Journal
PHYSICAL REVIEW A
Volume 104, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.104.023308
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This study investigates the two-body scattering of particles in a one-dimensional periodic potential and utilizes a convenient ansatz to separate center-of-mass and relative motion, resulting in a discrete Schrodinger equation resembling a tight-binding model. By defining distinct scattering lengths and discussing collision resonances, the research reveals the interaction between different bands and collision resonances in the excited band.
This study concerns the two-body scattering of particles in a one-dimensional periodic potential. A convenient ansatz allows for the separation of center-of-mass and relative motion, leading to a discrete Schrodinger equation in the relative motion that resembles a tight-binding model. A lattice Green's function is used to develop the Lippmann-Schwinger equation, and ultimately derive a multiband scattering K matrix which is described in detail in the two-band approximation. Two distinct scattering lengths are defined according to the limits of zero relative quasimomentum at the top and bottom edges of the two-body collision band. Scattering resonances occur in the collision band when the energy is coincident with a bound state attached to another higher or lower band. Notably, repulsive on-site interactions in an energetically closed lower band lead to collision resonances in an excited band.
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