Resonances and scattering in the classical limit

Pierre Gaspard

Huan-Qiang Zhou, Lin-Jie Jiang

The quantum inverse scattering method is used for the study of a nonlinear N-wave resonance interaction system. The Yang–Baxter relations are solved to get various commutation relations for the scattering data operators. The energy spectrum of the quantum Hamiltonian for the model is determined and the existence of the quantum bound states is analyzed. In the classical limit, the corresponding r matrix is found, and the well-established correspondence between the classical solitons and the quantum bound states is examined. Finally, the integrability of the same model but with both fermion fields and boson fields is discussed.

Huan-Qiang Zhou, Jian Zhang, Lin-Jie Jiang

The nonlinear N-wave resonance interaction system with both boson and fermion fields is studied in the framework of the quantum inverse scattering method. The model Hamiltonian is diagonalised and the degeneracy of the eigenstates and the existence of the quantum bound states are analysed. Moreover, the classical limit is also discussed.

F. J. Arranz, R. M. Benito, F. Borondo

Xiaomin Hu

The exponentially decaying semi-stationary states of an assembly of identical classical radiators can have decay rates and resonant frequencies significantly different from that of an isolated radiator. These coherent effects on classical radiators emitting classical waves apply also to the particle processes in quantum limits, leading to the superradiant and subradiant modes with widths(decay rates) greatly enhanced or suppressed and resonant energies significantly shifted. The purpose of this thesis is to investigate these coherent effects on slow neutron-heavy nuclei interaction. A simple field model is introduced to show the coherent effects on the decay rates and resonant energies of two identical decaying states and on the neutron widths and resonant energies of neutron-two nuclei scattering. The latter case is also obtained by multiple scattering theory and is extended to a more general case of neutron-N nuclei scattering. The coherent effects on neutron width near Bragg angle in a crystal are also investigated.

P. Schattschneider