超冷准一维硬核玻色子气体中杂质粒子的运动
Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons
摘要：
在杂质-玻色子质量比和耦合常数的所有取值下，得到了一维多个不可穿透点玻色子和一个运动杂质粒子的零程排斥相互作用系统的低本征态.运动的实体是一个由杂质包裹着的类极化子的复合体。作为一维玻色-费米混合问题的Fermi-Bose（FB）映射处理的一个特例，首先精确求解了具有点硬核形式的杂质-玻色相互作用和杂质-玻色质量比$m_i/m$为1的特殊情况.然后，利用玻色子的二次量子化和FB映射的二次量子化形式，通过Lee-Low-Pines正则变换消除杂质自由度，给出了更一般的处理方法。这产生了任意$m_i/m$和杂质玻色子相互作用强度的精确解。
英文摘要：
The low-lying eigenstates of a one-dimensional (1D) system of many impenetrable point bosons and one moving impurity particle with repulsive zero-range impurity-boson interaction are found for all values of the impurity-boson mass ratio and coupling constant. The moving entity is a polaron-like composite object consisting of the impurity clothed by a co-moving gray soliton. The special case with impurity-boson interaction of point hard-core form and impurity-boson mass ratio $m_i/m$ unity is first solved exactly as a special case of a previous Fermi-Bose (FB) mapping treatment of soluble 1D Bose-Fermi mixture problems. Then a more general treatment is given using second quantization for the bosons and the second-quantized form of the FB mapping, eliminating the impurity degrees of freedom by a Lee-Low-Pines canonical transformation. This yields the exact solution for arbitrary $m_i/m$ and impurity-boson interaction strength.
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