  We study a possible scenario of the Lorentz symmetry violation background
that allows us to build an analogue of the Landau system for a nonrelativistic
Dirac neutral particle interacting with a field configuration of crossed
electric and magnetic fields. We also discuss the arising of analogues of the
Rashba coupling, the Zeeman term and the Darwin term from the Lorentz symmetry
breaking effects, and the influence of these terms on the analogue of the
Landau system confined to a two-dimensional quantum ring. Finally, we show that
this analogy with the Landau system confined to a two-dimensional quantum ring
allows us to establish an upper bound for the Lorentz symmetry breaking
parameters.
