摘要
Two linear In this letter, we prove the following conclusions by introducing a function Fn（t）： （1） If a quantum system S with a time-dependent non-degenerate Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values Fn（t） for all t are always on the circle centered at 1 with radius 1; （2） If a quantum system S with a time-dependent Hamiltonian H（t） is initially in the n-th eigenstate of H（0）, then the state of the system at time t will remain c-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor if and only if the values F,（t） for all t are always outside of the circle centered at 1 with radius 1-ε. Moreover, some quantitative sufficient conditions for the state of the system at time t to remain ε-uniformly approximately in the n-th eigenstate of H（t） up to a multiplicative phase factor are established. Lastly, our results are illustrated by a spin-half particle in a rotating magnetic field.
Two linear In this letter, we prove the following conclusions by introducing a function Fn(t): (1) If a quantum system S with a time-dependent non-degenerate Hamiltonian H(t) is initially in the n-th eigenstate of H(0), then the state of the system at time t will remain in the n-th eigenstate of H(t) up to a multiplicative phase factor if and only if the values Fn(t) for all t are always on the circle centered at 1 with radius 1; (2) If a quantum system S with a time-dependent Hamiltonian H(t) is initially in the n-th eigenstate of H(0), then the state of the system at time t will remain-uniformly approximately in the n-th eigenstate of H(t) up to a multiplicative phase factor if and only if the values Fn(t) for all t are always outside of the circle centered at 1 with radius 1 . Moreover, some quantitative sufficient conditions for the state of the system at time t to remain-uniformly approximately in the n-th eigenstate of H(t) up to a multiplicative phase factor are established. Lastly, our results are illustrated by a spin-half particle in a rotating magnetic field.
基金
supported by the National Natural Science Foundation of China(Grant No. 11171197)
the IFGP of Shaanxi Normal University(Grant No. 2011CXB004)
the FRF for the Central Universities(Grant No. GK201002006)
