Geometric chaoticity leads to ordered spectra for randomly interacting fermions

Area of Science:

• Quantum mechanics
• Nuclear physics
• Statistical mechanics

Background:

• Empirical observations show ground states in certain systems predominantly possess zero or maximum spin.
• Understanding the underlying mechanisms for spin distribution in quantum systems is crucial.
• Previous models have not fully explained the dominance of these specific spin states.

Purpose of the Study:

• To realize and investigate a rotationally invariant random interaction ensemble in a single- j fermion model.
• To statistically explain the observed dominance of zero and maximum spin ground states.
• To analyze the role of random coupling of angular momenta in determining ground state properties.

Main Methods:

• Implementation of a rotationally invariant random interaction ensemble.
• Utilizing a single- j fermion model.
• Employing a statistical approach to analyze coupling mechanisms.
• Examining the structure of ground state wave functions.

Main Results:

• Successfully realized a rotationally invariant random interaction ensemble.
• Statistical analysis identified random coupling of individual angular momenta as the source of spin dominance.
• Ground states with zero and maximum spin were found to be empirically dominant.
• The structure of ground state wave functions supports this interpretation.

Conclusions:

• The study provides a statistical explanation for the prevalence of zero and maximum spin ground states.
• Random coupling of angular momenta is confirmed as a key factor in fermion system spin distributions.
• The findings offer insights into the statistical properties of quantum systems and their ground state configurations.