Fibre bundle geometry and geometric phases
(Old research topics)
Non-abelian or non-unitary geometric phases in quantum dynamics
Composite fibre bundles and applications to geometric phases which does not commute with dynamical phases, geometric phases of dissipative quantum systems.
Non-trivial topologies in quantum control
Topological defects of fibre bundles, gerbes associated with quantum resonance control, Cheon anholonomy in adiabatic transport of Floquet quasienergy states and associated gerbes.
Magnetic monopoles
Virtual magnetic monopoles in adiabatic quantum dynamics.
- D. Viennot, Transport adiabatique et phases de Berry : application au contrôle cohérent passif, J. Phys. IV France : proceedings 119, 289 (2004).
- D. Viennot, Principal bundle structure of quantum adiabatic dynamics with a Berry phase which does not commute with the dynamical phase, J. Math. Phys. 46, 072102 (2005).
- D. Viennot, Magnetic monopoles in quantum adiabatic dynamics and the immersion property of the control manifold, J. Math. Phys. 47, 092105 (2006).
- D. Viennot, The need for a flat higher gauge structure to describe a Berry phase associated with some resonance phenomena, J. Math. Phys. 50, 052101 (2009).
- D. Viennot, Geometric phases in adiabatic Floquet theory, abelian gerbes and Cheon's anholonomy, J. Phys. A : Math. Theor. 42, 395302 (2009).
- D. Viennot, Holonomy of a principal composite bundle connection, non-abelian geometric phases and gauge theory of gravity, J. Math. Phys. 51, 103501 (2010).
- D. Viennot, Geometric phases in quantum control disturbed by classical stochastic processes, J. Math. Phys. 53, 082106 (2012).
