Anomalous _spectral __function of ___superconductorsTomáš BzdušekAdvisor: Doc. RNDr. Richard Hlubina, CSc.

13. 11. 2012

#2

Laplace Jaynes

Jaynes

Take probability distribution which• is compatible with our

information,• and which has the maximum

possible entropy!

Jaynes

If cube is replaced with a many-particle system…

Jaynes

What is the use in my problem?

probabilistic interpretation!

Naïve method of analytic continuation:Padé approximants

Fresh resultsand a comparison to BCS model

Fresh results – A(x)

l = 1, T/w0 = 0.005, n = 2500, E=25, r = 30, s = 2, ek = 0

Fresh results – B(x)

l = 1, T/w0 = 0.005, n = 2500, E=25, r = 35, s = 2, ek = 0

Fresh results – Z(x) on real axis

l = 1, T/w0 = 0.005, n = 2500, E=25, r = 45, s = 2

RealImaginary

Fresh results – D(x) on real axis

l = 1, T/w0 = 0.005, n = 2500, E=25, r = 45, s = 2

RealImaginary

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)

RealImaginary

Thank you for your attention!