECs in the shallow trap with the periodic modulating of atom interaction by using the Feshbach resonance is also discussed. The results show that the collapse and diffusion of BECs in a shallow trap can be controlled by the temporal modulation of the scattering length.     

锶热原子束二维准直的动力学过程的蒙特卡罗模拟及实验研究

在考虑随机因素的情况下, 应用蒙特卡罗方法在理论上详细研究了锶原子束二维激光准直的动力学过程. 综合考虑原子横向发散角、初始原子位置、纵向速度分布、同位素等因素, 获得了激光二维准直后的原子横向空间分布的模拟结果以及随准直光失谐、光功率等参量因素的变化. 通过与实验数据比较, 理论值和实验值很好相符, 显示蒙特卡罗方法可以精确地描述锶原子束二维准直的动力学过程. 为原子束激光二维准直的精确控制, 高精度原子钟系统的优化, 提供了一种理论分析方法. 关键词： 二维准直 蒙特卡罗方法 横向空间分布     

Monte Carlo molecular dynamics simulations for two-dimensional magnets

A combined Monte Carlo molecular dynamics simulation technique is used to study thedynamic structure factor on a square lattice for isotropic Heisenberg and planar classical ferromagnetic spin Hamiltonians.     

Variational Monte Carlo study of the nematic state in iron-pnictide superconductors with a five-orbital model

We perform a variational Monte Carlo study of the nematic state in iron-pnictide superconductors within a realistic five-orbital model.Our numerical results show that the nematic state,formed by introducing an anisotropic hopping order into the projected wave function,is not stable unless the off-site Coulomb interaction V exceeds a critical value.This demonstrates that V plays a key role in forming the nematic state in iron-pnictide superconductors.In the nematic state,the orbital order and the anisotropic spin correlations are consistent with the experimental observations.We argue that the experimentally observed anisotropic magnetic couplings and structural transition are associated with the nematic state and can be understood in a unified framework.     

Effects of localized impurity on a dark soliton in a Bose--Einstein condensate with an external magnetic trap

The dynamics of a dark soliton has been investigated in a Bose--Einstein condensate with an external magnetic trap, and the effects of localized impurity on the dynamics are discussed by the variational approach based on the renormalized integrals of motion. The reciprocal movement of the dark soliton is discussed by performing a standard linear analysis, and it is found that the effects of the localized impurity depend strictly on the positive or negative value of the impurity strength corresponding to the repulsive or attractive impurity. The numerical results confirm the theoretical analysis, and show that the effects also depend on the effective nonlinear coefficient and the harmonic frequency.     

求解中子动力学方程的加权蒙特卡罗方法

为了实现基于蒙特卡罗方法的中子动力学计算,在传统的直接蒙特卡罗动力学方法的基础上,提出了一种加权蒙特卡罗动力学方法。该方法通过引入粒子权重的概念,隐式考虑中子俘获反应和裂变反应过程中中子数目的变化,避免了模拟粒子的数目随时间的变化,降低了统计偏差,消除了程序计算过程中粒子的存库操作,提高了计算精度。基于单能点堆模型,开发了中子动力学计算程序NECP-Dandi,进行了大量数值验证与分析,包括无缓发中子、单组缓发中子、六组缓发中子、正阶跃反应性引入、负阶跃反应性引入、正脉冲反应性、负脉冲反应性和正线性反应性引入等情况。数值结果表明,相比于直接蒙特卡罗动力学方法,加权蒙特卡罗动力学方法在计算结果的精度和计算效率上有较为明显的改进,程序结构更为简洁。     

Landau damping of collective modes in a harmonically trapped Bose--Einstein condensate

This paper proposes a method for calculating the Landau damping of a low-energy collective mode in a harmonically trapped Bose--Einstein condensate. Based on the divergence-free analytical solutions for ground-state wavefunction of the condensate and eigenvalues and eigenfunctions for thermally excited quasiparticles, obtained beyond Thomas--Fermi approximation, this paper calculates the coupling matrix elements describing the interaction between the collective mode and the quasiparticles. With these analytical results this paper evaluates the Landau damping rate of a monopole mode in a spherical trap and discusses its dependence on temperature, particle number and trapping frequency of the system.     

