average.m

From Spinach Documentation Wiki
Jump to: navigation, search

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

See also

rotframe.m, expmint.m, intrep.m


Version 2.2, authors: Alexander Karabanov, Walter Kockenberger, Ilya Kuprov