# Open Quantum Dynamics of a Three-Dimensional Rotor Calculated Using a Rotationally Invariant System-Bath Hamiltonian: Linear and Two-Dimensional Rotational Spectra

## TL;DR

This paper develops a quantum dynamical model for a three-dimensional rotor coupled to harmonic baths, deriving equations to compute linear and 2D rotational spectra, revealing quantum transitions in the system.

## Contribution

It extends previous 2D RISB models to a 3D case, deriving quantum master equations and hierarchical equations of motion for open quantum rotor dynamics.

## Key findings

- Quantum transitions between angular momentum and magnetic states are observed in 2D spectra.
- The 3D RISB model shows significant differences from the rotational Caldeira-Legget model.
- Derived equations enable detailed analysis of quantum rotational spectra.

## Abstract

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.