# Relaxation.m

The relaxation superoperator. All options are set during the call to create.m function. Syntax:

R=relaxation(spin_system,euler_angles)

where euler_angles should be used for solid state systems in which the thermal equilibrium state is orientation-dependent.

Further information is available in the following papers:

http://dx.doi.org/10.1016/j.jmr.2010.12.004 (Redfield) http://dx.doi.org/10.1002/mrc.1242 (Lindblad) http://dx.doi.org/10.1007/s00723-012-0367-0 (Nottingham DNP) http://dx.doi.org/10.1039/c2cp42897k (Weizmann DNP)

Note: Nottingham relaxation theory is only applicable to cross effect DNP systems and Weizmann relaxation theory to solid effect and cross effect DNP systems.

Note: The function has been written for minimal memory footprint and performs aggressive memory recycling. Relaxation superoperator dimen- sions in excess of 1,000,000 are in practice feasible.

Spinach implements a very general case of Bloch-Redfield-Wangsness relaxation theory, which includes all “difficult” contributions, such as interaction rhombicities, cross-correlations and dynamic frequency shifts. Contributions from all couplings present in the system (including quadrupolar and ZFS) are included. So long as the validity conditions of Redfield theory are satisfied, Spinach is not restricted to high-field systems – the role of H0 can be played, for example, by a large isotropic hyperfine coupling.