Abstract
Two linear In this letter, we prove the following conclusions by introducing a function F n (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 F n (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 ɛ-uniformly approximately in the n-th eigenstate of H(t) up to a multiplicative phase factor if and only if the values F n (t) for all t are always outside of the circle centered at 1 with radius 1−ɛ. Moreover, some quantitative sufficient conditions for the state of the system at time t to remain ɛ-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.
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Cao, H., Guo, Z., Chen, Z. et al. Quantitative sufficient conditions for adiabatic approximation. Sci. China Phys. Mech. Astron. 56, 1401–1407 (2013). https://doi.org/10.1007/s11433-013-5127-0
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DOI: https://doi.org/10.1007/s11433-013-5127-0