发表机构
Jilin University of Finance and Economics; Capital Normal University; Nankai University（吉林财经大学; 首都师范大学; 南开大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在三维Gross-Pitaevskii体系中传播量子涨落的第三谱矩，建立高阶矩的一致界，并确定激发能测度，证明接触严格为正，给出近似误差界。
AI 中文摘要
我们研究了三维Gross-Pitaevskii体系中量子涨落的高阶矩和微观关联能。对于光滑、紧支撑、非负的径向相互作用以及$H^6$中$N$无关的归一化初始凝聚体波函数，我们沿精确多体演化传播正关联能的第三谱矩。一个一致的初始界控制了耗尽数第三矩和集体单粒子涨落第六矩在每个紧时间区间上，且与$N$无关。对于非零相互作用和光滑、紧支撑的初始凝聚体，我们还确定了尺度为$N^2$的激发能测度，以第一能量加权。该极限适用于具有初始第三关联能矩一致界的范数收敛纯态族。其正能量部分是相对散射算子$-2\Delta+v$的谱测度，乘以时间依赖的修饰接触。我们计算了径向密度，并证明了对于具有有限动能和有限平均激发数的非零参考态，接触严格为正。相同的演化态具有有界的物理涨落矩和激发能矩，对于$p>1$，在扩展谱意义下，激发能矩下界为正的$N^{2p-2}$倍数。初始正能量的逆幂构造了允许的纯态和混合态族。对于范数收敛纯态类，我们确定了$1\le p<2$的缩放相互作用能矩，并将第二矩界定为$O(N^2)$。有限三次近似在能量形式域上具有范数误差$O(N^{-3/16})$，在其生成元的更强初始域上具有$O(N^{-5/4})$。
英文摘要
We study higher moments of quantum fluctuations and microscopic correlation energy in the three-dimensional Gross--Pitaevskii regime. For a smooth, compactly supported, nonnegative radial interaction and an $N$-independent normalized initial condensate wave function in $H^6$, we propagate the third spectral moment of a positive correlated energy along the exact many-body evolution. A uniform initial bound controls the third moment of the depletion number and sixth moments of collective one-particle fluctuations on every compact time interval, independently of $N$. For a nonzero interaction and a smooth, compactly supported initial condensate, we also identify the excitation-energy measure at scale $N^2$, weighted by the first energy. This limit holds for norm-convergent pure-state families with a uniform bound on the initial third correlated-energy moment. Its positive-energy part is a spectral measure of the relative scattering operator $-2Δ+v$, multiplied by a time-dependent dressed contact. We compute the radial density and prove strict positivity of the contact for nonzero references with finite kinetic energy and finite mean excitation number. The same evolving states have bounded physical fluctuation moments and excitation-energy moments of order $p>1$ bounded below by a positive multiple of $N^{2p-2}$, in the extended spectral sense. Inverse powers of the positive initial energy construct admissible pure and mixed families. For the norm-convergent pure-state class, we determine the scaled interaction-energy moments for $1\le p<2$ and bound the second moment by $O(N^2)$. A finite cubic approximation has norm error $O(N^{-3/16})$ on the energy form domain and $O(N^{-5/4})$ on a stronger initial domain of its generator.
Comments259 pages, 0 figure
