Phonon-Assisted Energy Transport in Inhomogeneously Broadened Systems

Abstract

Recent experiments have demonstrated Anderson localization in inhomogeneously broadened paramagnetic spin systems. We examine two-phonon processes which can frequency shift the individual spin packets, and thereby allow energy transfer to take place. We make specific application to ruby, and show that the dominant phonon-induced energy-transfer rate is directly proportional to the (spin-nonflip) $\overline{E}\to 2\overline{A}$ rate [varying as $\exp (-\frac{42}{T})$], and inversely proportional to the square of the energy mismatch of the participating spin packets.