Difference between revisions of "Path trace.m"

From Spinach Documentation Wiki
Jump to: navigation, search
(Created page with "Liouvillian path tracing. Treats the user-supplied Liouvillian as the adjacency matrix of a graph, computes the weakly connect- ed subgraphs of that graph and returns a cell ...")
 
(Update function See also links and function index membership)
 
(9 intermediate revisions by 2 users not shown)
Line 1: Line 1:
−
Liouvillian path tracing. Treats the user-supplied Liouvillian  
+
{{DISPLAYTITLE:path_trace.m}} __NOTOC__
−
as the adjacency matrix of a graph, computes the weakly connect-
+
Liouvillian path tracing. Treats the user-supplied Liouvillian as the adjacency matrix of a graph, computes the weakly connected subgraphs of that graph and returns a cell array of projectors into independently evolving populated subspaces.
−
ed subgraphs of that graph and returns a cell array of project-
 
−
ors into the corresponding independently evolving subspaces.
 
−
Syntax:
 
  
−
              projectors=reduce(spin_system,L,rho)
+
==Syntax==
  
−
where L is the Liouvillian and rho is the initial state (in the
 
−
case of source state screening) or the detection state (if des-
 
−
tination state screening is used). The output is a cell array of
 
−
projectors into independently evolving reduced subspaces. Those
 
−
projectors are to be used as follows:
 
  
−
          L_reduced=P'*L*P;    rho_reduced=P'*rho;
+
    projectors=path_trace(spin_system,L,rho)
  
−
Further information is available here:
+
==Parameters==
  
−
        http://link.aip.org/link/doi/10.1063/1.3398146
+
    L  -  Liouvillian matrix
−
        http://dx.doi.org/10.1016/j.jmr.2011.03.010
+
 +
    rho -  the initial state (source state screening)
 +
            or the detection state (destination state
 +
            screening)
 +
 
 +
==Outputs==
 +
 
 +
  projectors - a cell array of projectors into independently
 +
                evolving populated subspaces. The projectors
 +
                are to be used as follows:
 +
 +
                  L_reduced=P'*L*P;    (for matrices)
 +
                  rho_reduced=P'*rho;  (for state vectors)
 +
 
 +
==Notes==
 +
Further information on how this function works is available in our papers on this subject:
 +
 
 +
            http://dx.doi.org/10.1063/1.3398146
 +
            http://dx.doi.org/10.1016/j.jmr.2011.03.010
 +
 
 +
A significant number of independently evolving or dropped subspaces is often an indication of an overlooked symmetry or a conservation law – it is a good idea to examine the dropped subspaces and try finding out why they are not being populated. The efficiency of the path tracing procedure depends on the choice of the basis set. For the spherical tensor basis sets used in Spinach, there are usually at least two (in some EPR examples), and sometimes over a hundred (in large HSQC examples) independent subspaces, depending on the calculation type and spin interactions present.
 +
 
 +
==See also==
 +
[[reduce.m]], [[zte.m]], [[symmetry.m]], [[krylov.m]], [[adelim.m]], [[coherence.m]], [[correlation.m]], [[dfpt.m]], [[homospoil.m]], [[human2opspec.m]], [[lin2lm.m]], [[lin2lmn.m]], [[lm2lin.m]], [[lmn2lin.m]], [[scomponents.m]], [[sinkhole.m]], [[sparse2csr.m]], [[sphten2zeeman.m]], [[stitch.m]], [[Kernel_utilities]]
 +
 
 +
''Version 2.5, authors: [[Ilya Kuprov]], [[Matthew Krzystyniak]]''

Latest revision as of 19:39, 6 June 2026

Liouvillian path tracing. Treats the user-supplied Liouvillian as the adjacency matrix of a graph, computes the weakly connected subgraphs of that graph and returns a cell array of projectors into independently evolving populated subspaces.

Syntax

    projectors=path_trace(spin_system,L,rho)

Parameters

    L   -  Liouvillian matrix 

    rho -  the initial state (source state screening)
           or the detection state (destination state
           screening)

Outputs

  projectors - a cell array of projectors into independently
               evolving populated subspaces. The projectors 
               are to be used as follows:

                  L_reduced=P'*L*P;    (for matrices)
                  rho_reduced=P'*rho;  (for state vectors)

Notes

Further information on how this function works is available in our papers on this subject: 

            http://dx.doi.org/10.1063/1.3398146
            http://dx.doi.org/10.1016/j.jmr.2011.03.010

A significant number of independently evolving or dropped subspaces is often an indication of an overlooked symmetry or a conservation law – it is a good idea to examine the dropped subspaces and try finding out why they are not being populated. The efficiency of the path tracing procedure depends on the choice of the basis set. For the spherical tensor basis sets used in Spinach, there are usually at least two (in some EPR examples), and sometimes over a hundred (in large HSQC examples) independent subspaces, depending on the calculation type and spin interactions present.

See also

reduce.m, zte.m, symmetry.m, krylov.m, adelim.m, coherence.m, correlation.m, dfpt.m, homospoil.m, human2opspec.m, lin2lm.m, lin2lmn.m, lm2lin.m, lmn2lin.m, scomponents.m, sinkhole.m, sparse2csr.m, sphten2zeeman.m, stitch.m, Kernel_utilities

Version 2.5, authors: Ilya Kuprov, Matthew Krzystyniak

Retrieved from "https://spindynamics.org/wiki/index.php?title=Path_trace.m&oldid=9371"