蒙特卡罗模拟四极阱中原子的参变激发

在中性原子的磁囚禁实验中,磁阱线圈的电流噪声会激发磁阱中的原子运动,势必对原子团的温度和寿命产生不可忽视的影响。对于非简谐阱,这种激发具有能量选择特性,它又取决于电流噪声的频谱分布。选择了实验中常用的四极阱为研究对象,用直接模拟蒙特卡罗方法来模拟四极阱中原子运动的参变激发现象,得到了原子温度与原子数损失随激发频率的变化关系,并进一步计算了两个共振峰处原子温度随调制时间和调制深度的变化曲线。此外,还研究了弹性碰撞速率对参变激发过程中原子温度上升的影响。这些结果对四极阱参变激发的实验有较好的参考价值。     

Transition Matrix Monte Carlo Method

We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct multi-canonical and equal-hit algorithms. We discuss the performance of the methods. The results are compared with single histogram method, multi-canonical method, and other methods. In many aspects, the present method is an improvement over the previous methods.     

The Convergence of Markov Chain Monte Carlo Methods: From the Metropolis Method to Hamiltonian Monte Carlo

From its inception in the 1950s to the modern frontiers of applied statistics, Markov chain Monte Carlo has been one of the most ubiquitous and successful methods in statistical computing. The development of the method in that time has been fueled by not only increasingly difficult problems but also novel techniques adopted from physics. Here, the history of Markov chain Monte Carlo is reviewed from its inception with the Metropolis method to the contemporary state‐of‐the‐art in Hamiltonian Monte Carlo, focusing on the evolving interplay between the statistical and physical perspectives of the method.     

蒙卡燃耗中的氙振荡现象分析及计算研究

根据氙振荡产生的机理,按照燃耗步长来划分：在短步长条件下会产生物理氙振荡,在长步长条件下会产生数值氙振荡。研究发现,当燃耗步长增大到19 h,物理氙振荡的振幅最小,随着燃耗步长继续增大,表现为数值氙振荡,当燃耗步长27 d,数值氙振荡振幅最小。采用平衡氙方法强制使中子通量与氙浓度平衡,在堆芯物理计算程序(RMC)的输运模块中运用平衡氙方法对碘氙的浓度进行不断的迭代更新,在保证收敛的情况下抑制了氙振荡现象的发生。     

大粒子数二维硬核玻色子系统的量子蒙特卡罗模拟

采用随机级数展开的量子蒙特卡罗方法研究二维硬核的玻色-赫伯德模型的热力学性质. 首先通过算符变换将模型映射成为二维反铁磁准海森伯模型. 变换后的模型比通常的海森伯模型多一项, 该项正比于系统的格点总数 N, 对于大粒子数的系统, 该项使模拟耗时指数增加, 所以难以计算大粒子数系统.采用非局域操作循环更新后, 这个困难可以得到很好的解决, 可使粒子数总数增大到几千个.研究结果表明, 粒子数密度在0-0.5范围内增大时, 能量呈递减趋势, 并趋于某一定值, 随着正方晶格系统尺度增大, 能量也随之增大;正方晶格系统尺度一定时, 能量和磁化强度随着温度的升高而增大, 化学势的变化对能量和磁化强度没有影响, 能量随着正方晶格系统尺度增大而增大, 磁化强度却随之减小;正方晶格系统尺度一定时, 化学势的增大对比热没有影响, 随着温度的升高比热出现先增大后减小的趋势, 最后趋于某个值, 达到平衡, 而正方晶格系统尺度越大, 比热曲线增大部分的趋势越大, 减小部分的趋势也更明显, 参照朗道超流理论, 本文模拟的能量和比热曲线趋势与朗道二流体模型下He II的理论研究一致; 不同正方晶格系统尺度的影响不大, 均匀磁化率倒数在0-0.5(J/k_B)的低温范围内有很小的波动, J为耦合能, k_B为玻尔兹曼常数, 温度在0.5-2 (J/k_B)的范围内, 均匀磁化率的倒数随着温度的升高而增大, 且曲线的趋势显示了一种类似近藤行为.     

Monte Carlo Hamiltonian: Linear Potentials

We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.     

Error Estimation in the Histogram Monte Carlo Method

We examine the sources of error in the histogram reweighting method for Monte Carlo data analysis. We demonstrate that, in addition to the standard statistical error which has been studied elsewhere, there are two other sources of error, one arising through correlations in the reweighted samples, and one arising from the finite range of energies sampled by a simulation of finite length. We demonstrate that while the former correction is usually negligible by comparison with statistical fluctuations, the latter may not be, and give criteria for judging the range of validity of histogram extrapolations based on the size of this latter correction.     

