Cumulants associated with geometric phases

Geometric Phases

Off-diagonal geometric phases.

We investigate the adiabatic evolution of a set of nondegenerate eigenstates of a parametrized Hamiltonian. Their relative phase change can be related to geometric measurable quantities that extend the familiar concept of Berry phase to the evolution of more than one state. We present several physical systems where these concepts can be applied, including an experiment on microwave cavities for...

Geometric Properties of Quantum Phases

The Aharonov-Anandan phase is introduced from a physical point of view. Without reference to any dynamical equation, this phase is formulated by defining an appropriate connection on a specific fibre bundle. The holonomy element gives the phase. By introducing another connection, the Pancharatnam phase formula is derived following a different procedure.

Gauge symmetries in geometric phases

The analysis of geometric phases is briefly reviewed by emphasizing various gauge symmetries involved. The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry becomes explicit in this formulation and specifies physical observables; the choice of a basis set wh...

Geometric Phases and Related Structures +

The phase of a single state is not an observable quantity. In particular, the phase commutes with the observables which define the system. Nevertheless the change of states is generally accompanied by a change of the phase that can be called phase transport. If a state w is changed in two different ways to become another state w’, the transport of the phases may yield different phases. Then the...