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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We present a formal geometric framework for the study of adiabatic quantummechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. Thisframework generalizes earlier holonomy interpretations of the geometric phaseto non-cyclic states appearing for non-Hermitian Hamiltonians. We start with aninvestigation of the space of non-degenerate operators on a finite-dimensionalstate space. We then show how the energy bands of a Hamiltonian family form acovering space. Likewise, we show that the eigenrays form a bundle, ageneralization of a principal bundle, which admits a natural connectionyielding the (generalized) geometric phase. This bundle provides in addition anatural generalization of the quantum geometric tensor and derived tensors, andwe show how it can incorporate the non-geometric dynamical phase as well. Wefinish by demonstrating how the bundle can be recast as a principal bundle, sothat both the geometric phases and the permutations of eigenstates can beexpressed simultaneously by means of standard holonomy theory.

A Unified View on Geometric Phases and Exceptional Points in Adiabatic Quantum Mechanics