机构地区:[1]College of Mathematics and Information Science, Shaanxi Normal University [2]Section of Military Operation Research, Border Defence Academy [3]College of Mathematics and Information Science, Weinan Normal University
出 处:《Science China(Physics,Mechanics & Astronomy)》2015年第3期1-7,共7页中国科学:物理学、力学、天文学(英文版)
基 金:supported by the National Natural Science Foundation of China(Grant Nos.11371012,11171197 and 11401359);the Innovation Fund Project for Graduate Program of Shaanxi Normal University(GrantNo.2013CXB012);the Fundamental Research Funds for the Central Universities(Grant Nos.GK201301007 and GK201404001);the Science Foundation of Weinan Normal University(Grant No.14YKS006);the Foundation of Mathematics Subject of Shaanxi Province(Grant No.14SXZD009)
摘 要:The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr6dinger equation (SE) by choosing a single eigenstate of the Hamiltonian as the initial state. The superposition principle of quantum states enables us to mathematically discuss the exact solution to the SE starting from a superposition of two different eigenstates of the time-dependent Hamiltonian H(0). Also, we can construct an approximate solution to the SE in terms of the corresponding instantaneous eigenstates of H(t). On the other hand, any physical experiment may bring errors so that the initial state (input state) may be a superposition of different eigenstates, not just at the desired eigenstate. In this paper, we consider the generalized adiabatic evolution of a quantum system starting from a superposition of two different eigenstates of the Hamiltonian at t = 0. A generalized adiabatic approximate solution (GAAS) is constructed and an upper bound for the generalized adiabatic approximation error is given. As an application, the fidelity of the exact solution and the GAAS is estimated.The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr¨odinger equation(SE)by choosing a single eigenstate of the Hamiltonian as the initial state.The superposition principle of quantum states enables us to mathematically discuss the exact solution to the SE starting from a superposition of two different eigenstates of the time-dependent Hamiltonian H(0).Also,we can construct an approximate solution to the SE in terms of the corresponding instantaneous eigenstates of H(t).On the other hand,any physical experiment may bring errors so that the initial state(input state)may be a superposition of different eigenstates,not just at the desired eigenstate.In this paper,we consider the generalized adiabatic evolution of a quantum system starting from a superposition of two different eigenstates of the Hamiltonian at t=0.A generalized adiabatic approximate solution(GAAS)is constructed and an upper bound for the generalized adiabatic approximation error is given.As an application,the fidelity of the exact solution and the GAAS is estimated.
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