数值求解耦合Gross-Pitaevskii方程组基态解的离散归一化梯度流方法

Numerical method for the ground state solution of coupled Gross-Pitaevskii equations

摘要:

本文提出了一种求解磁场项为常数的耦合Gross-Pitaevskii方程组基态解的数值算法. 首先,基于单组分近似理论,本文将方程组的能量泛函等价为单组分的能量泛函, 然后基于降阶后的能量表达式提出了离散归一化梯度流数值方法. 数值算例表明，该方法高效且可靠.

Abstract:

In this paper, a numerical method for solving the ground state solution of the coupled Gross-Pitaevskii equations with constant magnetic field term is proposed. Based on the single mode approximation theory, energy functional of the equations is equivalently expressed by a reduced energy functional with single component. Then, based on the method of discrete normalized gradient flow, the method is proposed by using the expression of the reduced energy. Numerical examples illustrate the reliability and performance of the method.