Trapping of a Resonant Phonon in a Paramagnetic Spin System

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Abstract
The trapping of a resonant phonon in a noninteracting spin system is studied in the limit of zero temperature with the aid of the Heitler damping formalism. Starting from the initial condition that all but one of the spins are in the ground state, expressions are obtained for the distribution of emitted phonons and the distribution of excited spins. It is pointed out that the phonon distribution has a width which greatly exceeds the corresponding width in the single-spin problem. It is also noted that the spread of excitation cannot be characterized as a diffusive process, since the second moment of the spin distribution is asymptotically proportional to the square of the elapsed time. The significance of these results is discussed with particular reference to the normal modes of a coupled spin-lattice system.