Constrained Extrapolation Problem and Order‐Dependent Mappings

The problem of extrapolating the perturbation series for dilute Fermi gas in three dimensions to unitary limit infinite scattering length and into BEC region is considered, using available strong-coupling information constrain extrapolation problem. In this constrained (CEP), goal find classes approximants that give well-converged results already low perturbative truncation orders. First, it shown standard Padé Borel methods are too restrictive satisfactory CEP. A generalization given by so-called maximum-entropy (MaxEnt) method. However, MaxEnt requires extensive elaborations be applicable is, thus, not practical CEP case. Instead, order-dependent-mapping (ODME) as a simple, practical, general method proposed. It found ODME ground-state energy robust with respect changes mapping choice agree from quantum Monte Carlo simulations within uncertainties.