step.m

Time propagation function optimised for one-off calls, such as hard pulses or slices of shaped pulses. For trajectory calculation or detection periods of time-domain experiments, use evolution.m instead.

This function calculates the action by a matrix exponential on a vector without computing the matrix exponential. The actual implementation is more sophisticated, but the principle becomes apparent from the following equation:

\('"`UNIQ-MathJax1-QINU`"'\)

Syntax

    rho=step(spin_system,L,rho,time_step)

Arguments

     L          -  Liouvillian or Hamiltonian to be used for propagation

     rho        -  state vector or density matrix to be propagated

     time_step  -  length of the time step to take

Outputs

     rho        -  state vector or density matrix

Examples

See the source code of shaped_pulse_xy.m and most NMR pulse sequences (cosy.m, hsqc.m, and others) for examples of this function being used.

Notes

1. The sequence is programmed with a rather peculiar order of algebraic operations. This was carefully optimised to ensure best possible performance under a variety of scenarios (parallelisation, GPUs, large sparse arrays) in Matlab.
2. Long-term propagation under a static Liovillian should be handled with evolution.m or krylov.m functions instead.

See also

evolution.m, krylov.m, shaped_pulse_xy.m, shaped_pulse_af.m

Version 2.2, authors: Ilya Kuprov, Luke Edwards