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Journal Article

Scattering of two particles in a one-dimensional lattice

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Giannakeas,  Panagiotis
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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2106.07586.pdf
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Citation

Rittenhouse, S. T., Giannakeas, P., & Mehta, N. P. (2021). Scattering of two particles in a one-dimensional lattice. Physical Review A, 104(2). doi:10.1103/PhysRevA.104.023308.


Cite as: https://hdl.handle.net/21.11116/0000-0009-464F-1
Abstract
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.