标题： 经典相空间中的量子统计力学。 III. 相互作用的Lennard-Jones粒子的平均场近似基准测试 显示英文标题

标题： Quantum Statistical Mechanics in Classical Phase Space. III. Mean Field Approximation Benchmarked for Interacting Lennard-Jones Particles

摘要： 用于处理量子系统的经典相空间蒙特卡洛计算机模拟算法被提出。 位置和动量的非对易性通过平均场方法和瞬时有效简谐振子来考虑。 在二聚体和双二聚体层次上包含了波函数对称化。 定量测试是针对Hernando和Vaníček（2013）给出的无自旋氖-正氢体系的基准进行的，该体系被建模为一维谐波势中相互作用的Lennard-Jones粒子。 结果显示，平均场方法在高到中等温度$\beta \hbar \omega_\mathrm{LJ} < 7$和中等密度下具有定量准确性，$\rho \sigma \approx 1$。 氦的结果表明，在所研究的最低温度下，玻色子的平均能量比费米子低约4%。 认为平均场算法在三维中的表现将优于一维，并且其随着系统尺寸的增加将呈次线性增长。 显示英文摘要

摘要： A Monte Carlo computer simulation algorithm in classical phase space is given for the treatment of quantum systems. The non-commutativity of position and momentum is accounted for by a mean field approach and instantaneous effective harmonic oscillators. Wave function symmetrization is included at the dimer and double dimer level. Quantitative tests are performed against benchmarks given by Hernando and Van\'i\v{c}ek (2013) for spinless neon--parahydrogen, modeled as interacting Lennard-Jones particles in a one dimensional harmonic trap. The mean field approach is shown to be quantitatively accurate for high to moderate temperatures $\beta \hbar \omega_\mathrm{LJ} < 7$, and moderate densities, $\rho \sigma \approx 1$. Results for helium show that at the lowest temperature studied, the average energy is about 4\% lower for bosons than for fermions. It is argued that the mean field algorithm will perform better in three dimensions than in one, and that it will scale sub-linearly with system size.