TY - JOUR

T1 - Stochastic Boltzmann equation for magnetic relaxation in high-spin molecules

AU - Packwood, Daniel M.

AU - Katzgraber, Helmut G.

AU - Teizer, Winfried

N1 - Funding Information:
This research was supported by the World Premier Research Institute Initiative promoted by the Ministry of Education, Culture, Sports, Science, and Technology of Japan (MEXT) for the Advanced Institute for Materials Research, Tohoku University, Japan.
Publisher Copyright:
© 2016 The Author(s).

PY - 2016/3

Y1 - 2016/3

N2 - 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.

AB - 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.

KW - Boltzmann equation

KW - Molecule

KW - Spin

KW - Stochastic Boltzmann equation

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U2 - 10.1098/rspa.2015.0699

DO - 10.1098/rspa.2015.0699

M3 - Article

AN - SCOPUS:84962838987

VL - 472

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0962-8444

IS - 2187

M1 - 20150699

ER -