Boundary effects on quantum q-breathers in a Bose-Hubbard chain

Abstract

We investigate the spectrum and eigenstates of a Bose-Hubbard chain containing two bosons with fixed boundary conditions. In the noninteracting case the eigenstates of the system define a two-dimensional normal-mode space. For the interacting case weight functions of the eigenstates are computed by perturbation theory and numerical diagonalization. We identify paths in the two-dimensional normal-mode space which are rims for the weight functions. The decay along and off the rims is algebraic. Intersection of two paths (rims) leads to a local enhancement of the weight functions. We analyze nonperturbative effects due to the degeneracies and the formation of two-boson bound states.

10 pages, 11 figures. With minor corrections. Accepted in Physica D

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• Interaction-induced topological states of photon pairs
• Simulation of two-boson bound states using arrays of driven-dissipative coupled linear optical resonators
• Majorana representation of adiabatic and superadiabatic processes in three-level systems
• Resonant invisibility with finite range interacting fermions