Open AccessCONDITIONS FOR THE EXISTENCE OF NON-ZERO GEOMETRIC PHASE AND ITS FORMULA
Author(s) -
Li Chun-Fang,
Guo Guang-Can
Publication year - 1996
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.45.897
Subject(s) - geometric phase , adiabatic process , hamiltonian (control theory) , eigenvalues and eigenvectors , physics , zero (linguistics) , phase space , adiabatic quantum computation , mathematical physics , quantum , quantum mechanics , mathematical analysis , mathematics , quantum computer , mathematical optimization , linguistics , philosophy
First we put forward an essential condition, for the existence of the non-zero adiabatic geometric phase of a quantum-mechanical Hamiltonian system, that the Hamiltonian operators at different times do not commute. Then it is shown that constraint =0 determines completely the phase relation of normalized eigenstate vectors │n' (t)> at different times. According to this property, we advance the sufficient and necessary condition for the existence of the non-zero adiabatic geometric phase, which is |n′(T)>≠|n′(0)> when =0. And also we derive a general time-integral formula for the adiabatic geometric phase along the line. Finally, as an application of it, we calculate the geometric phase of a spin 1/2 system once discussed by Solem and Biedenharn. It is pointed out that the problem encountered by them lies in the multi-valuedness of the eigenstate vector in parameter space.