Topological Action Related to Berry's Phase and its Non-adiabatic Effects

Abstract：

For the general cases where the adiabatic conditions are broken, we use the path-integration to derive a topological action related to the Berry's phase and the corresponding effective Hamiltonian, and thereby obtain the probability amplitude of the non-adiabatic transition under the first-order approximation. These discussions manifest the universality of existence of the Berry's phase and induced gauge structure. As an example, the dynamics of induced monopole associated with Bitter-Dubbers experiment is discussed.