Geometric phases in adiabatic Floquet theory, abelian gerbes and Cheon's anholonomy

Abstract

We study the geometric phase phenomenon in the context of the adiabatic Floquet theory (the so-called the $(t,t^{\prime })$ Floquet theory). A double integration appears in the geometric phase formula because of the presence of two time variables within the theory. We show that the geometric phases are then identified with horizontal lifts of surfaces in an abelian gerbe with connection, rather than with horizontal lifts of curves in an abelian principal bundle. This higher degree in the geometric phase gauge theory is related to the appearance of changes in the Floquet blocks at the transitions between two local charts of the parameter manifold. We present the physical example of a kicked two-level system where these changes are involved via a Cheon's anholonomy. In this context, the analogy between the usual geometric phase theory and the classical field theory also provides an analogy with the classical string theory.

This new version presents a more complete geometric structure which is topologically non trivial

References in corpus (1)

• Cheon's anholonomies in Floquet operators

Cited by in corpus (14)

• Non-abelian higher gauge theory and categorical bundle
• Schrödinger-Koopman quasienergy states of quantum systems driven by a classical flow
• A new kind of geometric phases in open quantum systems and higher gauge theory
• Quantum anholonomies in time-dependent Aharonov-Bohm rings
• Bloch vector, disclination and exotic quantum holonomy
• Decoherence, relaxation and chaos in a kicked-spin ensemble
• The Fermi gerbe of Weyl semimetals
• Adiabatic theorem for bipartite quantum systems in weak coupling limit
• Chaos, decoherence and emergent extradimensions in D-brane dynamics with fluctuations
• Eigenvalue and eigenspace anholonomies in hierarchical systems
• Topological adiabatic dynamics in classical mass-spring chains with clamps
• Geometric phases, Everett's many-worlds interpretation of quantum mechanics, and wormholes
• Effective Hamiltonians for almost-periodically driven quantum systems
• Emergent gravity and D-brane adiabatic dynamics: emergent Lorentz connection