玻色气体正则系综的随机场方程

谐振势阱中Bose-Hubbard哈密顿量的正则轨线和临界耦合

Canonical Trajectories and Critical Coupling of the Bose-Hubbard Hamiltonian in a Harmonic Trap

利用量子蒙特卡罗（QMC）模拟和局域密度近似（LDA）方法，将束缚在谐波阱中的玻色哈伯德哈密顿量的定粒子数（正则）轨道映射到均匀系统的$(μ/U,t/U)$相图上.通常，这些曲线不与均匀系统的莫特绝缘体（MI）叶的尖端相交。这一观察需要澄清的临界耦合在实验中获得的捕获系统与QMC模拟中获得的比较。沿这些轨迹的密度分布和能见度也得到。密度分布从QMC在密闭的情况下进行了比较LDA的结果。

费米系统中正则-巨正则系综的不等价性？

Canonical-grandcanonical ensemble in-equivalence in Fermi systems?

我讨论了费米子凝聚在恒定态密度系统中的作用。我表明，冷凝导致校正的化学势和费米分布在典型的费米系统在低温下。这意味着正则系综和巨正则系综甚至对于费米系统也是不等价的。

介观玻色-爱因斯坦凝聚体的涨落统计：协调主方程与配分函数以重新讨论Uhlenbeck-Einstein困境

Fluctuation statistics of mesoscopic Bose-Einstein condensate: reconciling the master equation with the partition function to revisit the Uhlenbeck-Einstein dilemma

从几个不同的角度研究了理想介观玻色-爱因斯坦凝聚体的原子涨落统计。通过推广巨正则分析（适用于正则系综问题），我们得到了一个自洽的平均凝聚粒子数方程，该方程与激光主方程方法计算的微观结果相吻合。对于一个谐波陷阱的情况下，我们得到一个解析表达式的凝聚粒子数是非常准确的，在所有温度下，与数值正则系综结果相比。应用类似的广义巨正则处理的方差，我们得到一个准确的结果，只有低于临界温度。采用随机路径积分的形式主义，具有很好的精度的波动分布的所有高阶矩的分析结果。我们进一步讨论了一种混合处理，它将主方程/随机路径积分分析与基于正则系综准粒子形式主义获得的结果结合在一起[V. V. Kocharovsky等人，Phys.Rev.A61，053606（2000）]，在所有温度下产生与数值模拟基本上完美的一致。

微正则系综中玻色-爱因斯坦凝聚体的真相扩散：经典场研究

Genuine phase diffusion of a Bose-Einstein condensate in the microcanonical ensemble: A classical field study

在经典场模型中，我们发现玻色-爱因斯坦凝聚体的相位在微正则系综中经历了一个真正的扩散运动，凝聚体的相位变化在时间0和时间$t$之间的方差在$t$中线性增长。相扩散系数在热力学和Bogoliubov双重极限下服从一个简单的标度律。我们构建了一个近似计算的扩散系数，在公平的协议，在所考虑的温度范围内的数值结果，我们将这种近似计算的量子场。

Quantum Potential induced UV-IR coupling in Analogue Hawking radiation: From Bose-Einstein Condensates to canonical acoustic black holes

Arising out of a Non-local non-relativistic BEC, we present an Analogue gravity model upto $\mathcal{O}(ξ^{2})$ accuracy in the presence of the quantum potential term for a canonical acoustic BH in $(3+1)$-d spacetime where the series solution of the free minimally coupled KG equation for the large length scale massive scalar modes is derived. We systematically address the issues of the presence of the quantum potential term being the root cause of a UV-IR coupling between short wavelength `primary' modes which are supposedly Hawking radiated through the sonic horizon and the large wavelength …

One-body reduced density-matrix functional theory for the canonical ensemble

We establish one-body reduced density-matrix functional theory for the canonical ensemble in a finite basis set at an elevated temperature. Including temperature guarantees differentiability of the universal functional by occupying all states and additionally not fully occupying the states in a fermionic system. We use convexity of the universal functional and invertibility of the potential-to-1RDM map to show that the subgradient contains only one element which is equivalent to differentiability. This allows us to show that all 1RDMs with a purely fractional occupation number spectrum ($0 < n…