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Semiclassical quantization of the Bogoliubov spectrum
1Kirensky Institute of Physics, 660036 Krasnoyarsk, Russia.
Physical Review Letters
|August 7, 2007
Summary
We analyzed the Bogoliubov spectrum in a three-site Bose-Hubbard model. This quantum system
Area of Science:
- Quantum mechanics
- Condensed matter physics
Background:
- The Bose-Hubbard model describes interacting bosons on a lattice.
- Understanding the Bogoliubov spectrum is crucial for characterizing quantum systems.
Purpose of the Study:
- To analyze the Bogoliubov spectrum of a three-site Bose-Hubbard model with a finite number of particles.
- To connect the quantum Bogoliubov spectrum to the classical Hubbard model's regular component.
- To identify energy levels and critical transitions to chaos.
Main Methods:
- A semiclassical approach was employed.
- The integrals of motion for the regular component of the classical model were identified.
- Quantization of these integrals yielded the quantum system's energy levels.
Main Results:
- The Bogoliubov spectrum was linked to the low-energy regular component of the classical Hubbard model.
- A complete set of integrals of motion for the regular component was found.
- Critical energy values demarcating regular from chaotic spectral behavior were determined.
Conclusions:
- The semiclassical analysis provides a method for obtaining quantum energy levels from classical dynamics.
- The study elucidates the transition from regular to chaotic spectra in the Bose-Hubbard model.
- This work offers insights into the quantum-classical correspondence in many-body systems.
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