Decoherence without dissipation

The prototypical Schr\"{o}dinger cat state, i.e., an initial state corresponding to two widely separated Gaussian wave packets, is considered. The decoherence time is calculated solely within the framework of elementary quantum mechanics and equilibrium statistical mechanics. This is at variance with common lore that irreversible coupling to a dissipative environment is the mechanism of decoherence. Here, we show that, on the contrary, decoherence can in fact occur at high temperature even for vanishingly small dissipation.