论文标题
试验状态的BOSE气体：奇异尺度和不可积分的电势
Trial states for Bose gases: singular scalings and non-integrable potentials
论文作者
论文摘要
我们回顾了两个结果，其中讨论了玻色症哈密顿素的试验状态。最近通过证明与在较不奇异的缩放中找到更规律的系统的试验状态的问题，解决了在GROSS-PITAEVSKII制度中具有硬核潜力的系统试验状态的问题，该问题是$ n^{-1+3β} V（n^β\ cdot）$ n^$ n^β\ cdot $ bebebebebebeb的$ bebebebebebebebebeb。对于这两种模型，我们介绍了与基态能量上限的主要结果，并讨论了证明的关键步骤。
We review two results in which trial states for bosonic Hamiltonians were discussed. The problem of finding a trial state for a system with a hard-core potential in the Gross-Pitaevskii regime was recently solved by proving a link with the problem of finding a trial state for a system with a more regular potential in a less singular scaling, one of the type $N^{-1+3β}V(N^β\cdot)$ with $β\in(0,1)$. For both of these models we present the main result for the upper bound to the ground state energy, and discuss the key steps in the proof.
