We investigate nonlinear rheology of dilute liquid crystalline polymer
solutions under time dependent two-directional shear flow. We analyze the
Smoluchowski equation, which describes the dynamics of the orientation of a
liquid crystalline polymer, by employing technique of the full counting
statistics. In the adiabatic limit, we derive the expression for time
integrated currents generated by a Berry-like curvature. Using this expression,
it is shown that the expectation values of the time-integrated angular velocity
of a liquid crystalline polymer and the time-integrated stress tensor are
generally not zero even if the time average of the shear rate is zero. The
validity of the theoretical calculations is confirmed by direct numerical
simulations of the Smoluchowski equation. Nonadiabatic effects are also
investigated by simulations and it is found that the time-integrated stress
tensor depends on the speed of the modulation of the shear rate if we adopt the
isotropic distribution as an initial state.Comment: 22 pages, 2 figure
