Difference between revisions of "Path trace.m"

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(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 ...")
 
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Liouvillian path tracing. Treats the user-supplied Liouvillian  
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{{DISPLAYTITLE:function.m}}
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as the adjacency matrix of a graph, computes the weakly connect-
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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.
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ed subgraphs of that graph and returns a cell array of project-
 
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ors into the corresponding independently evolving subspaces.
 
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Syntax:
 
  
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              projectors=reduce(spin_system,L,rho)
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==Syntax==
  
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where L is the Liouvillian and rho is the initial state (in the
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    projectors=reduce(spin_system,L,rho)
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case of source state screening) or the detection state (if des-
 
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tination state screening is used). The output is a cell array of
 
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projectors into independently evolving reduced subspaces. Those
 
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projectors are to be used as follows:
 
  
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          L_reduced=P'*L*P;    rho_reduced=P'*rho;
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==Arguments==
  
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Further information is available here:
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    L  -  Liouvillian matrix
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    rho -  the initial state (source state screening)
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            or the detection state (destination state
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            screening)
  
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        http://link.aip.org/link/doi/10.1063/1.3398146
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==Outputs==
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        http://dx.doi.org/10.1016/j.jmr.2011.03.010
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  projectors - a cell array of projectors into independently
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                evolving populated subspaces. The projectors
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                are to be used as follows:
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                  L_reduced=P'*L*P;    (for matrices)
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                  rho_reduced=P'*rho;  (for state vectors)
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==Notes==
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Further information on how this function works is available in our papers on this subject:
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            http://dx.doi.org/10.1063/1.3398146
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            http://dx.doi.org/10.1016/j.jmr.2011.03.010
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==See also==
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[[reduce.m]], [[zte.m]], [[symmetry.m]], [[krylov.m]]
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''Version 2.2, authors: [[Ilya Kuprov]], [[Matthew Krzystyniak]]''

Revision as of 11:09, 30 August 2018

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=reduce(spin_system,L,rho)

Arguments

    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

See also

reduce.m, zte.m, symmetry.m, krylov.m


Version 2.2, authors: Ilya Kuprov, Matthew Krzystyniak

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