Spin-lattice relaxation in fractal systems

Stapleton and co-workers have measured the spin-lattice relaxation rates of a number of protein molecules and interpreted the results in terms of the fractal nature of these complex systems. We examine the theoretical foundation of their work by calculating in detail the normal modes, local strain, and the temperature dependence of the Raman spin-lattice relaxation rate 1/$T_1$ of an exactly soluble model system, the elastic Sierpinski gasket. No simple power-law dependence of 1/$T_1$ on temperature is found in the entire temperature range.