Can the trace formula describe weak localisation?

Abstract

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.

23 pages in Latex (with IOP style files), 3 eps figures included, to be a symposium paper in a Topical Issue of Waves in Random Media, 1999

References in corpus (2)

• Quantum Billiards with Surface Scattering: Ballistic Sigma-Model Approach
• Spectral statistics in disordered metals: a trajectories approach

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• The Leading Off-Diagonal Correction to the Form Factor of Large Graphs
• Ehrenfest time in the weak dynamical localization
• Loschmidt Echo and Lyapunov Exponent in a Quantum Disordered System
• The Ehrenfest Oscillations in The Level Statistics of Chaotic Quantum Dots
• Classical basis for quantum spectral fluctuations in hyperbolic systems
• Non-linear $\sigma$-model for long range disorder and quantum chaos
• Weak localization in disordered systems at the ballistic limit