Stephanie Matern (University of St. Andrews)

Title: Non-Markovian Decay of Nuclear Spins Coupled to Itinerant Electrons

Abstract: We study the full time evolution of a nuclear spin coupled to itinerant electrons through the hyperfine inter- action, with a particular focus on memory effects leading to a non-Markovian behavior. We show that even a noninteracting electron system causes a notable memory effect due to the restriction of fluctuations by the Fermi surface. The resulting short time dynamics of the nuclear spin is dominated by a logarithmic, temperature independent decay before crossing over to the standard, thermally induced exponential decay. But even at the longer time scales the initial non-Markovian decay causes a systematic reduction of the decay amplitude that should be detectable. Our approach is based on an expansion of the exact Nakashima-Zwanzig equation in the hyperfine coupling constant, set up to preserve the analytical structure of the memory kernel that causes the non- Markovian behavior. Our results are analytical and describe the full time range from the novel non-Markovian contributions to the well-known exponential decay expressions.