约束外推问题与序依赖映射
Constrained extrapolation problem and order-dependent mappings
摘要：
考虑了将三维稀费米气体的微扰级数外推到无限散射长度的幺正极限和BEC区域的问题，利用现有的强耦合信息来约束外推问题.在这个受约束的外推问题（CEP）的目标是找到类的近似，给出良好的收敛结果已经为低扰动截断订单。首先，我们表明，标准的Padé和Borel方法是过于严格，给这个CEP令人满意的结果。最大熵外推法（MaxEnt）是Borel外推法的一种推广。然而，我们表明，MaxEnt需要广泛的阐述是适用于稀释的费米气体，因此在这种情况下是不实际的CEP。相反，我们提出了顺序依赖映射外推（ODME）作为一个简单的，实用的，和一般的CEP方法。我们发现，ODME近似的基态能量的稀释费米气体的映射选择的变化是强大的，并同意从量子蒙特卡罗模拟的结果在不确定性。
英文摘要：
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.
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