The time evolution of system in two photon Jaynes Cummings (J C) model without rotating waves approximation (RWA) is obtained by using the theory of ordinary differential equations. Based on the evolution, the mean ...The time evolution of system in two photon Jaynes Cummings (J C) model without rotating waves approximation (RWA) is obtained by using the theory of ordinary differential equations. Based on the evolution, the mean value of the atom inversion operator 〈 S 3(t)〉 is gi ven. The influence of the “counter rotating term” on the collapse and revival phenomenon is discussed from the comparison between the cases with RWA and without RWA. It shows that the influence of the virtual photon field makes the quantum fluctuations appear on the collapse and revival phenomenon.展开更多
With the aid of symbolic computation, we present the symmetry transformations of the (2+1)-dimensionalCaudrey-Dodd Gibbon-Kotera-Sawada equation with Lou's direct method that is based on Lax pairs. Moreover, witht...With the aid of symbolic computation, we present the symmetry transformations of the (2+1)-dimensionalCaudrey-Dodd Gibbon-Kotera-Sawada equation with Lou's direct method that is based on Lax pairs. Moreover, withthe symmetry transformations we obtain the Lie point symmetries of the CDGKS equation, and reduce the equation withthe obtained symmetries. As a result, three independent reductions are presented and some group-invariant solutions ofthe equation are given.展开更多
文摘The time evolution of system in two photon Jaynes Cummings (J C) model without rotating waves approximation (RWA) is obtained by using the theory of ordinary differential equations. Based on the evolution, the mean value of the atom inversion operator 〈 S 3(t)〉 is gi ven. The influence of the “counter rotating term” on the collapse and revival phenomenon is discussed from the comparison between the cases with RWA and without RWA. It shows that the influence of the virtual photon field makes the quantum fluctuations appear on the collapse and revival phenomenon.
基金Supported by the Natural Key Basic Research Project of China under Grant No. 2004CB318000the 'Math + X' Key Project and Science Foundation of Dalian University of Technology under Grant No. SFDUT0808
文摘With the aid of symbolic computation, we present the symmetry transformations of the (2+1)-dimensionalCaudrey-Dodd Gibbon-Kotera-Sawada equation with Lou's direct method that is based on Lax pairs. Moreover, withthe symmetry transformations we obtain the Lie point symmetries of the CDGKS equation, and reduce the equation withthe obtained symmetries. As a result, three independent reductions are presented and some group-invariant solutions ofthe equation are given.
