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Chinese Physics Letters

Ground-State Properties of Charged Bosons Confined in a One-Dimensional Harmonic Double-Well Trap： Diffusion Monte Carlo Calculations

金晶, T. J. Yi

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

散开蒙特卡罗方法被使用学习控告的波色子的 groud-statepropertied 在在在一个泛音双井陷井限制的尺寸上。粒子冷淡地交往一个 Coulombic 1/r 潜力。数字结果证明井 seperation hassignifican 在系统的地面状态 propertied 上影响。当系统的相互作用是弱的时，地面状态精力与增加的井 seperation 减少并且有最小左值。如果井 seperation 增加不断地，地面状态精力增加和途径到一个常数逐渐地。这效果将是在强壮的交往系统的骆驼毛的织物桌子。另外，由计算系统的密度为与各种各样的 wellseperations 在相互作用力量不同，当井 seperation 在系统的中心大时，我们发现密度反常地增加。

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散开蒙特卡罗方法被使用学习控告的波色子的 groud-statepropertied 在在在一个泛音双井陷井限制的尺寸上。粒子冷淡地交往一个 Coulombic 1/r 潜力。数字结果证明井 seperation hassignifican 在系统的地面状态 propertied 上影响。当系统的相互作用是弱的时，地面状态精力与增加的井 seperation 减少并且有最小左值。如果井 seperation 增加不断地，地面状态精力增加和途径到一个常数逐渐地。这效果将是在强壮的交往系统的骆驼毛的织物桌子。另外，由计算系统的密度为与各种各样的 wellseperations 在相互作用力量不同，当井 seperation 在系统的中心大时，我们发现密度反常地增加。
为在一个泛音潜力套住很好的 Bose 爱因斯坦冷凝物，我们从解决时间依赖者的现在的数字结果非线性的 Schroedinger 方程基于的在 Crank-Nicolson 方法。与这个方法，我们能由发展试用发现扎根的州的波浪功能和精力在真实、想象的时间空格的起始的波浪功能分别地。在实时空间，结果与一致[Phys。加快。一 51 (1995 ) 4704 ] ，但是试用波浪功能在一个很小的范围被限制。在想象的时间空间，相反，试用波浪函数能广泛地被选择，而且，结果是稳定的。
The diffusion Monte Carlo method is applied to study the ground-state properties of charged bosons in one dimension confined in a harmonic double-well trap. The particles interact repulsively through a Coulombic 1/ r potential. Numerical results show that the well separation has significant influence on the ground-state properties of the system. When the interaction of the system is weak, ground-state energy decreases with the increasing well separation and has a minimal value. If the well separation increases continually, the ground-state energy increases and approaches to a constant gradually. This effect will be abatable in the strong interacting system. In addition, by calculating the density of the systems for different interaction strengths with various well separations, we find that the density increases abnormally when the well separation is large at the centre of the system.
We study the ground state properties of a quasi-one-dimensional electron gas interacting via an effective potential with a harmonic transversal confinement and long-range Coulomb tail. The exact correlation energy has been calculated for a wide range of electron densities by using the lattice regularized diffusion Monte Carlo method, which is a recent development of the standard projection Monte Carlo technique. In this case it is particularly useful as it allows one to sample the exact ground state of the system, even in the low-density regime when the exchange between electrons is extremely small. For different values of the width parameter bbb $(0.1\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*}\ensuremath{\leqslant}b\ensuremath{\leqslant}4\phantom{\rule{0.3em}{0ex}}{a}_{0}^{*})$, we give a simple parametrization of the correlation energy, which provides an accurate local density energy functional for quasi-one-dimensional systems. Moreover, we show that static correlations are in qualitative agreement with those obtained for the Luttinger liquid model with long-range interactions.
The ground-state properties of a single-component one-dimensional Coulomb gas are investigated. We use Bose-Fermi mapping for the ground-state wave function which permits solution of the Fermi sign problem in the following respects: (i) the nodal surface is known, permitting exact calculations; and (ii) evaluation of determinants is avoided, reducing the numerical complexity to that of a bosonic system and, thus, allowing simulation of a large number of fermions. Due to the mapping, the energy and local properties in one-dimensional Coulomb systems are exactly the same for Bose-Einstein and Fermi-Dirac statistics. The exact ground-state energy is calculated in homogeneous and trapped geometries using the diffusion Monte Carlo method. We show that in the low-density Wigner crystal limit an elementary low-lying excitation is a plasmon, which is to be contrasted with the high-density ideal Fermi gas/Tonks-Girardeau limit, where low-lying excitations are phonons. Exact density profiles are compared to the ones calculated within the local density approximation, which predicts a change from a semicircular to an inverted parabolic shape of the density profile as the value of the charge is increased.