Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1999-02-24
Waves in Random Media, 9, 179-200 (1999)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
23 pages in Latex (with IOP style files), 3 eps figures included, to be a symposium paper in a Topical Issue of Waves in Rando
Scientific paper
10.1088/0959-7174/9/2/307
We attempt to systematically derive perturbative quantum corrections to the Berry diagonal approximation of the two-level correlation function (TLCF) for chaotic systems. To this end, we develop a ``weak diagonal approximation'' based on a recent description of the first weak localisation correction to conductance in terms of the Gutzwiller trace formula. This semiclassical method is tested by using it to derive the weak localisation corrections to the TLCF for a semiclassically disordered system. Unfortunately the method is unable to correctly reproduce the ``Hikami boxes'' (the relatively small regions where classical paths are glued together by quantum processes). This results in the method failing to reproduce the well known weak localisation expansion. It so happens that for the first order correction it merely produces the wrong prefactor. However for the second order correction, it is unable to reproduce certain contributions, and leads to a result which is of a different form to the standard one.
Lerner Igor V.
Smith Robert A.
Whitney Robert S.
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