A new kind of geometric phases in open quantum systems and higher gauge theory

Abstract

A new approach extending the concept of geometric phases to adiabatic open quantum systems described by density matrices (mixed states) is proposed. This new approach is based on an analogy between open quantum systems and dissipative quantum systems which uses a $C^{\ast }$-module structure. The gauge theory associated with these new geometric phases does not take place in an usual principal bundle structure but in an higher structure, a categorical principal bundle (so-called principal 2-bundle or non-abelian bundle gerbes) which is sometimes a non-abelian twisted bundle. This higher degree in the gauge theory is a geometrical manifestation of the decoherence induced by the environment on the quantum system.

32 pages

References in corpus (4)

• Abelian and non-Abelian geometric phases in adiabatic open quantum systems
• Dynamical invariants and nonadiabatic geometric phases in open quantum systems
• Geometric phases in adiabatic Floquet theory, abelian gerbes and Cheon's anholonomy
• Holonomy of a principal composite bundle connection, non-abelian geometric phases and gauge theory of gravity

Cited by in corpus (8)

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• Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation
• Geometric phases, Everett's many-worlds interpretation of quantum mechanics, and wormholes
• Emergent gravity and D-brane adiabatic dynamics: emergent Lorentz connection