Gaussian wavepacket dynamics has proven to be a useful semiclassical approximation for quantum simulations of high-dimensional systems with low anharmonicity. Compared to Heller's original local harmonic method, the variational Gaussian wavepacket dynamics is more accurate, but much more difficult to apply in practice because it requires evaluating the expectation values of the potential energy, gradient, and Hessian. If the variational approach is applied to the local cubic approximation of the potential, these expectation values can be evaluated analytically, but still require the costly third derivative of the potential. To reduce the cost of the resulting local cubic variational Gaussian wavepacket dynamics, we describe efficient high-order geometric integrators, which are symplectic, time-reversible, and norm-conserving. For small time steps, they also conserve the effective energy. We demonstrate the efficiency and geometric properties of these integrators numerically on a multi-dimensional, nonseparable coupled Morse potential.

翻译：高斯波包动力学已被证明是用于低非简谐性高维系统量子模拟的一种有效的半经典近似。与Heller最初的局域谐波方法相比，变分高斯波包动力学更精确，但在实际应用中因需要计算势能、梯度及Hessian矩阵的期望值而更具挑战性。若将变分方法应用于势能的局域立方近似，这些期望值虽可通过解析方式求得，但仍需计算昂贵的势能三阶导数。为降低由此产生的局域立方变分高斯波包动力学的计算成本，我们描述了高效的高阶几何积分器，这些积分器具有辛结构、时间可逆性且保范数特性。在小时间步长下，它们还能守恒有效能量。我们通过多维、非可分离的耦合Morse势算例，数值验证了这些积分器的效率与几何性质。