# trajan.m

From Spinach Documentation Wiki

Trajectory analysis function. Plots the time dependence of the density matrix norm, partitioned into user-specified property classes. See http://dx.doi.org/10.1016/j.jmr.2013.02.012 for further information.

## Contents

## Syntax

trajan(spin_system,trajectory,property)

## Arguments

trajectory - a stack of state vectors of any length. The number of rows in the trajectory array must match the number of states in the basis. property - if set to 'correlation_order', returns the time dependence of the total populations of one-spin, two-spin, three-spin, etc. corre- lations in the system. if set to 'coherence_order', returns the ti- me dependence of different orders of coheren- ce in the system, where a coherence order is defined as the sum of projection quantum num- bers in the spherical tensor representation of each state. if set to 'total_each_spin', returns the ti- me dependence of total state space populati- on that involves each individual spin in the system in any way (all local populations and coherences of the spin as well as all of its correlations to all third party spins). if set to 'local_each_spin', returns the ti- me dependence of the population of the sub- space of states that are local to each indi- vidual spin and do not involve any correla- tions to other spins in the system. if set to 'level_populations', returns the populations of the Zeeman energy levels.

The trajectory would usually come out of the evolution.m or krylov.m run from a given starting point under a given Liouvillian.

## Outputs

This function writes into the current figure.

## Examples

Figures 2, 4, and 5 in http://dx.doi.org/10.1016/j.jmr.2013.02.012 were created using this function, as well as Figure 5 in https://doi.org/10.1002/mrc.4660

## Notes

This function is only applicable to the trajectories recorded in sphten-liouv formalism.

## See also

trajsimil.m, basis.m, evolution.m, krylov.m

*Version 2.2, authors: Gareth Charnock, Ilya Kuprov, Luke Edwards*