Hannay angle and geometric phase shifts under adiabatic parameter changes in classical dissipative systems

Geometric phase shifts under adiabatic parameter changes in classical dissipative systems.

Adiabatic Berry Phase and Hannay Angle for Open Paths

We obtain the adiabatic Berry phase by defining a generalised gauge potential whose line integral gives the phase holonomy for arbitrary evolutions of parameters. Keeping in mind that for classical integrable systems it is hardly clear how to obtain open-path Hannay angle, we establish a connection between the open-path Berry phase and Hannay angle by using the parametrised coherent state appro...

Classical adiabatic angles and quantal adiabatic phase

A semiclassical connection IS established between quantal and classical properties of a system whose Hamiltonian is slowly cycled by varying its parameters round a circuit. The quantal property is a geometrical phase shift y,, associated with an eigenstate with quantum numbers n = {n,}: the classical property is a shift A@,(I) in the Ith angle variable for motion round a phase-space torus with ...

Geometric Phase in Dissipative System

In non-Hamiltonian dissipative systems that have attracting limit cycles there are phase shifts analogous to the geometric phase of Hamiltonian quantum systems. Here the phase variable is the equal-time parametrization of a limit cycle. The phase shift is calculable when the direrentia1 equations of the variables of the systems are known. We study such a system with both numerical and analytica...

Relativistic Adiabatic Approximation and Geometric Phase

A relativistic analogue of the quantum adiabatic approximation is developed for Klein-Gordon fields minimally coupled to electromagnetism, gravity and an arbitrary scalar potential. The corresponding adiabatic dynamical and geometrical phases are calculated. The method introduced in this paper avoids the use of an inner product on the space of solutions of the Klein-Gordon equation. Its practic...