Exact results for the one-dimensional many-body problem with contact interaction: Including a tunable impurity
Exact results for the one-dimensional many-body problem with contact interaction: Including a tunable impurity
复制标题
具有接触相互作用的一维多体问题的精确结果：包括可调杂质
DOI：
10.1142/s0129055x07002973
复制
发表时间：
2005
影响因子：
1.8
通讯作者：
N. Crampé
中科院分区：
文献类型：
--
作者：
V. Caudrelier;N. Crampé
本文沿着Bethe坐标系研究了具有可调透射和反射杂质的N粒子接触相互作用的一维问题。结果表明，通过确定本征函数和能谱，该系统是精确可解的。后者是由我们建立的不同的边界条件下的杂质的存在下的Bethe anomalies方程的解决方案。这些杂质Bethe方程包含作为特殊情况下，众所周知的Bethe方程的系统的半线。我们通过一个和两个粒子的玩具例子来简单地研究它们。事实证明，杂质可以被调整以提升能量的简并，并且当它具有足够的吸引力时可以创建束缚态。一个位于盒子中心并破坏宇称不变性的杂质的例子表明，这种杂质可以用来非对称地限制定态。这可能在凝聚态物理学中有有趣的应用。
The one-dimensional problem of N particles with contact interaction in the presence of a tunable transmitting and reflecting impurity is investigated along the lines of the coordinate Bethe ansatz. As a result, the system is shown to be exactly solvable by determining the eigenfunctions and the energy spectrum. The latter is given by the solutions of the Bethe ansatz equations which we establish for different boundary conditions in the presence of the impurity. These impurity Bethe equations contain as special cases well-known Bethe equations for systems on the half-line. We briefly study them on their own through the toy-examples of one and two particles. It turns out that the impurity can be tuned to lift degeneracies in the energies and can create bound states when it is sufficiently attractive. The example of an impurity sitting at the center of a box and breaking parity invariance shows that such an impurity can be used to confine a stationary state asymmetrically. This could have interesting applications in condensed matter physics.