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To study the rate of energy and momentum loss of a heavy quark in QGP, specif-ically in the hydrodynamic regime, we use fluid/gravity duality and construct a perturbative procedure to find the string solution in gravity side. We show that by this construction, the position of the world-sheet horizon and thereby the drag force exerted on the quark can be computed perturbatively, order by order in a boundary derivative expansion, for a wide range of quark velocities. At ideal order, our result is just the localized expression of the drag force exerted on a moving quark in thermal plasma, while for a quark whose velocity does not belong to the mentioned range, we predict a nonlocal drag force. Furthermore, we apply this procedure to a transverse quark in Bjorken flow and compute the first-derivative corrections, namely viscous corrections, to the drag force. We show that the diffusion time depends on the initial momentum of the transverse quark and can be about 4fm for a high energy quark which has been created sufficiently late.
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