Periodic mean-field solutions and the spectra of discrete bosonic fields: Trace formula for Bose-Hubbard models.

@article{Engl2015PeriodicMS,
  title={Periodic mean-field solutions and the spectra of discrete bosonic fields: Trace formula for Bose-Hubbard models.},
  author={Thomas Engl and Juan Diego Urbina and Klaus Richter},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2015},
  volume={92 6},
  pages={
          062907
        }
}
We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number N. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, nonperturbative solutions of the, typically nonlinear, wave equation of the classical (mean-field) limit. To this end, we construct the semiclassical approximation for both the smooth and oscillatory parts of the… CONTINUE READING
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