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Chaos in the three-site Bose-Hubbard model: Classical versus quantum
Goran Nakerst1,2, Masudul Haque1,2,3
1Department of Theoretical Physics, Maynooth University, County Kildare, Ireland.
Physical Review. E
|March 18, 2023
Summary
This study compares quantum and classical chaos in a Bose-Hubbard system, finding a strong correspondence between quantum measures and classical Lyapunov exponents.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Chaos theory
Background:
- The Bose-Hubbard model describes interacting bosons on a lattice.
- Understanding quantum chaos is crucial for condensed matter physics.
- Distinguishing chaotic from integrable behavior in quantum systems is challenging.
Purpose of the Study:
- To compare quantum and classical measures of chaos.
- To investigate the Bose-Hubbard system with a mixed chaotic-integrable nature.
- To establish a link between quantum and classical chaos indicators.
Main Methods:
- Analysis of quantum eigenvalue statistics and eigenvector structure.
- Calculation of classical Lyapunov exponents.
- Comparison across varying energy and interaction strengths.
Main Results:
- A strong correspondence was found between quantum and classical chaos measures.
- The system exhibits a mixture of chaotic and integrable behaviors.
- The largest Lyapunov exponent is a multivalued function of energy, unlike in purely chaotic or integrable systems.
Conclusions:
- Quantum and classical chaos measures are strongly correlated in this system.
- The Bose-Hubbard model serves as a valuable testbed for quantum-classical correspondence.
- The multivalued nature of the largest Lyapunov exponent highlights unique system dynamics.
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