Statistical properties of the quantum anharmonic oscillator in one spatial dimension

TL;DR

This paper investigates the statistical properties of eigenenergies in a family of one-dimensional quantum anharmonic oscillators, comparing numerical results with predictions from random matrix theory to understand their spectral behavior.

Contribution

It provides a numerical analysis of eigenenergy statistics for quantum anharmonic oscillators and compares findings with random matrix theory predictions, highlighting their applicability.

Findings

Eigenenergy distributions align with random matrix theory predictions

Spectral statistics exhibit characteristics of complex quantum systems

Results support the use of RMT in modeling quantum anharmonic oscillators

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 in one spatial dimension 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.