Open AccessBLOCH THEOREM FOR THE EVOLUTION OF STATES IN THE CYCLIC QUANTUM SYSTEMS AND THE UNIFICATION OF RESONANT GEOMETRIC PHASES
Author(s) -
Bo-Zang Li,
Degang Zhang,
Jianguo Wu,
Yan Feng-Li
Publication year - 1997
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.46.227
Subject(s) - geometric phase , degenerate energy levels , bloch sphere , quantum , adiabatic process , berry connection and curvature , bloch wave , hamiltonian (control theory) , physics , quantum mechanics , mathematical physics , theoretical physics , mathematics , qubit , mathematical optimization
The Bloch theorem holds also for the evolution of states in the cyclic quantum systems in which the Hamiltonian varies cyclically with time.In light of the theorem a new type of geometric phases——Bloch phases——is defined.In this paper it is shown that the resonant-(i.e.,acquired by certain states after evolving a cycle)geometric phases so far discovered can all be unified into the Bloch phases.That is,the Bloch phases are identical with the Pancharatnam phases,Aharonov-Anandan phases and Lewis-Riesenfeld phases,and reduce to the Berry phases in adiabatic approximation.To this end,the equivalent alternation of defining the former three types of quantum phases and the generalization of Lewis-Riesenfeld phases and Berry phases to the degenerate case are made.In addition,two methods are given for efficiently searching for the Bloch phases.