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Current algebra for a generalized two-sites Bose-Hubbard model

In: Physical and Mathematical Aspects of Symmetries

Author

Listed:
  • Gilberto N. Santos Filho

    (Centro Brasileiro de Pesquisas Físicas - CBPF, Rua Dr. Xavier Sigaud)

Abstract

I present a current algebra for a generalized two-sites Bose-Hubbard model and use it to get the quantum dynamics of the currents. Different choices of the Hamiltonian parameters yield different dynamics. The current algebra is isomorphic to the SO(3)-algebra of the angular momentum. Using the wave functions I discuss the symmetries of the system. The Hamiltonian has one conserved quantity, the total number of atoms N, that is related to its global U(1) gauge symmetry. The $$ \mathbb {Z}_2 $$ symmetry is associated with the parity of the wave function and is related to the parity of N. I generalize the Heisenberg equation of motion to write the second time derivative of any operator.

Suggested Citation

  • Gilberto N. Santos Filho, 2017. "Current algebra for a generalized two-sites Bose-Hubbard model," Springer Books, in: Sergio Duarte & Jean-Pierre Gazeau & Sofiane Faci & Tobias Micklitz & Ricardo Scherer & Francesco To (ed.), Physical and Mathematical Aspects of Symmetries, pages 299-304, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-69164-0_44
    DOI: 10.1007/978-3-319-69164-0_44
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