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Floquet-Bloch operator for the Bose-Hubbard model with static field
Andrey R Kolovsky1, Andreas Buchleitner
1Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
Summary
Researchers studied the spectral properties of cold atoms in optical lattices. The system
Area of Science:
- Quantum physics
- Condensed matter physics
Background:
- The Bose-Hubbard model describes interacting cold atoms in optical lattices.
- External fields can significantly alter the system's behavior.
Purpose of the Study:
- To analyze the spectral properties of a one-dimensional Bose-Hubbard model with an external static field.
- To understand the transition between regular and chaotic spectral behavior.
Main Methods:
- Utilized the Floquet-Bloch operator to analyze system evolution over one Bloch period.
- Investigated the spectral properties under varying model parameters.
Main Results:
- The spectral properties were found to be either regular or chaotic, depending on parameter choices.
- In the chaotic regime, the Floquet-Bloch operator matrix resembled a random matrix from the circular orthogonal ensemble.
Conclusions:
- The addition of a static field introduces rich spectral dynamics to the Bose-Hubbard model.
- The chaotic spectral behavior can be accurately described by random matrix theory, specifically the circular orthogonal ensemble.
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