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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 perfectreflection 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 theboundary of the bulk. The excited modes of the brane in the bulk render themirror undergoing Brownian motion. For small displacement of the mirror, wederive the analytical results of the correlation functions and responsefunctions. The dynamics of the mirror due to small fluctuations around thebrane vacuum state in the bulk is found supraohmic so that after initialgrowth, the velocity fluctuations approach a saturated value at late time witha power-law behavior. On the contrary, in the Lifshitz black hole background,the mirror in thermal fluctuations shows that its relaxation dynamics becomesohmic, and the saturation of velocity fluctuations is reached exponentially intime. Finally a comparison is made with the result of a moving mirror driven byfree fields.

Holographic Approach to Nonequilibrium Dynamics of Moving Mirrors Coupled to Quantum Critical Theories