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

Abstract

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.

8 pages; analysis made more rigorous in the revised version

References in corpus (4)

• A proof of the Gutzwiller Semiclassical Trace Formula using Coherent States Decomposition
• Random Matrix Elements and Eigenfunctions in Chaotic Systems
• On the Accuracy of the Semiclassical Trace Formula
• Semiclassical Non-Trace Type Formulas for Matrix Element Fluctuations and Weighted Densities of States

Cited by in corpus (4)

• Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
• Periodic orbit quantization of chaotic systems with strong pruning
• Classical, semiclassical, and quantum investigations of the 4-sphere scattering system
• Eigenstate Thermalization Hypothesis and Random Matrix Theory Universality in Few-Body Systems