Open quantum dynamics of a three-dimensional rotor calculated using a rotationally invariant system-bath Hamiltonian: Linear and two-dimensional rotational spectra.

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 harmonic-oscillator baths through functions of the rotor's Euler angles. While this model has been developed to study the 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. Specifically, the treatment presented here is carried out as an extension of a previous work [Y. Iwamoto and Y. Tanimura, 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-Leggett model. To illustrate the 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 for the 3D RISB model in the high-temperature case. Using the QME, we compute linear and 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 can be clearly observed in 2D rotational spectroscopy.