where ξ identifies the variable(s) which the connection depends on. If γ (C) depends on the geometry of the path, it is called a geometric phase. Usually, however, the con-cept of geometric phase has been discussed in relation to the adiabatic approximation (not that of time-dependent DFT), namely when considering that the Hamiltonian of the system depends on some parameter that varies slowly, i.e. adiabatically. In this case, when an eigenstate of the Hamiltonian is tranported along a closed path in the parameter space, the eigenstate can pick up a geometric phase factor in addition to the standard dynamical phase factor that comes from the Schrödinger equation.