球面上对角配对库仑密度矩阵：数值研究
Diagonal Pair Coulomb Density Matrix on a Sphere: a numerical study
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- Università di Trieste（的里雅斯特大学）
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中文总结 AI 辅助
本研究通过数值计算球面上配对库仑密度矩阵的幂次，揭示量子统计物理在弯曲表面上无需人为正则化即可处理粒子接触，与经典情形根本不同。
中文摘要 AI 辅助
我们在球面上对配对库仑密度矩阵的原始近似的$n$次幂进行对角列表，最高至$n=5$，并讨论随着$n$增大其在粒子接触时的行为。我们的结果表明，即使在弯曲表面上，量子统计物理也从根本上不同于其经典对应物。在后者中，需要人为引入对发散吸引库仑势的正则化以防止粒子接触，例如使用硬核，而在前者中则无此必要。
英文摘要
We tabulate, on the diagonal, the $n$th power of the primitive approximation for the pair Coulomb density matrix on a sphere, with up to $n=5$, and we discuss its behavior at particles contact as $n$ grows. Our results show that even on a curved surface quantum statistical physics is fundamentally different from its classical counterpart. If in the latter one needs to artificially introduce a regularization of the divergent attractive Coulomb potential preventing particles contact, for example with a hard core, in the former this is not necessary.
