发表机构
University of Haifa（海法大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对三维双阱哈密顿量，在激发能级上构造满足level-3量子bootstrap所有约束但对应非负多项式取负值的线性泛函，证明该松弛存在无量子态实现的内点，揭示矩矩阵高层块不携带能级信息。
AI 中文摘要
对于耦合的三维双阱哈密顿量 $H=\tfrac12|p|^2+2\sum_i(q_i^2-1)^2-\sum_{i<j}q_i^2q_j^2$，我们在第一激发能级（以及基态）上展示了一个关于次数 $\le 6$ 的多项式的线性泛函，该泛函满足标准level-3本征态bootstrap的所有约束，具有严格正定的矩矩阵，然而却给一个非负多项式赋予负值。因此，它是level-3松弛的一个内点，但没有任何量子态能实现它。这一构造反映了一个在每个能级都成立的事实：本征态的行从未达到最高次数的动量矩。在level-3，由于存在严格可行点，这意味着矩矩阵的相应块不携带关于哪些能量允许一个本征态的信息。每个代数成分都是精确的有理数证书，唯一的数值成分（本征函数的谱包络）在严格的区间算术中执行。
英文摘要
For the coupled three-dimensional double well $H=\tfrac12|p|^2+2\sum_i(q_i^2-1)^2-\sum_{i<j}q_i^2q_j^2$ we exhibit, at the first excited energy level (and also at the ground state), a linear functional on polynomials of degree $\le 6$ that satisfies every constraint of the standard level-3 eigenstate bootstrap, has a \emph{strictly} positive definite moment matrix, and nevertheless assigns a negative value to a nonnegative polynomial. It is therefore an interior point of the level-3 relaxation that is realized by no quantum state. The construction reflects a fact that holds at every level: the eigenstate rows never reach the top-degree momentum moments. At level 3, where strictly feasible points exist, this means that the corresponding block of the moment matrix carries no information about which energies admit one. Every algebraic ingredient is an exact rational certificate, and the only numerical ingredients (spectral enclosures of an eigenfunction) are carried out in rigorous ball arithmetic.
Comments14 pages. Code and certificates included as ancillary files. Updated reference to companion paper arXiv:2610.07775; results unchanged
