  We calculate electron and nuclear spin relaxation rates in a quantum dot due
to the combined action of Nyquist noise and electron-nuclei hyperfine or
spin-orbit interactions. The relaxation rate is linear in the resistance of the
gate circuit and, in the case of spin-orbit interaction, it depends essentially
on the orientations of both the static magnetic field and the fluctuating
electric field, as well as on the ratio between Rashba and Dresselhaus
interaction constants. We provide numerical estimates of the relaxation rate
for typical system parameters, compare our results with other, previously
discussed mechanisms, and show that the Nyquist mechanism can have an
appreciable effect for experimentally relevant systems.

Mesoscale and Nanoscale Physics