Thermalized Liouville formalism applied to the onset and development of Rabi oscillations

Pierre G. Averbuch

To describe the oscillations of the excitation energy between a small system, such as a nucleus, and a thermal bath having an excitation energy roughly tuned to the small system, a formalism is proposed where the motion of the density matrix is described in a Liouville space, with a metric adapted to the temperature of the bath. The obtained equation of motion is characterized by a memory kernel. A second order approximation of the kernel gives the onset of the oscillations, but is not absolutely coherent. An approximate calculation of the kernel, where the phase evolution is ``motional-narrowed'', is proposed, giving an answer satisfying physical conditions. Its low temperature limit is evaluated

PACS: 03.65.Yz, 23.20.Nx, 33.40.+f, 42.50.Md