When we add the disorder to the strong correlated Fermi gases in optical lattices, what is the most convenient way to evaluate the degree of localization of system numerically? Thank you very much in advance . . .
Hi.
As you know, adding disorder to a periodic electronic or optical system leads to defects states/modes in its electronic structure or optical response. For a 2D case, the answer of the master equation might be something like this: f(x,y)=exp(i*k_x*x)g(y), where g(y)=Aexp(k_y*y)+Bexp(-k_y*y). And, therefore, |1/Re(k_y)| could be the best estimate for the localization length of defect modes of the considered system.
Thank you very much for your kind answer. In my system, the localization is induced by the disorder, which is, to some extant , similar to the Anderson localization. And if I want to know how much.... or maybe the degree of the localization in the system, what kind of quantities should I choose to describe this situation? Of course the localization length is a good choice, but it is not very convenient to measure this quantity in my calculation. So, Do you have any other advice? say, some special correlation functions. Thank you very much ...
Thank you very much. Actually I have calculated that quantity. But it seem that this quantum can just figure out the point when the localization started to form. I hope to know the further information in the latter process when I strengthen the disorder, especially when the system is totally localized (when most of the order in the system is broken). Thank you~~
Dear Chen, There are many methods to measure the localization effect and degree of localization as well. The measurement of quantum dispersion in position, momentum or energy space and its comparison with the respective classical dispersion will show the signature of Localization. If one compare the behaviour of classical and quantum dispersion with time he can find the signature of dynamical localization.
Another way to measure localization is to measure the escape probability from a specified regions. Behaviour of escape probability by changing the length of specified region will give you the localization length and of course the degree of localization.
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