In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics,which yields that a state of the PT-symmetric quantum system at any time will remain approxim...In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics,which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.展开更多
An alternative proof of factorization theorem for Drell–Yan process that works at operator level is presented in this paper. Contributions of interactions after the hard collision for such inclusive processes are pro...An alternative proof of factorization theorem for Drell–Yan process that works at operator level is presented in this paper. Contributions of interactions after the hard collision for such inclusive processes are proved to be canceled at operator level according to the unitarity of time evolution operator. After this cancellation, there are no longer leading pinch singular surface in Glauber region in the time evolution of electromagnetic currents. Effects of soft gluons are absorbed into Wilson lines of scalar-polarized gluons. Cancelation of soft gluons is attribute to unitarity of time evolution operator and such Wilson lines.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11171197 and 11371012)the Science Research Foundation of Education Department of Shaanxi Provincial Government(Grant No.11JK0513)+2 种基金the Fundamental Research Funds for the Central Universities(Grant No.GK201402005 and GK201301007)the Postdoctoral Science Foundation of China(Grant No.2014M552405)the Natural Science Research Program of Shaanxi Province(Grant No.2014JQ1010)
文摘In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics,which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.
基金Supported by the National Natural Science Foundation of China under Grant No.11275242
文摘An alternative proof of factorization theorem for Drell–Yan process that works at operator level is presented in this paper. Contributions of interactions after the hard collision for such inclusive processes are proved to be canceled at operator level according to the unitarity of time evolution operator. After this cancellation, there are no longer leading pinch singular surface in Glauber region in the time evolution of electromagnetic currents. Effects of soft gluons are absorbed into Wilson lines of scalar-polarized gluons. Cancelation of soft gluons is attribute to unitarity of time evolution operator and such Wilson lines.
