Eigenvalue and eigenspace anholonomies in hierarchical systems
Department of Physics, Tokyo Metropolitan University - Hachioji, Tokyo 192-0397, Japan
2 Department of Physics Education, Pusan National University - Busan 609-735, South Korea
3 Laboratory of Physics, Kochi University of Technology - Tosa Yamada, Kochi 782-8502, Japan
Accepted: 17 August 2011
An adiabatic cycle of parameters in a quantum system can yield the quantum anholonomies, non-trivial evolution not just in the phase of states, but also in eigenvalues and eigenstates. Such exotic anholonomies imply that an adiabatic cycle rearranges eigenstates even without spectral degeneracy. We show that an arbitrarily large quantum circuit generated by recursive extension can also exhibit the eigenvalue and eigenspace anholonomies.
PACS: 03.65.Vf – Phases: geometric; dynamic or topological / 03.67.-a – Quantum information
© EPLA, 2011