# Correlations in eigenfunctions of quantum chaotic systems with sparse Hamiltonian matrices

## TL;DR

This paper investigates correlations in eigenfunctions of quantum chaotic systems with sparse Hamiltonian matrices, deriving explicit formulas and validating them through numerical simulations, with applications to transition probabilities.

## Contribution

It provides new analytical expressions for eigenfunction correlations in sparse Hamiltonian systems, supported by numerical validation and an application to transition probabilities.

## Key findings

- Derived explicit correlation functions for eigenfunctions
- Validated analytical results with numerical simulations
- Established a relation between correlations and transition probabilities

## Abstract

In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation functions with respect to energy. The analytical results are tested in several models by numerical simulations. An application is given for a relation between transition probabilities.