Non-Abelian geometric effect in quantum adiabatic transitions

Non-Abelian geometric effect in quantum adiabatic transitions.

Non-Abelian Geometrical E ect in Quantum Adiabatic Transitions

We establish a new formula for the probability of a quantum adiabatic transition between two permanently degenerated energy-levels which do not cross. This formula corresponds to the non-abelian generalization of the Landau-Dykhne formula valid for the non-degenerate case. It applies in particular in cases of symmetry induced degener-acy, a typical example being the Kramer's degeneracy.

Abelian and non-Abelian geometric phases in adiabatic open quantum systems

We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases, based on an adiabatic approximation developed within an inherently open-systems approach. This expression provides a natural generalization of the analogous one...

Particle creation and non-adiabatic transitions in quantum cosmology

The aim of this paper is to compute transitions amplitudes in quantum cosmology, and in particular pair creation amplitudes and radiative transitions. To this end, we apply a double adiabatic development to the solutions of the Wheeler-DeWitt equation restricted to mini-superspace wherein gravity is described by the scale factor a. The first development consists in working with instantaneous ei...

Recent Results on Non–Adiabatic Transitions in Quantum Mechanics

We review mathematical results concerning exponentially small corrections to adiabatic approximations and Born–Oppenheimer approximations.