Difference between revisions of "Corrfun.m"

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Rotational correlation function, normalized to be the correlation func-
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{{DISPLAYTITLE:corrfun.m}} __NOTOC__
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tion between second rank Wigner functions. Syntax:
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Wigner matrix element correlation function under isotropic, axial, and rhombic rotational diffusion.
  
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              [weights,rates]=corrfun(spin_system,k,m,p,q)
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==Syntax==
  
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where the indices k,m,p,q correspond to the four indices found in the
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    [weights,rates,states]=corrfun(spin_system,n,k,m,p,q)
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ensemble-averaged Wigner function product:
 
  
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                        G=<D2(k,m)'*D2(p,q)>
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==Arguments==
  
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the function requires spin_system.rlx.tau_c to be either a single cor-
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    spin_system - the output of [[create.m]] to which ro-
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relation time (in which case the isotropic rotational diffusion model
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                    tational correlation time should have
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is used) or vector with two correlation times (in which case they are
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                    been supplied. For a single correlation
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assumed to be correlation times for rotation around and perpendicular-
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                    time, the isotropic rotational diffusi-
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ly to the main axis respectively) or vector with three correlation ti-
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                    on model is used; a vector with two
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mes (in which case those are assumed to be the correlation times for
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                    correlation times is assumed to be cor-
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the rotation around the XX, YY and ZZ direction respectively of the
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                    relation times for rotation around and
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rotational diffusion tensor).
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                    perpendicularly to the main axis res-
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                    pectively); a vector with three corre-
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                    lation times is assumed to be the cor-
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                    relation times for the rotation around
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                    the XX, YY and ZZ direction respecti-
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                    vely of the rotational diffusion tensor.
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      n,k,m,p,q  - the five indices found in the ensemble-
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                    averaged Wigner function product:
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                          <D{n}{k,m}(0)*D{n}{p,q}(t)'>
  
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The function returns the weights and decay rates of the individual ex-
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==Outputs==
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ponentials in the correlation function. Note that the decay rates re-
 
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turned are negative numbers.
 
  
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Note: Wigner function indices are sorted in descending order, that is,
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      weights    - a cell array (one element for each che-
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[1 2 3 4 5] in the input maps onto [2 1 0 -1 -2].
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                    mical species) of vectors listing the
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                    weights of the exponential components
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                    of the decays
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      rates      - a cell array (one element for each che-
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                    mical species) of vectors listing the
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                    decay rates (negative numbers) of the
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                    exponential components of the decays
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      states      - a cell array (one element for each che-
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                    mical species) of logical vectors indi-
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                    cating which states in the basis set
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                    belong to which chemical species
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==Notes==
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# Wigner function indices are sorted in descending order, that is, k=[1 2 3 4 5] in the input represents [2 1 0 -1 -2] for n=2.
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# Second rank rotational correlation times (as per Spinach input) will be updated automatically if other ranks are specified.
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==See also==
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[[relaxation.m]], [[lindbladian.m]], [[rwalk.m]]
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''Version 2.3, authors: [[Ilya Kuprov]]''

Revision as of 18:14, 27 December 2018

Wigner matrix element correlation function under isotropic, axial, and rhombic rotational diffusion.

Syntax

    [weights,rates,states]=corrfun(spin_system,n,k,m,p,q)

Arguments

    spin_system - the output of create.m to which ro-
                   tational correlation time should have 
                   been supplied. For a single correlation
                   time, the isotropic rotational diffusi-
                   on model is used; a vector with two
                   correlation times is assumed to be cor-
                   relation times for rotation around and
                   perpendicularly to the main axis res-
                   pectively); a vector with three corre-
                   lation times is assumed to be the cor-
                   relation times for the rotation around
                   the XX, YY and ZZ direction respecti-
                   vely of the rotational diffusion tensor.

     n,k,m,p,q   - the five indices found in the ensemble-
                   averaged Wigner function product:

                         <D{n}{k,m}(0)*D{n}{p,q}(t)'>

Outputs

     weights     - a cell array (one element for each che-
                   mical species) of vectors listing the 
                   weights of the exponential components
                   of the decays

     rates       - a cell array (one element for each che-
                   mical species) of vectors listing the 
                   decay rates (negative numbers) of the
                   exponential components of the decays

     states      - a cell array (one element for each che-
                   mical species) of logical vectors indi-
                   cating which states in the basis set
                   belong to which chemical species

Notes

  1. Wigner function indices are sorted in descending order, that is, k=[1 2 3 4 5] in the input represents [2 1 0 -1 -2] for n=2.
  2. Second rank rotational correlation times (as per Spinach input) will be updated automatically if other ranks are specified.

See also

relaxation.m, lindbladian.m, rwalk.m


Version 2.3, authors: Ilya Kuprov

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