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Updated: Aug 9, 2026
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Published on: December 4, 2017
Spectral statistics in noninteracting many-particle systems
L Muñoz1, E Faleiro, R A Molina
1Departamento de Física Atómica, Molecular y Nuclear, Universidad Complutense de Madrid, E-28040 Madrid, Spain.
Summary
Noninteracting many-body systems exhibit Poisson-like spectral fluctuations at high energies. However, chaotic mean fields cause deviations from these statistics beyond a critical energy scale, revealing quantum chaos characteristics.
Area of Science:
- Quantum mechanics
- Statistical physics
- Chaos theory
Background:
- Energy level spectra statistical properties are key to understanding quantum chaos.
- Noninteracting many-body systems are assumed to show Poisson fluctuations, but lack rigorous proof.
- Previous studies focused on systems like quantum billiards, atoms, and atomic nuclei.
Purpose of the Study:
- To rigorously investigate the spectral fluctuations of noninteracting identical particles in a mean field.
- To analyze how these fluctuations evolve with the number of particles (N) and energy.
- To determine the conditions under which Poisson statistics hold and when deviations occur.
Main Methods:
- Systematic numerical calculations were performed.
- A rigorous derivation was developed.
- The study analyzed spectral fluctuations in relation to particle number and energy levels.
Main Results:
- For N ≥ 2, spectra exhibit Poisson fluctuations at sufficiently high excitation energies.
- A critical energy scale, L(c), was identified.
- Beyond L(c), fluctuations deviate from Poisson statistics when the mean field is chaotic.
Conclusions:
- Noninteracting many-body systems display Poisson fluctuations at high energies, confirming prior assumptions.
- The chaotic nature of the mean field influences spectral statistics beyond a critical energy.
- This work provides a rigorous framework for understanding quantum chaos in many-body systems.
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