  Ballistic transport of a quantum system can be characterized by Drude weight,
which quantifies the response of the system to a uniform electric field in the
infinitely long timescale. The Drude weight is often discussed in terms of the
Kohn formula, which gives the Drude weight by the derivative of the energy
eigenvalue of a finite-size system with the periodic boundary condition in
terms of the Aharonov-Bohm flux. Recently, the Kohn formula is generalized to
nonlinear responses. However, the nonlinear Drude weight determined by the Kohn
formula often diverges in the thermodynamic limit. In order to elucidate the
issue, in this work we examine a simple example of a one-dimensional
tight-binding model in the presence of a single defect at zero temperature. We
find that its linear and non-linear Drude weights given by the Kohn formula (i)
depend on the Aharonov-Bohm flux and (ii) diverge proportionally to a power of
the system size. We argue that the problem can be attributed to different order
of limits. The Drude weight according to the Kohn formula (``Kohn--Drude
weight'') indicates the response of a finite-size system to an adiabatic
insertion of the Aharonov-Bohm flux. While it is a well-defined physical
quantity for a finite-size system, its thermodynamic limit does not always
describe the ballistic transport of the bulk. The latter should be rather
characterized by a ``bulk Drude weight'' defined by taking the thermodynamic
limit first before the zero-frequency limit. While the potential issue of the
order of limits has been sometimes discussed within the linear response, the
discrepancy between the two limits is amplified in nonlinear Drude weights. We
demonstrate the importance of the low-energy excitations of $O(1/L)$, which are
excluded from the Kohn--Drude weight, in regularizing the bulk Drude weight.
