Density Matrix Equation for a Bathed Small System and its Application to Molecular Magnets

TL;DR

This paper details a density matrix equation approach for small quantum systems interacting with a bath, emphasizing its application to molecular magnets near tunneling resonances, with a universal relaxation term formulation.

Contribution

It introduces a nonsecular density matrix equation tailored for molecular magnets, avoiding unknown parameters and simplifying the inclusion of anisotropy effects.

Findings

Universal form of relaxation terms for molecular magnets

Exact basis states and transition frequencies used in the model

Mathematica code provided for implementation

Abstract

The technique of density matrix equation (DME) for a small system interacting with a bath is explained in detail. Special attention is given to the nonsecular DME that is needed in the vicinity of overdamped tunnelling resonances in molecular magnets (MM). The relaxation terms of the DME for MM are represented in the universal form that does not employ any unknown spin-lattice coupling constants and absorbs the information about the spin Hamiltonian in the exact basis states and transition frequencies. This makes adding new types of anisotropy easy and error-free. The Mathematica code is available from the author.