We discuss the scaling of the interaction energy with particle numbers for a harmonically trapped two-species mixture at thermal equilibrium experiencing interactions of arbitrary strength and range. In the limit of long-range interactions and weak coupling, we recover known results for the integrable Caldeira-Leggett model in the classical limit. In the case of short-range interactions and for a balanced mixture, numerical simulations show scaling laws with exponents that depend on the interaction strength, its attractive or repulsive nature, and the dimensionality of the system. Simple analytic considerations based on equilibrium statistical mechanics and small interspecies coupling quantitatively recover the numerical results. The dependence of the scaling on interaction strength helps to identify a threshold between two distinct regimes. Our thermalization model covers both local and extended interactions allowing for interpolation between different systems such as fully ionized gases and neutral atoms, as well as parameters describing integrable and chaotic dynamics.
State diagrams for harmonically trapped bosons in optical lattices
利用量子蒙特卡罗模拟方法，得到了一维和二维强关联格点玻色子在简谐约束势作用下的零温态图。由于谐波陷阱产生的超流和莫特绝缘域的共存，我们使用局部量，如量子波动的密度和局部可压缩性，以确定存在于不均匀的密度分布的相位。我们强调使用的“特征密度”，以产生一个状态图，是相关的实验光晶格系统，无论玻色子或陷阱曲率的数量和有效性的局域密度近似。结果表明，陷阱中出现Mott绝缘畴的临界U/t值与系统中的填充有关，一般大于均匀系统中的U/t值。Spielman等人最近的实验结果[Phys. Rev. Lett. 100，120402（2008）]进行了分析，在我们的二维状态图的上下文中，并显示出表现出与模拟良好一致的临界点的值。我们还研究了有限的，但低（T<t/2），温度的影响。我们发现，在两个维度上，他们对我们的零温度结果的影响很小，而他们的效果是更明显的一维。
The distribution of the moment of inertia for harmonically trapped noninteracting Bosons at finite temperature: large deviations
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础科学研究所国际理论科学中心）；LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay（巴黎南大学萨克雷大学法国国家科学研究中心理论与物质物理实验室）；Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589（索邦大学法国国家科学研究中心高能理论与物理实验室）
