https://doi.org/10.1140/epjb/e2013-31134-1
Regular Article
Time delay matrix at the spectrum edge and the minimal chaotic cavities
1 Service de Physique de l’État
Condensé (CNRS URA 2464), IRAMIS/SPEC, CEA Saclay, 91191
Gif-sur-Yvette,
France
2 Laboratoire CRISMAT, UMR 6508 CNRS,
ENSICAEN et Université de Caen Basse Normandie, 6 Boulevard Maréchal Juin, 14050
Caen,
France
a e-mail: adel.abbout@ensicean.fr
Received:
17
December
2012
Received in final form:
20
January
2013
Published online:
27
March
2013
Using the concept of minimal chaotic cavities, we give the distribution of the proper
delay times of at the spectrum edge with a scattering matrix
belonging to circular ensembles. The three classes of
symmetry (β = 1,2 and 4) are analyzed to show how it
differs from the distribution obtained in the bulk of the spectrum. In this new class of
universality at the spectrum edge, more attention is given to the Wigner’s time
τw = Tr(Q) and its
distribution is given analytically in the case of two-mode scattering. The results are
presented exactly at all the Fermi energies without approximation and are tested
numerically with an excellent precision.
Key words: Mesoscopic and Nanoscale Systems
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013