Bloch theorem for the evolution of states in a cyclic quantum system and a new type of quantum phases

摘要

It is found that in a quantum system with cyclic Hamiltonian the time-dependent Schroedinger equation admits the Bloch type solutions which have the form of Bloch function with respect to the time. These solutions constitute an orthonormal basis of the solution space and lead to a new type of quantum phases. The new phases, called Bloch phases by the authors, are the special Aharonov-Anandan phases, and reduce to the Berry phases under the adiabatic approximation if the degeneracy of instantaneous eigen-energy is time-independent. The above conclusions are proved and calculation for the evolution of spin magnetic moments in a magnetic field processing with constant angular velocity is exemplified.