论文标题
限制外推问题和订单依赖性映射
Constrained extrapolation problem and order-dependent mappings
论文作者
论文摘要
我们考虑使用可用的强耦合信息来限制外推问题的稀释式费米气体的扰动序列，以将稀释性费米气体的扰动序列推出到无限散射长度的单位限制，并进入BEC区域。在这个受约束的外推问题（CEP）中，目标是找到近似值的类别，这些类别为低扰动截短顺序提供了良好的融合结果。首先，我们表明标准的PADé和Borel方法过于限制，无法为此CEP带来令人满意的结果。 Borel外推的概括是通过所谓的最大熵外推法（Maxent）给出的。但是，我们表明，Maxent需要广泛的详细说明，以适用于稀释的费米气体，因此在这种情况下对CEP不实用。取而代之的是，我们将依赖订单的映射外推（ODME）作为CEP的简单，实用且一般的方法。我们发现，稀费米斯气体的基态能量的ODME近似因素在映射选择的变化方面具有鲁棒性，并且与不确定性内量子蒙特卡洛模拟的结果一致。
We consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to constrain the extrapolation problem. In this constrained extrapolation problem (CEP) the goal is to find classes of approximants that give well converged results already for low perturbative truncation orders. First, we show that standard Padé and Borel methods are too restrictive to give satisfactory results for this CEP. A generalization of Borel extrapolation is given by the so-called Maximum Entropy extrapolation method (MaxEnt). However, we show that MaxEnt requires extensive elaborations to be applicable to the dilute Fermi gas and is thus not practical for the CEP in this case. Instead, we propose order-dependent-mapping extrapolation (ODME) as a simple, practical, and general method for the CEP. We find that the ODME approximants for the ground-state energy of the dilute Fermi gas are robust with respect to changes of the mapping choice and agree with results from quantum Monte Carlo simulations within uncertainties.
