We study a system of $N$ noninteracting particles on a line in the presence of a harmonic trap $U(x)=μ\bigl[x-z(t)\bigr]^2/2$, where the trap center $z(t)$ undergoes a bounded stochastic modulation. We show that this stochastic modulation drives the system into a nonequilibrium stationary state, where the joint distribution of the positions of the particles is not factorizable. This indicates strong correlations between the positions of the particles that are not inbuilt, but rather get generated by the dynamics itself. Moreover, we show that the stationary joint distribution can be fully characterized and has a special conditionally independent and identically distributed (CIID) structure. This special structure allows us to compute several observables analytically even in such a strongly correlated system, for an arbitrary bounded drive $z(t)$. These observables include the average density profile, the correlations between particle positions, the order and gap statistics, as well as the full counting statistics. We then apply our general results to two specific examples where (i) $z(t)$ represents a dichotomous telegraphic noise, and (ii) $z(t)$ represents an Ornstein-Uhlenbeck process. Our analytical predictions are verified in numerical simulations, finding excellent agreement.
Density profile of noninteracting fermions in a rotating $2d$ trap at finite temperature
本文研究了在具有一个附加的排斥中心势$γ/r^2$的$2d$谐振阱中，以恒定频率$Ω$旋转的$2d$无自旋非相互作用费米子的平均密度.最近在Phys. Rev. A $\textbf{103}$，033321（2021）中研究了零温度下的平均密度，并且在大$N$极限中发现了一种有趣的多层“婚礼蛋糕”结构，其中心具有“孔”。本文研究了有限温度下的平均密度。我们演示了如何在有限的温度下修改这种“婚礼蛋糕”的结构。这些大的$N$结果保证远远超出标准的局域密度近似。我们还将我们的结果推广到各种各样的陷阱势，并证明了相关的标度函数的普遍性，无论是在散装和边缘的“婚礼蛋糕”。
Experimental evidence for strong emergent correlations between particles in a switching trap
LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay（巴黎南大学萨克雷大学）；Laboratoire de Physique, CNRS, ENS de Lyon（里昂高等师范学校）；ICTS, Tata Institute of Fundamental Research（塔塔基础研究院）；Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, Sorbonne Université（索邦大学）
The distribution of the moment of inertia for harmonically trapped noninteracting Bosons at finite temperature: large deviations
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础科学研究所国际理论科学中心）；LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay（巴黎南大学萨克雷大学法国国家科学研究中心理论与物质物理实验室）；Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589（索邦大学法国国家科学研究中心高能理论与物理实验室）
Sluggish quantum mechanics of noninteracting fermions with spatially varying effective mass
Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，巴黎文理研究大学，法国国家科学研究中心，索邦大学，巴黎西岱大学）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay（理论与数学物理实验室，法国国家科学研究中心，巴黎第十一大学，萨克雷大学）；Raman Research Institute（拉曼研究所）
研究非相互作用费米子在空间变化有效质量下的量子行为，推导出精确的本征函数和量子传播子，揭示了多体 ground state 的确定性点过程及关联核的尺度形式。
