Geometric phases in open tripod systems

Geometric phase in open systems.

We calculate the geometric phase associated with the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main sources of decoherence are considered: dephasing and spontaneous decay. We show that the geometric phase is completely insensitive to the former, i.e., it is indepen...

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...

Base-controlled mechanical systems and geometric phases

In this paper, we carry a detailed study of mechanical systems with configuration space Q −→ Q/G for which the base Q/G variables are being controlled. The overall system ́s motion is considered to be induced from the base one due to the presence of general nonholonomic constraints. It is shown that the solution can be factorized into dynamical and geometrical parts. Moreover, under favorable ki...

Geometric Phases

Geometric magnetism in open quantum systems

An isolated classical chaotic system, when driven by the slow change in several parameters, responds with two reaction forces: geometric friction and geometric magnetism. By using the theory of quantum fluctuation relations, we show that this holds true also for open quantum systems and provide explicit expressions for those forces in this case. This extends the concept of Berry curvature to th...