We investigate the finite-lifetime effects on first-order correlation functions of dissipative Bose-Einstein condensates. By taking into account the phase fluctuations up to all orders, we show that the finite-lifetime effects are negligible for the spatial first-order correlation functions, but have an important effect on the temporal correlations. As an application, we calculate the one-particle density matrix of a quasicondensate of photons. Finally, we also consider the photons in the normal state and we demonstrate that the finite-lifetime effects decrease both the spatial and temporal first-order correlation functions. © 2014 American Physical Society
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