This title appears in the Scientific Report :
2024
How functional averaging of spectra gives rise to Maximum-Rényi-Entropy principles
How functional averaging of spectra gives rise to Maximum-Rényi-Entropy principles
The analytic continuation of numerically given correlation functions from the imaginary to the real axis is an ill-conditioned problem with many solutions of comparable quality. The MaxEnt method resolves that ambiguity by preferring solutions with large Shannon entropy relative to a default model....
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Personal Name(s): | Koch, Erik (Corresponding author) |
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Contributing Institute: |
Jülich Supercomputing Center; JSC |
Imprint: |
2024
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Conference: | IFP Seminar, Wien (Austria), 2024-02-20 - |
Document Type: |
Talk (non-conference) |
Research Program: |
Domain-Specific Simulation & Data Life Cycle Labs (SDLs) and Research Groups |
Publikationsportal JuSER |
The analytic continuation of numerically given correlation functions from the imaginary to the real axis is an ill-conditioned problem with many solutions of comparable quality. The MaxEnt method resolves that ambiguity by preferring solutions with large Shannon entropy relative to a default model. An alternative is to calculate the average over all solutions, weighted by their quality. This average spectrum method appears to require no a-priori information, but the choice of the functional measure actually does imply the introduction of a default model. We will discuss how the result of the functional average, in fact, becomes equivalent to a maximum-entropy method, where the entropy is, however, not limited to the conventional Shannon entropy but may be any of the family of Rényi entropies. The choice of the functional measure / entropy has profound consequences for the shape of peaks in the analytically continued spectra. |