论文标题
多体密度和被困的冷玻色子的连贯性
Many-body density and coherence of trapped cold bosons
论文作者
论文摘要
多体密度和相关功能对于理解量子多体物理学至关重要。在这里，我们提出了一种计算它们的方法。我们的方法是一般的，并且基于骨器或费米子歼灭场对多体波函数的作用。我们分析了$ n = 6 $ quasi二维的谐波固定玻色子，具有弱至强接触强度，直至tonks-girardeau限制限制，并使用多fi依的无限时间依赖性的hartree方法用于无形的hartree方法，用于不可区分的颗粒（MCTDH-X）。我们将MCTDH-X溶液与无限排斥方案中的分析溶液以及所谓相关的配对波函数方法进行了比较，并找到了良好的一致性。由于数值近似与已知分析溶液的情况没有结合，因此我们证明了一种一般方法，用于研究高阶降低密度矩阵和相关函数，而分析溶液未知的系统中的相关功能。我们追踪从弱相互作用到tonks-girardeau限制的交叉中相关特征的构建，发现高阶相关函数和密度类似于Tonks-Girardeau限制的相互作用的相互作用的相互作用，而不是仅预期的一体密度。
Many-body densities and correlation functions are of paramount importance for understanding quantum many-body physics. Here, we present a method to compute them; our approach is general and based on the action of bosonic or fermionic annihilation field operators on the many-body wavefunction. We analyze $N = 6$ quasi-one-dimensional harmonically-trapped bosons with weak to strong contact interaction strength up to the Tonks-Girardeau limit with infinite repulsion using the MultiConfigurational Time-Dependent Hartree method for indistinguishable particles (MCTDH-X). We compare our MCTDH-X solutions to the analytical ones in the infinite repulsion regime as well as to the so-called correlated pair wavefunction approach and find a good agreement. Since numerical approximations are not bound to the cases where analytical solutions are known, we thus demonstrate a general method to investigate high-order reduced density matrices and correlation functions in systems for which analytical solutions are unknown. We trace the build-up of correlation features in the crossover from weak interactions to the Tonks-Girardeau limit and find that the higher-order correlation functions and densities resemble those in the Tonks-Girardeau limit for way smaller interactions than anticipated from just the one-body density.
