  In this work, we consider a torque caused by the well known quantum
mechanical Casimir effect arising from quantized field fluctuations between
plates with inhomogeneous, sharply discontinuous, dielectric properties. While
the Casimir effect is a relatively well understood phenomenon, systems
resulting in lateral or rotational forces are far less developed; to our
knowledge, a theoretical study of discontinuous dielectric variants of such
systems has not been attempted. We utilize a Proximity Force Approximation in
conjunction with the Lifshitz dielectric formula to perform theoretical
analyses of resultant torques in systems with bisected and quadrisected
dielectric regions. We also develop a high precision Monte Carlo type numerical
integrator to approximate our derived expressions. Our calculations of an
energy density linear with the alignment angle result in a constant torque and
have implications in NEMS (nano electromechanical systems) and MEMS (micro
electromechanical systems), including a postulated nanoscale oscillating drive
mechanism powered by quantum field interactions.
