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Journal Article

Coulomb potential V(r)=1/r problem on the Bethe lattice

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Petrova,  Olga
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Moessner,  Roderich
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Petrova, O., & Moessner, R. (2016). Coulomb potential V(r)=1/r problem on the Bethe lattice. Physical Review E, 93(1): 012115. doi:10.1103/PhysRevE.93.012115.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-A820-D
Abstract
We study the problem of a particle hopping on the Bethe lattice in the presence of a Coulomb potential. We obtain an exact solution to the particle's Green's function along with the full energy spectrum. In addition, we present a mapping of a generalized radial potential problem defined on the Bethe lattice to an infinite number of one-dimensional problems that are easily accessible numerically. The latter method is particularly useful when the problem admits no analytical solution.