Krylov.m

Krylov propagation function. Avoids matrix exponentiation, but can be slow. Should be used when the Liouvillian exponential does not fit into the system memory, but the Liouvillian itself does.

Syntax

    answer=krylov(spin_system,L,coil,rho,time_step,nsteps,output)

Parameters

     L      - the Liouvillian to be used during evolution

     rho    - the initial state vector or a horizontal stack thereof

     output - a string giving the type of evolution that is required

               'final' - returns the final state vector or a horizontal
                         stack thereof.

               'trajectory' - returns the stack of state vectors giving
                              the trajectory of the system starting from
                              rho with the user-specified number of steps
                              and step length.

               'refocus' - evolves the first vector for zero steps,
                           second vector for one step, third vector for
                           two steps, etc., consistent with the second
                           stage of evolution in the indirect dimension
                           after a refocusing pulse.

               'observable' - returns the time dynamics of an observable
                              as a vector (if starting from a single ini-
                              tial state) or a matrix (if starting from a
                              stack of initial states).

               'multichannel' - returns the time dynamics of several
                                observables as rows of a matrix. Note
                                that destination state screening may be
                                less efficient when there are multiple
                                destinations to screen against.

     coil   - the detection state, used when 'observable' is specified as
              the output option. If 'multichannel' is selected, the coil
              should contain multiple columns corresponding to individual
              observable vectors.

Outputs

    answer - a vector or a matrix, depending on the options set during
             the call.

Notes

This function does not support the zeeman-hilb formalism; in zeeman-wavef, L is the Hamiltonian matrix, rho is a wavefunction or a horizontal stack thereof, coil is a reference wavefunction, and observables are overlap trajectories.

We initially had a faithful implementation of the Krylov process here - subspace, orthogonalisation, projection, etc., but in all our testing it was much inferior to the reordered Taylor process that is currently implemented.

GPUs are supported, add 'gpu' to sys.enable array during calculation setup.

See also

evolution.m, step.m, propagator.m, isergen.m, iserstep.m, steady.m, Kernel_functions

Version 2.2, authors: Ilya Kuprov