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We study a two-dimensional gas of inelastic smooth hard dimers. Since thecollisions between dimers are dissipative, being characterized by a coefficientof restitution $\alpha<1$, and no external driving force is present, the energyof the system decreases in time and no stationary state is achieved. However,the resulting non equilibrium state of the system displays several interestingproperties in close analogy with systems of inelastic hard spheres, whoserelaxational dynamics has been thoroughly explored. We generalise to inelasticsystems a recently method introduced [G.Ciccotti and G.Kalibaeva, J. Stat.Phys. {\bf 115}, 701 (2004)] to study the dynamics of rigid elastic bodies madeup of different spheres hold together by rigid bonds. Each dimer consists oftwo hard disks of diameter $d$, whose centers are separated by a fixed distance$a$. By describing the rigid bonds by means of holonomic constraints andderiving the appropriate collision rules between dimers, we reduce the dynamicsto a set of equations which can be solved by means of event driven simulation.After deriving the algorithm we study the decay of the total kinetic energy,and of the ratio between the rotational and the translational kinetic energy ofinelastic dimers. We show numerically that the celebrated Haff's homogeneouscooling law $t^{-2}$, describing how the kinetic energy of an inelastic hardsphere system with constant coefficient of restitution decreases in time, holdseven in the case of these non spherical particles. We fully characterize thishomogeneous decay process in terms of appropriate decay constants and confirmnumerically the scaling behavior of the velocity distributions.Comment: 21 pages, 6 figures and 2 tables, submitted to JC

The inelastic hard dimer gas: A nonspherical model for granular matter