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Updated: Aug 7, 2026
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Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Quantum chaotic patterns in the E (b1 + b2) Jahn-Teller model
1Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, Bratislava, Slovak Republic. fyziemar@savba.sk
Summary
Statistical properties of excited levels in the Jahn-Teller model reveal a stable nearest-neighbor spacing distribution, differing from Wigner predictions. This distribution resembles the semi-Poisson law, potentially indicating universal behavior in phase transitions.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Statistical physics
Background:
- The Jahn-Teller effect describes geometric distortions in molecules and solids.
- Avoided crossings in energy levels are often associated with quantum chaos.
- Understanding level spacing distributions is crucial for characterizing quantum systems.
Purpose of the Study:
- To investigate the statistical properties of excited energy levels in the E (b(1) + b(2)) Jahn-Teller model.
- To determine if the distribution of nearest-neighbor spacings indicates quantum chaos.
- To analyze the behavior of this distribution across different model parameters.
Main Methods:
- Analysis of the E (b(1) + b(2)) Jahn-Teller model.
- Calculation of energy level statistics.
- Comparison of nearest-neighbor spacing distributions with known statistical laws (e.g., Wigner, semi-Poisson).
Main Results:
- The nearest-neighbor spacing distribution is largely stable across parameter variations, except for two limiting cases.
- The distribution deviates from the Wigner distribution typically associated with quantum chaos.
- A limiting distribution is observed that exhibits approximate radical S scaling for small spacings and resembles the semi-Poisson law for larger spacings.
Conclusions:
- The studied Jahn-Teller model, in general, does not exhibit the Wigner distribution characteristic of quantum chaos.
- The observed semi-Poisson-like distribution suggests potential universality, possibly linked to phenomena like metal-insulator transitions.
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