arXiv subjects

Gilles Poirot

Publications and source records attributed to Gilles Poirot.

4 recordsLinked to original sources

arXiv2000

Rigorous Schrieffer-Wolff transformation for the Anderson impurity model

With the help of computer algebra, I devise an exact unitary transformation for the Anderson impurity model which allows to kill the hybridization term in the slightly simplified case of zero chemical potential. Then I compute explicitly the outcome of this transformation. This is a rigorous version of the well known Schrieffer-Wolff transformation. It should be possible to treat the general case at the price of increased computation time.

cond-mat.str-el↗

arXiv1998

Ward type identities for the 2d Anderson model at weak disorder

Using the particular momentum conservation laws in dimension d=2, we can rewrite the Anderson model in terms of low momentum long range fields, at the price of introducing electron loops. The corresponding loops satisfy a Ward type identity, hence are much smaller than expected. This fact should be useful for a study of the weak-coupling model in the middle of the spectrum of the free Hamiltonian.

cond-mat.dis-nn↗

arXiv1997

A Single Slice 2d Anderson Model at Weak Disorder

We introduce a matrix-operator formulation of the Anderson model in d=2. In a single slice, we can then derive an analogy between our model and a standard random matrices problem. This enables us to construct and control the Green function in one slice, which is an important prerequisite to a full multi-scale study of the problem using the Renormalisation Group approach.

cond-mat.dis-nn↗

arXiv1997

Mean Green's function of the Anderson model at weak disorder with an infra-red cut-off

We develop a polymer expansion with large/small field conditions for the mean resolvent of a weakly disordered system. Then we show that we can apply our result to a two-dimensional model, for energies outside the unperturbed spectrum or in the free spectrum provided the potential has an infra-red cut-off. This leads to an asymptotic expansion for the density of states. We believe this is an important first step towards a rigourous analysis of the density of states in the free spectrum of a random Schrödinger operator at weak disorder.

cond-mat.dis-nn↗