Gross‐Pitaevskiiの非線形量子力学と条件付き等価プロセス‐‐歴史的な意見‐

Takeuchi Hiromitsu

Habib Ouerdiane, Samah Horrigue

In this paper, we introduce and study a noncommutative extension of the Gross Laplacian, called quantum Gross Laplacian. Then, applying the quantum Gross Laplacian to the particular case where the operator is the multiplication operator, we find a relation between classical and quantum Gross Laplacian. As application, we give explicit solution of linear quantum white noise differential equation. In particular, we give a explicit solution of the quantum Gross heat equation.

Neslihan Üzar, Han, D., T. T ufekci +1 more

In this study, after we have briefly introduced the standard Gross-Pitaevskii equation, we have suggested fractional Gross-Pitaevskii equations to investigate the time-dependent ground state dynamics of the Bose-Einstein condensation of weakly interacting bosonic particle system which can includes non-Markovian processes or non-Gaussian distributions and long-range interactions. Only we focused the time-fractional Gross-Pitaevskii equation and have obtained solutions of the standard Gross-Pitaevskii and time-fractional Gross-Pitaevskii equations for attractive and repulsive interactions in the case external trap potentials $V(x)=0$ and optical lattice potential $V(x) =\pm\sin^{2}x$ by using Homotopy Perturbation Method. We have found that the Homotopy Perturbation Method solutions of the Gross-Pitaevskii equation for these potentials and interactions are the same analytical results of it. Furthermore we have also found that solutions of the time-fractional Gross-Pitaevskii equation for these potentials and interactions can be given in terms of Mittag-Leffler function. The solutions of the time-fractional Gross-Pitaevskii equation provide that the time evolution of the ground state dynamics of Bose-Einstein condensation of bosonic particles deviates exponential form, and evolutes with time as stretched exponentially.

吕东燕, Yuan Zhou

本文将类高斯模型用于准二维玻色气体系统,通过求解描述基态波函数的Gross-Pitaevskii方程,得到类高斯分布波函数,并将该波函数与已有的数值解和托马斯-费米近似解做了比较,发现非常吻合.其次通过求解能量泛函得出系统的基态能量以及化学势.分析了维度的变化对系统性质的影响.

车立新, 罗香怡, 苏明辉

从理论上应用辛算法数值求解一维含时GP方程,研究存在陷浮势和陷浮势为零时三个玻色-爱因斯坦凝聚体间的干涉.当陷浮势存在时,玻色-爱因斯坦凝聚体间发生弹性碰撞;如果在t=0时陷浮势为零,三个凝聚体间发生干涉现象,并且发现几率密度随着时间的演化是振荡的.

Stepan P. Pokatov, T. Yu. Ivanova, D. A. Ivanov

Abstract We propose an artificial neural network (ANN) design to solve the inverse problem for a 1D Gross–Pitaevskii equation (GPE). More precise, the ANN takes the squared modulus of the stationary GPE solution as an input and returns the parameters of the potential function and the factor in front of the GPE non-linear term. From the physical point of view the ANN predicts the parameters of a trap potential and the interaction constant of 1D Bose–Einstein condensate by its density distribution. Using the results of numerical solution of GPE for more than <?CDATA $30\,000$?> 30 000 sets of GPE parameters as train and validation datasets we build the ANN as a fast and accurate inverse GPE solver.