  We study the open system dynamics of a heavy quark in the quark-gluon plasma
using a Lindblad master equation. Applying the quantum state diffusion approach
by Gisin and Percival, we derive and numerically solve a nonlinear stochastic
Schr\"odinger equation for wave functions, which is equivalent to the Lindblad
master equation for the density matrix. From our numerical analysis in one
spatial dimension, it is shown that the density matrix relaxes to the Boltzmann
distribution in various setups (with and without external potentials),
independently of the initial conditions. We also confirm that quantum
dissipation plays an essential role not only in the long-time behavior of the
heavy quark but also at early times if the heavy quark initial state is
localized and quantum decoherence is ineffective.
