  We investigate relaxation and dephasing of an electron spin confined in a
semiconductor quantum dot and subject to spin-orbit coupling. Even in vanishing
magnetic field, B = 0, slow noise coupling to the electron's orbital degree of
freedom leads to dephasing of the spin due to a random, in general non-Abelian
Berry phase acquired by the spin. For illustration we first present a simple
quasiclassical description, then consider a model with 2 orbital states only,
and finally present a perturbative quantum treatment appropriate for an
electron in a realistic (roughly parabolic, not too strongly confining) quantum
dot. We further compare the effect of different sources of noise. While at
large magnetic fields phonons dominate the relaxation processes, at low fields
electron-hole excitations and possibly 1/f noise may dominate.
