Seminari del Dipartimento

Fisica Matematica

In this talk, I will present the existence of Large Deviation Principles in the scope of fermionic systems at equilibrium. The physical motivations beyond these studies are experimental measures of electric resistance of nanowires in silicon doped with phosphorus atoms. The latter demonstrates that quantum effects on charge transport almost disappear for nanowires of lengths larger than a few nanometers,  even at a very low temperature (4.2 K). This presentation is closely related to proving (mathematically speaking) for interacting fermions (in presence of impurities) at equilibrium these experimental results.

In the first part, I will describe the existence of a Large Deviation Principle for free fermion systems subjected to external electric fields. After that, I will state that for weakly interacting fermions on the lattice, the logarithm moment generating function of probability distributions associated with KMS states can be written as the limit of logarithms of Gaussian Berezin integrals. The covariances of the Gaussian integrals are shown to have a uniform determinant bound and to be summable even in the disorder setting. Finally, I will discuss how to prove a Large Deviation Principle for current observables in the interacting setting.

Based on joint works with J. B. Bru and W. de Siqueira Pedra.
 
org: GIULIANI Alessandro