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Chaotic Dynamics in a Quantum Fermi-Pasta-Ulam Problem.
Alexander L Burin1, Andrii O Maksymov1, Ma'ayan Schmidt1
1Department of Chemistry, Tulane University, New Orleans, LA 70118, USA.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
We studied quantum Fermi-Pasta-Ulam systems to understand chaotic vibrations in atomic chains. Chaotic behavior emerges at lower energies in systems with free or fixed ends compared to periodic ones.
Area of Science:
- Quantum mechanics
- Condensed matter physics
- Nonlinear dynamics
Background:
- The Fermi-Pasta-Ulam problem explores energy localization in anharmonic systems.
- Understanding chaotic dynamics is crucial for predicting material properties.
Purpose of the Study:
- Investigate the emergence of chaotic dynamics in a quantum Fermi-Pasta-Ulam problem.
- Analyze anharmonic vibrations in atomic chains.
- Determine the crossover energy between chaotic and localized phases.
Main Methods:
- Semi-quantitative analysis of resonant interactions.
- Exact diagonalization numerical studies.
- Analysis of boundary conditions (free, fixed, periodic).
Main Results:
- Estimated the crossover energy separating chaotic and localized phases.
- Found crossover energy decreases inversely with the number of atoms, saturating in the quantum regime.
- Chaotic behavior appears at lower energies for free/fixed ends compared to periodic systems.
Conclusions:
- The study provides insights into quantum chaos in anharmonic atomic chains.
- Results are relevant for understanding energy transport and stability in molecular systems.
- Boundary conditions significantly influence the onset of chaos.
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