Monte Carlo Hamiltonian:Inverse Potential

The Monte Carlo Hamiltonian method developed recently allows to investigate the ground state and low-lying excited states of a quantum system, using Monte Carlo (MC) algorithm with importance sampling. However, conventional MC algorithm has some difficulties when applied to inverse potentials. We propose to use effective potential and extrapolation method to solve the problem. We present examples from the hydrogen system.     

热辐射输运问题的高效蒙特卡罗模拟方法

惯性约束聚变研究中,热辐射光子在介质中的输运以及热辐射光子与介质的相互作用是重要研究课题,蒙特卡罗方法是该类问题的重要研究手段之一.隐式蒙特卡罗方法虽然能正确地模拟热辐射在介质中的输运过程,但当模拟重介质(材料的吸收系数大)问题时,该方法花费的计算时间将变得很长,导致模拟效率很低.本文以离散扩散蒙特卡罗方法为基础,开发了"离散扩散蒙特卡罗方法辐射输运模拟程序",可以较好地解决重介质区的计算效率问题,但是离散扩散蒙卡罗方法在模拟轻介质区时精度不够高.辐射输运问题中通常既有轻介质也有重介质,为了能同时解决蒙特卡罗方法模拟的效率和精度问题,本文研究了离散扩散蒙特卡罗方法与隐式蒙特卡罗方法相结合的模拟方法,并提出了新的扩散区与输运区界面处理方法,研制了混合蒙特卡罗方法的辐射输运模拟程序.典型辐射输运问题模拟显示:在模拟重介质问题时,该程序能大幅缩短模拟时间,且能取得与隐式蒙特卡罗方法一致的结果;在模拟轻重介质均存在的问题时,与隐式蒙特卡罗方法相比,混合蒙特卡罗方法的模拟精度与其相当且计算效率同样能够得到显著提升.     

Fully parallel code for Monte Carlo simulation

We present a fully parallel version of Monte Carlo simulation of the Ising model using the Metropolis algorithm. In the 3-dimensional version the performance can be enhanced by a factor >20 in 16-bit word processors relative to other multispin codes. This factor could be further increased if implemented in 64-bit word computers.     

BEAVRS基准模型热零功率状态的JMCT分析

使用JMCT (J Monte Carlo Transport Code)对来自MIT的全堆芯pin-by-pin精细建模的国际基准模型BEAVRS的热零功率(HZP)状态进行了模拟计算, 并与测试数据进行了对比和分析. 比较的物理量包括临界本征值、控制棒价值、反应性温度系数、轴向积分的全堆探测器测量值和不同位置四个组件轴向相对功率密度分布. HZP状态下不同控制棒位置插入和硼浓度的临界本征值计算, JMCT结果与理论值1.000 的误差小于0.2%, 控制棒价值计算结果与测量值符合. JMCT对轴向积分的探测器径向相对功率分布和四个组件的轴向归一化的探测器的计算结果与测量值进行了比较和分析, 计算结果与测量值一致, 同时清晰地展示了模型增加格架后, 轴向功率曲线在相应位置出现下凹的现象. 此外, JMCT给出了轴向积分的组件径向相对功率密度分布和轴向相对功率最大处(Z轴位置)的pin径向相对功率密度分布, 并与国际知名程序MC21结果进行了对比, 两个图像都符合得非常好. 随着计算机与并行计算的高速发展, 蒙特卡罗程序开始从传统的反应堆校验工具向反应堆设计工具转变.     

蒙特卡洛模拟漫辐射时两种确定表面发射方向方法的比较

介绍一种有效的确定能束发射方向的方法——切球法.分析传统方法和切球法确定发射方向的原理及实施过程,说明切球法更为方便.采用2种方法对一简单的几何模型的角系数进行蒙特卡洛计算,所得结果与文献中积分结果进行比较,说明了切球法的可行性,计算精度能满足工程要求.同时对2种方法的计算耗时进行比较,切球法可以节省计算时间.将切球法应用到复杂系统中其优越性将会得到更加充分体现.     

用蒙特卡罗方法研究生物组织中的光分布

本文利用蒙特卡罗方法研究准直光束通过生物组织时其内部光吸收剂量分布的特点．计算模型设定的条件为：组织与其边界折射率不同、组织为纵向有一定宽度的层状结构．理论的计算模拟结果已同组织模拟体的实验结果作了比较，两者能较好的吻合．