This quantity is acquired by the instantaneous  eigenstate of a quantum system described by a cyclic time-dependent Hamiltonian, depends on the topology of the parameter  space, and is in addition to the dynamical phase.
This quantity causes the change in sign of the electronic wave function discovered by Herzberg and Longuet-Higgins. The  restoration of the single-valuedness of the electron wavefunction for triatomic molecules by Mead and Truhlar was  achieved using this as-yet undiscovered factor. This quantity was shown to be an element from the holonomy group for a  fibre bundle with a certain connection by Barry (*) Simon. It equals one-half the solid angle subtended at the origin by the  closed loop traced by a time-varying magnetic field for a spin one-half particle. This quantity is acquired by the instantaneous  eigenstate of a quantum system described by a cyclic time-dependent Hamiltonian, depends on the topology of the parameter  space, and is in addition to the dynamical phase. For 10 points, name this factor commonly seen in the Aharonov-Bohm effect.
This quantity causes the change in sign of the electronic wave function discovered by Herzberg and Longuet-Higgins.
Pancharatnam-Berry phase [or geometric phase; prompt on Pancharatnam phase]