Cold atom systems in optical lattices provide a promising platform for a wide variety of applications, ranging from quantum simulation to quantum metrology, due to their extremely high tunability and the ability to derive microscopic models under well-controlled approximations that give access to accurate descriptions. The proper characterization of those systems requires, in many scenarios, taking into account that they are subject to some dissipation sources, as dissipation can drastically modify the behaviour of the known phases of matter or even generate new ones. However, the description of open systems can quickly become numerically unaffordable.
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