论文标题
使用适应性波算子方法计算参数依赖性汉密尔顿人的特征值和特征向量
Calculating eigenvalues and eigenvectors of parameter-dependent hamiltonians using an adaptative wave operator method
论文作者
论文摘要
我们提出了一种使用适应性的活动子空间来计算大参数依赖性矩阵的特征值和特征向量的波动方法。我们考虑一种依赖外部可调或绝热参数的哈密顿量，使用适应性投影仪在修改可调参数时遵循连续特征的投影仪。该方法还可以处理非官方的哈密顿人。迭代算法是通过使用固定的活动空间和标准块戴维森方法与标准波算子算法进行比较得出和测试的。所提出的方法具有竞争力，它以持续的内存成本在几十次迭代范围内收敛。我们首先在4-D耦合振荡器模型哈密顿量上说明了该方法的能力。还提出了在强度或频率不同的激光场下对分子光解离的更现实的应用。在特殊点附近，H $ {} _ 2^+$的光解离共振的地图被计算为说明性示例。
We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices, using an adaptative active subspace. We consider a hamiltonian which depends on external adjustable or adiabatic parameters, using adaptative projectors which follow the successive eigenspaces when the adjustable parameters are modified. The method can also handle non-hermitian hamiltonians. An iterative algorithm is derived and tested through comparisons with a standard wave operator algorithm using a fixed active space and with a standard block-Davidson method. The proposed approach is competitive, it converges within a few dozen iterations at constant memory cost. We first illustrate the abilities of the method on a 4-D coupled oscillator model hamiltonian. A more realistic application to molecular photodissociation under intense laser fields with varying intensity or frequency is also presented. Maps of photodissociation resonances of H${}_2^+$ in the vicinity of exceptional points are calculated as an illustrative example.
