  We employ the holographic method to study fluctuations and dissipation of an
$n$-dimensional moving mirror coupled to quantum critical theories in $d$
spacetime dimensions. The bulk counterpart of the mirror with perfect
reflection is a D$(n+1)$ brane in the Lifshitz geometry of $d+1$ dimensions.
The motion of the mirror can be realized from the dynamics of the brane at the
boundary of the bulk. The excited modes of the brane in the bulk render the
mirror undergoing Brownian motion. For small displacement of the mirror, we
derive the analytical results of the correlation functions and response
functions. The dynamics of the mirror due to small fluctuations around the
brane vacuum state in the bulk is found supraohmic so that after initial
growth, the velocity fluctuations approach a saturated value at late time with
a power-law behavior. On the contrary, in the Lifshitz black hole background,
the mirror in thermal fluctuations shows that its relaxation dynamics becomes
ohmic, and the saturation of velocity fluctuations is reached exponentially in
time. Finally a comparison is made with the result of a moving mirror driven by
free fields.
