Evolution.m - Revision history

Kuprov: sync with Spinach main f053e432: manual Liouvillian assembly note (L=H+1iR+1iK); wavefunction calculation call signature paragraph added

2026-08-30T05:43:11Z

sync with Spinach main f053e432: manual Liouvillian assembly note (L=H+1i*R+1i*K); wavefunction calculation call signature paragraph added

Kuprov: Update function See also links and function index membership

2026-06-06T18:36:29Z

Update function See also links and function index membership

Kuprov: Rename Arguments section heading to Parameters

2026-06-05T17:48:46Z

Rename Arguments section heading to Parameters

Kuprov: Normalise sequential blank lines

2026-04-25T11:25:00Z

Normalise sequential blank lines

Kuprov: Restore pre-bulk-edit wiki content

2026-04-05T14:48:34Z

Restore pre-bulk-edit wiki content

Kuprov: Sync syntax/arguments/outputs with current Spinach source

2026-04-05T14:05:34Z

Sync syntax/arguments/outputs with current Spinach source

Kuprov: /* See also */

2021-06-15T19:39:29Z

‎See also

Kuprov at 18:18, 29 November 2020

2020-11-29T18:18:33Z

Kuprov at 18:17, 29 November 2020

2020-11-29T18:17:38Z

Admin at 11:32, 15 December 2018

2018-12-15T11:32:52Z

@@ Line 15: / Line 15: @@
 ==Parameters==
-Arguments for Liouville space calculations:
+For Liouville space calculations:
-       L      - the Liouvillian to be used during evolution
+       L      - the Liouvillian to be used during evolution. If L
        rho    - the initial state vector or a horizontal stack thereof
@@ Line 60: / Line 63: @@
                      screening.
-Arguments for Hilbert space calculations:
+For Hilbert space calculations:
         L         - Hamiltonian matrix
@@ Line 91: / Line 94: @@
         destination - this argument is ignored.
 ==Outputs==

@@ Line 105: / Line 105: @@
 ==See also==
-[[Kernel_functions#Time_evolution|Time evolution functions]], [[step.m]], [[krylov.m]], [[reduce.m]], [[propagator.m]], [[shaped_pulse_af.m]], [[shaped_pulse_xy.m]]
+[[step.m]], [[krylov.m]], [[reduce.m]], [[propagator.m]], [[shaped_pulse_af.m]], [[shaped_pulse_xy.m]], [[isergen.m]], [[iserstep.m]], [[steady.m]], [[Kernel_functions]]
 ''Version 2.3, authors: [[Ilya Kuprov]], [[Luke Edwards]], [[Ohad Levinkron]]''

@@ Line 14: / Line 14: @@
       answer=evolution(spin_system,L,coil,rho,timestep,nsteps,output,destination)
-==Arguments==
+==Parameters==
 Arguments for Liouville space calculations:

@@ Line 106: / Line 106: @@
 ==See also==
 [[Kernel_functions#Time_evolution|Time evolution functions]], [[step.m]], [[krylov.m]], [[reduce.m]], [[propagator.m]], [[shaped_pulse_af.m]], [[shaped_pulse_xy.m]]
 ''Version 2.3, authors: [[Ilya Kuprov]], [[Luke Edwards]], [[Ohad Levinkron]]''

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:evolution.m}} __NOTOC__
 Time evolution function optimised for ''extended evolution periods with multiple time steps'', such as trajectory calculation and detection stages of time-domain experiments. For brief one-off evolution events (hard pulses, slices of shaped pulses) or time-dependent Liouvillians use [[step.m]] instead.
@@ Line 13: / Line 12: @@
 ==Syntax==
-answer=evolution(spin_system,L,coil,rho,timestep,nsteps,output,destination)
+     answer=evolution(spin_system,L,coil,rho,timestep,nsteps,output,destination)
 ==Arguments==
 Arguments for Liouville space calculations:
@@ Line 96: / Line 94: @@
 ==Outputs==
-answer - a vector, a matrix, or a cell array or matrices,
+     answer - a vector, a matrix, or a cell array or matrices,
-                depending on the options set during the call
+              depending on the options set during the call
 ==Notes==
 # Calculation of final states and observables in Hilbert space is parallelised (http://dx.doi.org/10.1063/1.3679656) and tested all the way to 128-core (16 nodes, 8 cores each) configuations. Parallelization of the trajectory calculation does not appear to yield any benefits due to large amount of inter-thread communication.
 # One-off propagation events (e.g. a hard pulse) should be computed with [[step.m]], which is more efficient in those cases.
@@ Line 118: / Line 105: @@
 ==See also==
 [[Kernel_functions#Time_evolution|Time evolution functions]], [[step.m]], [[krylov.m]], [[reduce.m]], [[propagator.m]], [[shaped_pulse_af.m]], [[shaped_pulse_xy.m]]
 ''Version 2.3, authors: [[Ilya Kuprov]], [[Luke Edwards]], [[Ohad Levinkron]]''

@@ Line 6: / Line 6: @@
 <center><math>{\bf{\rho }}\left( {t + \Delta t} \right) = \exp \left[ { - i{\bf{L}}\Delta t} \right]{\bf{\rho }}\left( t \right)</math></center>
-Such analysis is only warranted if the propagation time is long and the Liouvillian matrix is large - this module should not be used for one-off events, such as hard pulses. It should also not be used with small spin systems or time-dependent Hamiltonians because the expensive preliminary analysis would in that case dominate the calculation time. The analysis may be run manually by calling [[reduce.m]] - this is often useful because the reduction module would often expose symmetries or unpopulated states that may later be excluded at the basis set level.
+Such analysis is only warranted if the propagation time is long and the Liouvillian matrix is large - this module should not be used for one-off events, such as hard pulses. It should also not be used with small spin systems or time-dependent Hamiltonians because the expensive preliminary analysis would in that case dominate the calculation time.
 The default propagation mechanism inside [[evolution.m]] is matrix exponentiation with the propagators obtained by calling [[propagator.m]]. When this function detects that the dimension of the Liouvillian is too big for exponentiation, it calls [[krylov.m]] with the same parameters. If the function detects that the Liouvillian is too small (fewer then five spins) to bother with any sophisticated state space reduction, it simply calls Matlab's expm function.

@@ Line 2: / Line 2: @@
 Time evolution function optimised for ''extended evolution periods with multiple time steps'', such as trajectory calculation and detection stages of time-domain experiments. For brief one-off evolution events (hard pulses, slices of shaped pulses) or time-dependent Liouvillians use [[step.m]] instead.
-This function runs trajectory state space analysis (https://doi.org/10.1016/j.jmr.2008.08.008), partitions the state space into the smallest possible independently evolving subspaces, and runs exponential time propagation in each subspace:
+This function runs trajectory level state space analysis (https://doi.org/10.1016/j.jmr.2008.08.008), partitions the state space into the smallest possible independently evolving subspaces, and runs exponential time propagation in each subspace:
 <center><math>{\bf{\rho }}\left( {t + \Delta t} \right) = \exp \left[ { - i{\bf{L}}\Delta t} \right]{\bf{\rho }}\left( t \right)</math></center>