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Anomalous Spectral Function of Superconductors: New Insights and Analytical Comparisons

A study on anomalous spectral functions in superconductors with fresh results and comparison to BCS model using maximum-entropy method and Padé approximants. References to key works like Jaynes' Information Theory and Statistical Mechanics are included.

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Anomalous Spectral Function of Superconductors: New Insights and Analytical Comparisons

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  1. #2 Anomalous_spectral__function of___superconductors Tomáš Bzdušek Advisor: Doc. RNDr. Richard Hlubina, CSc. 13. 11. 2012

  2. Laplace Jaynes

  3. Take probability distribution which • is compatible with our information, • and which has the maximum possible entropy! Jaynes

  4. If cube is replaced with a many-particle system… Jaynes

  5. What is the use in my problem? Jaynes

  6. probabilistic interpretation!

  7. Naïve method of analytic continuation:Padé approximants

  8. Fresh results and a comparison to BCS model

  9. Fresh results – A(x) l = 1, T/w0 = 0.005, n = 2500, E=25, r = 30, s = 2, ek= 0

  10. Fresh results – B(x) l = 1, T/w0 = 0.005, n = 2500, E=25, r = 35, s = 2,ek= 0

  11. Fresh results – Z(x) on real axis Real Imaginary l = 1, T/w0 = 0.005, n = 2500, E=25, r = 45, s = 2

  12. Fresh results – D(x) on real axis Real Imaginary l = 1, T/w0 = 0.005, n = 2500, E=25, r = 45, s = 2

  13. References • E. T. Jaynes: Information Theory and Statistical Mechanics, Phys. Rev. 106, 620—630 (1957) • R. N. Silver, D. S. Sivia, J. E. Gubernatis: Maximum-entropy method for analytic continuation of quantum Monte Carlo data, Phys. Rev. B 41, 2380—2389 (1990) • H. J. Vidberg, J. W. Serene: Solving the Eliashberg equations by means of N-point Padé approximants, J. of Low Temperature Physics 3-4, 179—192 (1977) • K. S. D. Beach, R. J. Gooding, F. Marsiglio: Reliable Padé analytical continuation method based on a high-accuracy symbolic computation algorithm, Phys. Rev. B 61, 5147—5157 (2000)

  14. Thank you for your attention! Real Imaginary

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