# Average.m

From Spinach Documentation Wiki

Average Hamiltonian theories under Zeeman interaction rotating frame transformations. Syntax:

H=average(spin_system,Hp,H0,Hm,omega,theory)

Parameters:

Hp - the part of the rotating frame Hamiltonian that has positive frequency under the rotating frame transformation

H0 - the part of the rotating frame Hamiltonian that has zero frequency under the rotating frame transformation

Hm - the part of the rotating frame Hamiltonian that has negative frequency under the rotating frame transformation

omega - the frequency of the rotating frame transformation, rad/s

theory - the level of the average Hamiltonian theory:

'ah_first_order' - first order in Waugh theory

'ah_second_order' - second order in Waugh theory

'ah_third_order' - third order in Waugh theory

'matrix_log' - exact algorithm (very expensive, uses dense matrix algebra)

'kb_first_order' - first order in Krylov-Bogolyubov theory (DNP experiments only)

'kb_second_order' - second order in Krylov-Bogolyubov theory (DNP experiments only)

'kb_second_order' - third order in Krylov-Bogolyubov theory (DNP experiments only)

Note: Krylov-Bogolyubov averging theory as applied to DNP systems is described in detail here:

http://dx.doi.org/10.1039/C2CP23233B http://dx.doi.org/10.1007/s00723-012-0367-0