  We investigate non-standard Hamiltonian effects on neutrino oscillations,
which are effective additional contributions to the vacuum or matter
Hamiltonian. Since these effects can enter in either flavor or mass basis, we
develop an understanding of the difference between these bases representing the
underlying theoretical model. In particular, the simplest of these effects are
classified as ``pure'' flavor or mass effects, where the appearance of such a
``pure'' effect can be quite plausible as a leading non-standard contribution
from theoretical models. Compared to earlier studies investigating particular
effects, we aim for a top-down classification of a possible ``new physics''
signature at future long-baseline neutrino oscillation precision experiments.
We develop a general framework for such effects with two neutrino flavors and
discuss the extension to three neutrino flavors, as well as we demonstrate the
challenges for a neutrino factory to distinguish the theoretical origin of
these effects with a numerical example. We find how the precision measurement
of neutrino oscillation parameters can be altered by non-standard effects alone
(not including non-standard interactions in the creation and detection
processes) and that the non-standard effects on Hamiltonian level can be
distinguished from other non-standard effects (such as neutrino decoherence and
decay) if we consider specific imprint of the effects on the energy spectra of
several different oscillation channels at a neutrino factory.
