Acta Physica Sinica

BLOCH THEOREM FOR THE EVOLUTION OF STATES IN THE CYCLIC QUANTUM SYSTEMS AND THE UNIFICATION OF RESONANT GEOMETRIC PHASES

Bo‐Zang Li, Degang Zhang, WU JIAN-HUA, Yan Feng-Li, (1)北京大学物理系; (2)河北师范大学物理系; (3)四川师范大学固体物理研究所; (4)中国科学院物理研究所

Published Jan 1, 1997• 5 citations

Abstract

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.

DOI: 10.7498/aps.46.227

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