Difference between revisions of "Reduce.m"

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(Created page with "Symmetry and trajectory-level state space restriction for a user-specified Liouvillian L and initial state rho. Applies all reduction methods (unless disabled during the call ...")
 
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Symmetry and trajectory-level state space restriction for a user-specified Liouvillian L and initial state rho. Applies all reduction methods (unless disabled during the call to create.m) and returns a cell array of projectors into a set of independent reduced subspaces. See the Kuprov group publications for the details and validity conditions of the many methods and approximations involved. The default settings guarantee accurate simulations in all cases, but considerable speed-ups can often be achieved by relaxing the various tolerances from their ultra-conservative default values. Syntax:
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{{DISPLAYTITLE:function.m}}
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Symmetry and trajectory-level state space reduction. Tries all applicable reduction methods (unless disabled during the call to [[create.m]]) and returns a cell array of projectors into a set of independently evolving reduced subspaces.
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==Syntax==
  
 
     projectors=reduce(spin_system,L,rho)
 
     projectors=reduce(spin_system,L,rho)
  
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where L is the Liouvillian and rho is the initial state (in the case of source state screening) or the detection state (if destination 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:
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==Arguments==
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    L   -  Liouvillian matrix
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    rho -  initial state (source state screening) or
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            destination state (destination state screening)
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==Outputs==
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  projectors - a cell array of projectors into independently
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                evolving reduced subspaces. The projectors are
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                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 what this function does is available in our papers on this subject
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              http://dx.doi.org/10.1016/j.jmr.2008.08.008
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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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            L_reduced=P'*L*P;    (for matrices)
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Briefly, the function tries symmetry factorisation, followed by zero track elimination, followed by disconnected subspace identifcation by path tracing.
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            rho_reduced=P'*rho;  (for state vectors)
 
  
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Further information is available here:
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==See also==
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[[zte.m]], [[path_trace.m]], [[symmetry.m]], [[perm_group.m]]
  
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        http://dx.doi.org/10.1016/j.jmr.2008.08.008
 
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        http://link.aip.org/link/doi/10.1063/1.3398146
 
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        http://dx.doi.org/10.1016/j.jmr.2011.03.010
 
  
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Unless they are specifically disabled, symmetry and trajectory-level pruning algorithms are applied automatically and transparently every time a call is made to the time evolution.m function. See function header for more information.
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''Version 2.2, authors: [[Ilya Kuprov]], [[Luke Edwards]], [[Matthew Krzystyniak]]''

Revision as of 10:27, 30 August 2018

Symmetry and trajectory-level state space reduction. Tries all applicable reduction methods (unless disabled during the call to create.m) and returns a cell array of projectors into a set of independently evolving reduced subspaces.

Syntax

    projectors=reduce(spin_system,L,rho)

Arguments

    L   -  Liouvillian matrix

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

Outputs

  projectors - a cell array of projectors into independently
               evolving reduced 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 what this function does is available in our papers on this subject 

             http://dx.doi.org/10.1016/j.jmr.2008.08.008
             http://dx.doi.org/10.1063/1.3398146
             http://dx.doi.org/10.1016/j.jmr.2011.03.010

Briefly, the function tries symmetry factorisation, followed by zero track elimination, followed by disconnected subspace identifcation by path tracing.

See also

zte.m, path_trace.m, symmetry.m, perm_group.m


Version 2.2, authors: Ilya Kuprov, Luke Edwards, Matthew Krzystyniak

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