## 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 relaxationtime approximation can be obtained by performing simple trajectory simulations for the case of a boson gas environment. Cases where the relaxationtime 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.

Original language | English |
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Article number | 20150699 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 472 |

Issue number | 2187 |

DOIs | |

Publication status | Published - 2016 Mar |

## Keywords

- Boltzmann equation
- Molecule
- Spin
- Stochastic Boltzmann equation

## ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)