English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we define a non-dynamical phase for a spin-1/2 particle in arotating magnetic field in the non-adiabatic non-cyclic case, and this phasecan be considered as a generalized Berry phase. We show that this phase reducesto the geometric Berry phase, in the adiabatic limit, up to a factorindependent of the parameters of the system. We could add an arbitrary phase tothe eigenstates of the Hamiltonian due to the gauge freedom. Then, we fix thisarbitrary phase by comparing our Berry phase in the adiabatic limit with theBerry's result for the same system. Also, in the extreme non-adiabatic limitour Berry phase vanishes, modulo $2\pi$, as expected. Although, our Berry phaseis in general complex, it becomes real in the expected cases: the adiabaticlimit, the extreme non-adiabatic limit, and the points at which the state ofthe system returns to its initial form, up to a phase factor. Therefore, thisphase can be considered as a generalization of the Berry phase. Moreover, weinvestigate the relation between the value of the generalized Berry phase, theperiod of the states and the period of the Hamiltonian.

Non-adiabatic Non-cyclic Generalization of the Berry Phase for a Spin-1/2 Particle in a Rotating Magnetic Field