Stochastic Boltzmann Equation for Magnetic Relaxation in High-Spin Molecules

TL;DR

This paper introduces the stochastic Boltzmann equation (SBE) to model spin dynamics in magnetic molecules, providing a new simulation approach for environments akin to a boson gas, relevant for single-molecule experiments.

Contribution

The paper develops the stochastic Boltzmann equation framework with a relaxation-time approximation for magnetic molecules in stochastic environments, enabling trajectory-based simulations.

Findings

SBE can be solved via simple trajectory simulations.

Relaxation-time approximation simplifies the analysis.

Applicable to environments similar to a boson gas.

Abstract

We introduce the stochastic Boltzmann equation (SBE) as an approach for exploring the spin dynamics of magnetic molecules coupled to a stochastic environment. The SBE is a time-evolution equation for the probability density of the spin density matrix of the system. This probability density is relevant to experiments which take measurements on single molecules, in which probabilities of observing particular spin states (rather than ensemble averages) are of interest. By analogy with standard treatments of the regular Boltzmann equation, we propose a relaxation-time approximation for the SBE, and show that solutions to the SBE under the relaxation-time approximation can be obtained by performing simple trajectory simulations for the case of a boson gas environment. Cases where the relaxation-time approximation are satisfied can therefore be investigated by careful choice of the parameters for the boson gas environment, even if the actual environment is quite different from a boson gas. The application of the SBE approach is demonstrated through an illustrative example.