Step.m

Propagation step function. Computes the action by a matrix exponential without computing that exponential. Supports one-, two-, and three-point product quadratures.

Syntax

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

Parameters

     L          -  Liouvillian or Hamiltonian to be used for propagation;
                   centre point piecewise-constant rule if one matrix is
                   supplied, piecewise-linear rule if two matrices {left,
                   right} are supplied, and piecewise-quadratic rule if
                   three matrices {left, midpoint, right} are supplied.
                   If L is assembled manually from Hamiltonian commutation
                   superoperator H, relaxation superoperator R, and kinetics
                   superoperator K, use L=H+1i*R+1i*K.
                   State-dependent evolution generators are also supported:
                   if L{1} is a function handle, L{2} is current time, and
                   L{3} is the method, the problem is routed to iserstep.m

     rho        -  state vector or density matrix

     time_step  -  length of the time step to take

Outputs

     rho        -  state vector or density matrix

Examples

A 90-degree pulse in X phase on protons:

   Lx=operator(spin_system,'Lx','1H');
   rho=step(spin_system,Lx,rho,pi/2);

A 1 millisecond evolution period under a Hamiltonian H:

   rho=step(spin_system,H,rho,1e-3);

A 45-degree pulse with a 60-degree phase on carbon:

   Lx=operator(spin_system,'Lx','13C');
   Ly=operator(spin_system,'Ly','13C');
   rho=step(spin_system,cosd(60)*Lx+sind(60)*Ly,rho,pi/4);

See also 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

This function originally used a faithful Krylov process, but testing found it inferior to the reordered Taylor process now used in the implementation. The current algebraic operation order is designed to minimise memory footprint in large cases.

See also

evolution.m, krylov.m, propagator.m, shaped_pulse_xy.m, shaped_pulse_af.m, cosy.m, hsqc.m, isergen.m, iserstep.m, steady.m, Kernel_functions

Version 2.8, authors: Ilya Kuprov, Luke Edwards, Anupama Acharya, C Musselwhite