A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems

Details A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems A Trace Formula for Products of Diagonal Matrix Elements in Chaotic Systems

1999-08-05

arxiv.org/abs/chao-dyn/9908009v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

8 pages; analysis made more rigorous in the revised version

Scientific paper

10.1103/PhysRevE.61.R2180

We derive a trace formula for $\sum_n A_{nn}B_{nn}...\delta(E-E_n)$, where $A_{nn}$ is the diagonal matrix element of the operator $A$ in the energy basis of a chaotic system. The result takes the form of a smooth term plus periodic-orbit corrections; each orbit is weighted by the usual Gutzwiller factor times $A_p B_p ...$, where $A_p$ is the average of the classical observable $A$ along the periodic orbit $p$. This structure for the orbit corrections was previously proposed by Main and Wunner (chao-dyn/9904040) on the basis of numerical evidence.

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