average.m

Average Hamiltonian theories under Zeeman interaction rotating frame transformations.

Syntax

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


Arguments

    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)


Outputs

     H  -  average Hamiltonian


Notes

Krylov-Bogolyubov averging theory as applied to DNP systems is described in detail here in http://dx.doi.org/10.1039/C2CP23233B and http://dx.doi.org/10.1007/s00723-012-0367-0