  We introduce a method for solving the problem of an externally controlled
electron spin in a quantum dot interacting with host nuclei via the hyperfine
interaction. Our method accounts for generalized (non-unitary) evolution
effected by external controls and the environment, such as coherent lasers
combined with spontaneous emission. As a concrete example we develop the
microscopic theory of the dynamics of nuclear-induced frequency focusing, as
first measured in Science 317, 1896 (2007); we find that the nuclear relaxation
rates are several orders of magnitude faster than those quoted in that work.
