二维位形相互作用方法中接触相互作用的重整化
On the renormalization of contact interactions for the configuration-interaction method in two dimensions
摘要：
计算量子力学少体系统精确本征态的组态相互作用（CI）方法在应用于通过接触力相互作用的粒子时存在问题。在大于1的维度上，由于狄拉克δ势的病理学，这种方法失败了，使得不可能通过逐渐增加希尔伯特空间的大小来达到收敛。然而，这个问题可以通过在截断希尔伯特空间中对角化时重新归一化接触势的强度以相当简单的方式解决。因此，依赖于CI结果的比较，两体基态能量通过薛定谔方程的正则化接触相互作用的精确解获得。我们在这里讨论一个方案，提供截断独立的少体物理观测。将该方法应用于受二维谐振子约束的超冷原子少体系统。
英文摘要：
The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach fails due to the pathology of the Dirac delta-potential, making it impossible to reach convergence by gradually increasing the size of the Hilbert space. However, this problem may be cured in a rather simple manner by renormalizing the strength of the contact potential when diagonalizing in a truncated Hilbert space. One hereby relies on the comparison of the CI results to the two-body ground-state energy obtained by the exact solution of the Schroedinger equation for a regularized contact interaction. We here discuss a scheme that provides cutoff-independent few-body physical observables. The method is applied to a few-body system of ultracold atoms confined by a two-dimensional harmonic oscillator.
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