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#230 Setup general Lindblad equation

0.3.5
done
nobody
None
nobody
2022-12-30
2022-11-18
Ulf Lorenz
No
What and Why

The paper https://arxiv.org/pdf/2004.01469.pdf seems to present an interesting way to setup a general Lindblad equation.

There may still be surprises, e.g., that you do not end up in thermal equilibrium, but at least you can reduce the problem of setting up a Lindblad operator to the problem of setting up the spectral density.

Acceptance criteria
  • I understand the paper, maybe have the published reference
  • There is a utility function that, given coupling operator, spectral density etc. as input generates the Lindblad Liouvillian.
  • There are a few utility functions to generate simple spectral densities
    • ideas: Ohmian spectral density, Lorentz-broadened peaks, ...
  • There is a highlighted demo that shows the issue in action. Preferably based on some reference calculations. Maybe two demos? Harmonic oscillator and Morse oscillator, for example?
    • Can the MolVibration/OH/3 demo be converted to such a highlighted demo?

Implemented; only implemented a Lorentzian as functor; converted MolVibration/OH/3 to use this scheme with spectral density 1/E.

I am not quite sure yet about the usage of functors for spectral densities, which is why only a single Lorentzian was implemented. Needs some more playtesting to get a good feeling for what you might want to do.

Along the way, I am also not quite sure what to do with the terms that are not easy to calculate (time-dependent Lindblad, Lamb shift); altogether, using a Lindblad Liouvillian feels again awkward like what you do not want to use. Maybe I should try out the exact non-Markovian approach of Tannor etc.

Related

Tickets: #158

Discussion

  • Ulf Lorenz

    Ulf Lorenz - 2022-12-24
    • Milestone: 0.4 goal --> 0.3.5
     
  • Ulf Lorenz

    Ulf Lorenz - 2022-12-24
    • Description has changed:

    Diff:

    --- old
    +++ new
    @@ -11,3 +11,4 @@
     * There are a few utility functions to generate simple spectral densities
         * ideas: Ohmian spectral density, Lorentz-broadened peaks, ...
      * There is a highlighted demo that shows the issue in action. Preferably based on some reference calculations. Maybe two demos? Harmonic oscillator and Morse oscillator, for example?
    +     * Can the MolVibration/OH/3 demo be converted to such a highlighted demo?
    
     
  • Ulf Lorenz

    Ulf Lorenz - 2022-12-25
    • status: open --> assigned
    • assigned_to: Ulf Lorenz
     
  • Ulf Lorenz

    Ulf Lorenz - 2022-12-30
    • Description has changed:

    Diff:

    --- old
    +++ new
    @@ -12,3 +12,11 @@
         * ideas: Ohmian spectral density, Lorentz-broadened peaks, ...
      * There is a highlighted demo that shows the issue in action. Preferably based on some reference calculations. Maybe two demos? Harmonic oscillator and Morse oscillator, for example?
          * Can the MolVibration/OH/3 demo be converted to such a highlighted demo?
    +
    +----
    +
    +Implemented; only implemented a Lorentzian as functor; converted MolVibration/OH/3 to use this scheme with spectral density 1/E.
    +
    +I am not quite sure yet about the usage of functors for spectral densities, which is why only a single Lorentzian was implemented. Needs some more playtesting to get a good feeling for what you might want to do.
    +
    +Along the way, I am also not quite sure what to do with the terms that are not easy to calculate (time-dependent Lindblad, Lamb shift); altogether, using a Lindblad Liouvillian feels again awkward like what you do not want to use. Maybe I should try out the exact non-Markovian approach of Tannor etc.
    
    • status: assigned --> done
    • assigned_to: Ulf Lorenz --> nobody
     

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