论文标题
2D费米极化子的基态耦合极限
Weak coupling limit for the ground state energy of the 2D Fermi polaron
论文作者
论文摘要
我们通过两体相互作用分析了二维盒中n个费物的基态能量。我们允许质量比在杂质质量和费米昂的质量之间进行m> 1.225，并考虑任意较大的盒子尺寸，同时保持费米能的固定。我们的主要结果表明，弱耦合极限的基态能由极性能量给出。极性能量是基于试验状态在颗粒孔扩展中的一阶的基础上的能量估计，这是雪佛兰在物理文献中提出的。为了证明，我们采用了Griesemer和Linden最近获得的Birman-Schwinger原则。一种主要的新成分是北极能量的合适定位。
We analyze the ground state energy for N fermions in a two-dimensional box interacting with an impurity particle via two-body point interactions. We allow for mass ratios M > 1.225 between the impurity mass and the mass of a fermion and consider arbitrarily large box sizes while keeping the Fermi energy fixed. Our main result shows that the ground state energy in the limit of weak coupling is given by the polaron energy. The polaron energy is an energy estimate based on trial states up to first order in particle-hole expansion, which was proposed by Chevy in the physics literature. For the proof we apply a Birman-Schwinger principle that was recently obtained by Griesemer and Linden. One main new ingredient is a suitable localization of the polaron energy.
