  The transport coefficient of shear viscosity is studied for a hadron matter
through microscopic transport model, the Ultra--relativistic Quantum Molecular
Dynamics (UrQMD), using the Green--Kubo formulas. Molecular--dynamical
simulations are performed for a system of light mesons in a box with periodic
boundary conditions. Starting from an initial state composed of $\pi, \eta
,\omega ,\rho ,\phi$ with a uniform phase--space distribution, the evolution
takes place through elastic collisions, production and annihilation. The system
approaches a stationary state of mesons and their resonances, which is
characterized by common temperature. After equilibration, thermodynamic
quantities such as the energy density, particle density, and pressure are
calculated. From such an equilibrated state the shear viscosity coefficient is
calculated from the fluctuations of stress tensor around equilibrium using
Green--Kubo relations. We do our simulations here at zero net baryon density so
that the equilibration times depend on the energy density. We do not include
hadron strings as degrees of freedom so as to maintain detailed balance. Hence
we do not get the saturation of temperature but this leads to longer
equilibration times.
