6,939 research outputs found
Beyond Fermi pseudopotential: a modified GP equation
We present an effective potential and the corresponding modified
Gross-Pitaevskii equation that account for the energy dependence of the
two-body scattering amplitude through an effective-range expansion. For the
ground state energy of a trapped condensate, the theory leads to what we call a
shape-dependent confinement correction that improves agreements with diffusion
Monte Carlo calculations. The theory illustrates, for relatively strong
confinement and/or high density, how the shape dependence on atom-atom
interaction can come into play in a many-atom quantum system.Comment: 8 pages, 5 figure
Topological Band Theory for Non-Hermitian Hamiltonians
We develop the topological band theory for systems described by non-Hermitian
Hamiltonians, whose energy spectra are generally complex. After generalizing
the notion of gapped band structures to the non-Hermitian case, we classify
"gapped" bands in one and two dimensions by explicitly finding their
topological invariants. We find nontrivial generalizations of the Chern number
in two dimensions, and a new classification in one dimension, whose topology is
determined by the energy dispersion rather than the energy eigenstates. We then
study the bulk-edge correspondence and the topological phase transition in two
dimensions. Different from the Hermitian case, the transition generically
involves an extended intermediate phase with complex-energy band degeneracies
at isolated "exceptional points" in momentum space. We also systematically
classify all types of band degeneracies.Comment: 6 pages, 3 figures + 6 pages of supplemental materia
- …