In the course of two sessions, I will report on lattice QCD studies of two aspects of nucleon structure.
The primary focus will lie on electric polarizabilities of the neutron. One particular difficulty encountered
in investigating these polarizabilities is the evaluation of disconnected contributions; this motivated a
secondary study of the strange quark content of the nucleon, which counts among the simplest contexts
in which disconnected contributions arise.

Polarizabilities encode the response of hadrons to external fields. A calculational scheme, based on a
four-point function approach to the background field method, is developed for obtaining both the static
and the spin electric polarizabilities of the neutron in fully dynamical lattice QCD. Particular emphasis is
placed on the physical role of spatially constant external gauge fields on a finite lattice; the presence of
these fields implies isospin-breaking Bloch momenta, the effects of which have to be carefully disentangled
from the polarizabilities themselves. Calculations are carried out in a mixed action scheme employing domain
wall valence quarks and quark loops on MILC asqtad dynamical fermion ensembles. The results of these
lattice calculations are confronted with chiral effective theory.

In order to gain further insight into the behavior of disconnected contributions to nucleon correlators within
a simpler context, both the scalar strange content of the nucleon as well as the strange quark contribution to
nucleon spin are investigated within the same mixed action scheme. The convergence behavior of stochastic
estimation is seen to depend strongly on the matrix element. Nonzero signals are obtained for both quantities;
neither result is unnaturally large to an extent which would impact either dark matter searches or the nucleon
spin budget.