CorrelationFunctions with IndexedOperators

[j-moser]

• added possibility to create a CorrelationFunction with IndexedOperators as op1 and op2
• added possbility to evaluate CorrelationFunction
• added a dispatch for MTK.ODESystem for indexed equations, since conjugate substituation is different
• a CorrelationFunction can now be evaluated using a specified NumberedOperator by calling evaluate with additional number parameters
• added test cases for the above

This update should also solve the issues 157,160 and 161

[codecov]

Codecov Report

Merging #164 (109e1ca) into master (546ca6d) will increase coverage by 0.41%.
The diff coverage is 80.88%.

❗ Current head 109e1ca differs from pull request most recent head a00822f. Consider uploading reports for the commit a00822f to get more accurate results

@@            Coverage Diff             @@
##           master     #164      +/-   ##
==========================================
+ Coverage   81.05%   81.47%   +0.41%     
==========================================
  Files          24       24              
  Lines        4445     4598     +153     
==========================================
+ Hits         3603     3746     +143     
- Misses        842      852      +10     

Impacted Files	Coverage Δ
src/QuantumCumulants.jl	100.00% <ø> (ø)
src/utils.jl	90.34% <0.00%> (-6.00%)	⬇️
src/index_average.jl	82.49% <71.42%> (+0.19%)	⬆️
src/index_correlation.jl	83.61% <78.66%> (+0.47%)	⬆️
src/index_utils.jl	94.82% <95.00%> (+1.49%)	⬆️
src/correlation.jl	88.82% <100.00%> (+1.56%)	⬆️
src/diffeq.jl	100.00% <100.00%> (ø)
src/equations.jl	96.49% <100.00%> (+0.41%)	⬆️
src/index_scale.jl	66.99% <100.00%> (+6.14%)	⬆️
src/qnumber.jl	90.25% <100.00%> (ø)

... and 1 file with indirect coverage changes

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[tnadolny]

Hi, I was using the code from this pull request to do some things that did not work in the master branch. I thought I leave some comments, hoping they help to improve the package.

• in test_indexed_correlation.jl, line 133: corr2_sc = scale(corr); Is this a typo? Should it be corr2_sc = scale(corr2);? Using the latter leads to an error in u0_c2 = correlation_u0(corr2_sc, sol.u[end]). This error is avoided when adding filter_func = phase_invariant to the definition of corr2 (this is needed, since eqs_c are also built with the filter function, right?).

• I suggest to add a test including

S2_sc = Spectrum(corr2_sc)
ω = [-10:0.01:10;]Γ_
S2_sc(ω,sol.u[end],p0)

• I still encounter problems with the function correlation_u0. I believe the elements in lhs = [average(substitute(op, subs)) for op in ops] are not always ordered properly, and therefore I sometimes get the error("Could not find initial value for $l !")

• A similar problem occurs when I want to compute a spectrum using S(ω,sol.u[end],p0) and there are two different transitions involved, e.g.

hc = FockSpace(:cavity)
hA = NLevelSpace(:atomA,2)
hB = NLevelSpace(:atomB,2)
h = hc ⊗ hA ⊗ hB

When calling S(ω,sol.u[end],p0), I get an error UndefVarError: ⟨σᴮ121*σᴬ211⟩ not defined. I can imagine that the other order (⟨σᴬ211*σᴮ121⟩) would be defined. Is it possible that somewhere in generating the functions for the Spectrum, one should reorder according to the order of Hilbert spaces?

Thanks!

[ChristophHotter]

Hi @tnadolny
Thank you for your comments. The new version v0.2.18 includes this PR from @j-moser.
I think all of the above comments are addressed and the issues #157 , #160 and #161 are solved in the new version.

[tnadolny]

Yes, the three issues are indeed solved. Thank you!