  We develop a quantum theory for a variety of nuclear spin dynamics such as
dephasing, relaxation, squeezing, and narrowing due to the hyperfine
interaction with a generic, dissipative electronic system. The first-order
result of our theory reproduces and generalizes the nonlinear Hamiltonian for
nuclear spin squeezing [M. S. Rudner, Phys. Rev. Lett. 107, 206806 (2011)]. The
second-order result of our theory provides a good explanation to the
experimentally observed $^{13}$C nuclear spin bath narrowing in diamond
nitrogen-vacancy center [E. Togan, Nature 478, 497 (2011)
