  Kilometer$^3$-scale neutrino detectors such as IceCube, ANTARES, and the
proposed Km3Net neutrino observatory in the Mediterranean have measured, and
will continue to characterize, the atmospheric neutrino spectrum above 1 TeV.
Such precise measurements enable us to probe new neutrino physics, in
particular, those that arise from Lorentz violation. In this paper, we first
relate the effective new physics hamiltonian terms with the Lorentz violating
literature. Second, we calculate the oscillation probability formulas for the
two-level $\nu_\mu-\nu_\tau$ sector. Finally, we comment on some of the
challenges and outlook for this analysis.
