  We investigate geometric phase (GP) effects in nonadiabatic transitions
through a conical intersection (CI) in an N-dimensional linear vibronic
coupling (ND-LVC) model. This model allows for the coordinate transformation
encompassing all nonadiabatic effects within a two-dimensional (2D) subsystem
while the other N-2 dimensions form a system of uncoupled harmonic oscillators
identical for both electronic states and coupled bi-linearly with the subsystem
coordinates. The 2D subsystem governs ultra-fast nonadiabatic dynamics through
the CI and provides a convenient model for studying GP effects. Parameters of
the original ND-LVC model define the Hamiltonian of the transformed 2D
subsystem and thus influence GP effects directly. Our analysis reveals what
values of ND-LVC parameters can introduce symmetry breaking in the 2D subsystem
that diminishes GP effects.
