Saturday, May 23, 2009

Habemus double-Gap!

Looking at the first plot here, you see that the theoretical model doesn’t fit exceptionally well to the experimental points, although discrepancy may suggest some interesting questions.

The answers are in the double-gap feature of superconducting magnesium diboride.

Several models are proposed in literature; one of the simplest (from a computer programmer’s perspective) is here (eq. 1, 2, 3) .

Something more complex (again, from the point of view of a C programmer who doesn’t like too many parameters) is found here and here.

A graphical representation of the best-fit, before and after the “cure”, follows.



Γ = 0.26395 ± 0.00233
Δ = 2.23258 ± 0.00232
χ2/DoF = 18.5991



Γ = 0.188159 ± 0.001936
Δ1 = 1.776936 ± 0.004897
Δ2 = 3.237412 ± 0.007159
α1 = 0.654955 ± 0.002637
α2 = 1 - α1
χ2/DoF = 3.582845

***

UPDATE: added support for double Gammas.
The reduced χ2 is slightly smaller, but there’s not a great improvement (and, frankly, the two peaks fit even worse...).


Γ1 = 0.198691 ± 0.005649
Γ2 = 0.099561 ± 0.027511
Δ1 = 1.756131 ± 0.006112
Δ2 = 3.173761 ± 0.010527
α1 = 0.660000 ± 0.010597
α2 = 1 - α1
χ2/DoF = 3.417491

***

UPDATE 2:
just out of curiosity, let’s drop the constraint α1>0.66, changing, in common.h:

#define CONSTRAINT_ALPHA1_MIN 0.66

into:

#define CONSTRAINT_ALPHA1_MIN 0.00

The result is a pretty good fit.


Γ1 = 0.049868 ± 0.008484
Γ2 = 0.319827 ± 0.012638
Δ1 = 1.495814 ± 0.004703
Δ2 = 2.820209 ± 0.005726
α1 = 0.384509 ± 0.006055
α2 = 1 - α1
χ2/DoF = 2.793498

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