I Theory of fluctuations in disordered systems

giulio_hep
Messages
104
Reaction score
6
TL;DR Summary
In the computation of the dynamic exponents from the
cubic expansion, I'm asking clarifications and a clear explanation about the interaction term and what are the symmetries in the monomials
I'm reading the https://www.phys.uniroma1.it/fisica/sites/default/files/DOTT_FISICA/MENU/03DOTTORANDI/TesiFin26/Urbani.pdf at paragrph 4.6.2 "The interaction term".

They write a right hand side:

< f(na,nb) f(nc,nd) f(ne,nf) >

and they want to use a symmetry, for example they assume that <na3ndnf2> is equal to <na3nb2nc>

It looks like c = d and b = f at first sight, but which is the correct symmetry really? I can't find an explanation in the previous pages: any idea? Thanks
 
Physics news on Phys.org
Indeed my doubt is somehow reinforced from what I read in "Static replica approach to critical correlations in glassy systems" (same authors, among which again Pierfrancesco Urbani and this year's Nobel Prize, Giorgio Parisi) ref. 12A540-22 paragraph "C. Expression of λ in HNC", page 23, where it is written:

Here we have again to symmetrize Eq. (153) with respect to the exchanges
a ↔ b, c ↔ d, e ↔ f, ab ↔ cd, ab ↔ ef, cd ↔ ef
because these have been used explicitly to derive Eq. (97).

Again, while the exchange of c with d would make sense for symmetry of f(.,.), my intuition was also able to get the exchange of ab with ef, but it is still a mystery for me to understand the exchange of just b with f... or (put together) of df ↔ cb
 
From the BCS theory of superconductivity is well known that the superfluid density smoothly decreases with increasing temperature. Annihilated superfluid carriers become normal and lose their momenta on lattice atoms. So if we induce a persistent supercurrent in a ring below Tc and after that slowly increase the temperature, we must observe a decrease in the actual supercurrent, because the density of electron pairs and total supercurrent momentum decrease. However, this supercurrent...
Back
Top