用转动不变系统计算三维转子的开放量子动力学--巴斯哈密顿量：线性和二维转动谱
Open Quantum Dynamics of a Three-Dimensional Rotor Calculated Using a Rotationally Invariant System-Bath Hamiltonian: Linear and Two-Dimensional Rotational Spectra
摘要：
我们考虑一个旋转不变的系统浴（RISB）模型在三维空间中描述的线性刚性转子独立耦合到三套谐波振荡器浴作为函数的欧拉角。虽然这个模型已经被开发来研究溶剂化中偶极分子的介电弛豫作为经典德拜弛豫的问题，但在这里，我们将其作为开放量子动力学的问题进行研究，作为我们先前工作的扩展[J. Chem. Phys，149，084110（2018）]，其中我们研究了二维（2D）RISB模型，到三维（3D）RISB模型。与2D情况一样，由于总汉密尔顿的能量离散化的差异，3D RISB模型描述的动力学与旋转Caldeira-Legget（RCL）模型描述的动力学显着不同。为了说明由角动量和磁量子数描述的量子三维转子系统的特征，我们推导了高温情况下三维RISB模型的量子主方程（QME）和分层运动方程（HEOM）。使用QME，我们计算线性和二维（2D）旋转光谱，定义的线性和非线性响应函数的转子偶极子，分别。在二维转动光谱中可以清楚地观察到极化斯塔克场引起的角动量态和磁态之间的量子跃迁以及系统-浴相互作用。
英文摘要：
We consider a rotationally invariant system-bath (RISB) model in three-dimensional space that is described by a linear-rigid rotor independently coupled to three sets of harmonic-oscillator baths as functions of the Euler angle. While this model has been developed to study a dielectric relaxation of a dipolar molecule in solvation as a problem of classical Debye relaxation, here we investigate it as a problem of open quantum dynamics as an extension of our previous work [J. Chem. Phys, 149, 084110 (2018)], in which we studied a two-dimensional (2D) RISB model, to a three-dimensional (3D) RISB model. As in the 2D case, due to a difference in the energy discretization of the total Hamiltonian, the dynamics described by the 3D RISB model differ significantly from those described by the rotational Caldeira-Legget (RCL) model. To illustrate characteristic features of the quantum 3D rotor system described by angular momentum and magnetic quantum numbers, we derive a quantum master equation (QME) and hierarchical equations of motion (HEOM) for the 3D RISB model in the high-temperature case. Using the QME, we compute linear and two-dimensional (2D) rotational spectra, defined by the linear and nonlinear response functions of the rotor dipole, respectively. The quantum transitions between the angular momentum states and magnetic states arising from polarized Stark fields as well as the system-bath interactions are clearly observed in 2D rotational spectroscopy.
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