论文标题
正规化的零范围哈密顿量，用于具有杂质的bose气体
Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity
论文作者
论文摘要
我们研究了与杂质相互作用的N相同玻色子系统的哈密顿量，即通过零距离的尺寸三个方面相互作用，即不同的粒子。众所周知，按照标准方法，人们获得了ter-martirosyan skornyakov hamiltonian，该方法是从下面无限的。为了避免这种不稳定问题，我们引入了三体力，该力在短距离内作用。这种力的效果是将两个粒子之间的零范围相互作用的强度（即杂质和玻色子）降低，当另一个玻色子接近前两个粒子的共同位置时。我们表明，如果三体力的强度足够大，则用这种正则相互作用定义的哈密顿量是自我伴侣的，并且从下方界定。证明的方法基于对相应二次形式的仔细分析。
We study the Hamiltonian for a system of N identical bosons interacting with an impurity, i.e., a different particle, via zero-range forces in dimension three. It is well known that, following the standard approach, one obtains the Ter-Martirosyan Skornyakov Hamiltonian which is unbounded from below. In order to avoid such instability problem, we introduce a three-body force acting at short distances. The effect of this force is to reduce to zero the strength of the zero-range interaction between two particles, i.e., the impurity and a boson, when another boson approaches the common position of the first two particles. We show that the Hamiltonian defined with such regularized interaction is self-adjoint and bounded from below if the strength of the three-body force is sufficiently large. The method of the proof is based on a careful analysis of the corresponding quadratic form.
