Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2008-10-15
Math.Comput.Simul.80:732,2009
Physics
Condensed Matter
Other Condensed Matter
14 pages, 2 figures; to appear in Journal of Mathematics and Computers in Simulation
Scientific paper
10.1016/j.matcom.2009.08.025
In this work, we highlight the correspondence between two descriptions of a system of ultracold bosons in a one-dimensional optical lattice potential: (1) the discrete nonlinear Schr\"{o}dinger equation, a discrete mean-field theory, and (2) the Bose-Hubbard Hamiltonian, a discrete quantum-field theory. The former is recovered from the latter in the limit of a product of local coherent states. Using a truncated form of these mean-field states as initial conditions, we build quantum analogs to the dark soliton solutions of the discrete nonlinear Schr\"{o}dinger equation and investigate their dynamical properties in the Bose-Hubbard Hamiltonian. We also discuss specifics of the numerical methods employed for both our mean-field and quantum calculations, where in the latter case we use the time-evolving block decimation algorithm due to Vidal.
Carr Lincoln D.
Mishmash Ryan V.
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