Statistical properties of the quantum anharmonic oscillator

TL;DR

This paper investigates the statistical properties of eigenenergies in quantum anharmonic oscillators and compares numerical results with predictions from random matrix theory, enhancing understanding of complex quantum systems.

Contribution

It provides a numerical analysis of eigenenergy statistics in quantum anharmonic oscillators and compares these with random matrix theory predictions, offering new insights into their spectral properties.

Findings

Eigenenergy distributions align with random matrix theory predictions.

Statistical properties vary with different anharmonic potentials.

Results support the applicability of RMT to complex quantum systems.

Abstract

The random matrix ensembles (RME) of Hamiltonian matrices, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applicable to following quantum statistical systems: nuclear systems, molecular systems, condensed phase systems, disordered systems, and two-dimensional electron systems (Wigner-Dyson electrostatic analogy). A family of quantum anharmonic oscillators is studied and the numerical investigation of their eigenenergies is presented. The statistical properties of the calculated eigenenergies are compared with the theoretical predictions inferred from the random matrix theory. Conclusions are derived.