从硬核玻色子到自由费米子
From hardcore Bosons to free Fermions with Painlev{é} V
摘要：
本文计算了一维量子粒子通过$δ$ -势与费米海相互作用的零温格林函数、密度-密度关联和期望值。Bethe-Anglands可解模型的本征函数可以表示为行列式。这使我们能够获得额外粒子的格林函数的紧凑表达式。在硬核极限中，所得的表达式可以用Painlev超越进一步分析。结果表明，随着额外粒子动量的增加，其格林函数经历了从硬核玻色子的格林函数到自由费米子的格林函数的转变。
英文摘要：
We calculate zero temperature Green's function, the density--density correlation and expectation values of a one--dimensional quantum particle which interacts with a Fermi--sea via a $δ$--potential. The eigenfunctions of the Bethe-Ansatz solvable model can be expressed as a determinant. This allows us to obtain a compact expression for the Green's function of the extra particle. In the hardcore limit the resulting expression can be analysed further using Painlev{é} V transcendents. It is found that depending on the extra particles momentum its Green's function undergoes a transition of that for hardcore Bosons to that of free Fermions.
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