Quench dynamics of two unequal Luttinger liquids: "Large-scale" thermalization, prethermalization and impact of the temperature

We study the effect of a quantum quench between two tunnel coupled Tomonaga-Luttinger liquids (TLLs) with different speed of sound and interaction parameter. The quench dynamics is induced by switching off the tunnelling and letting the two systems evolve independently. Both the case of zero and finite temperature in the initial state are considered. We focus on correlation functions associated with the antisymmetric and symmetric combinations of the two TLLs (relevant for interference mea- surements), which turn out to be coupled due to the asymmetry in the two systems’ Hamiltonians. The rich phenomenology that emerges can play a crucial role for the correct description of currently running cold atoms experiments.