Abstract
We study long-time dynamics of a bosonic system after suddenly switching on repulsive delta-like interactions. As initial states, we consider two experimentally relevant configurations: a rotating BEC and two counter-propagating BECs with opposite momentum, both on a ring. In the first case, the rapidity distribution function for the stationary state is derived analytically and it is given by the distribution obtained for the same quench starting from a BEC, shifted by the momentum of each boson. In the second case, the rapidity distribution function is obtained numerically for generic values of repulsive interaction and initial momentum. The significant differences for the case of large versus small quenches are discussed.
Highlights
In the last ten years, out-of-equilibrium many-body quantum physics has become a very active area of research, especially fuelled by the experimental realizations developed in cold-atomic setups [1,2,3,4]
In the case of the initially rotating BEC, we have found that the global shape of the rapidity root distribution in the asymptotic state is not affected by the rotation of the BEC and it is just shifted uniformly with respect to the static BEC case by the momentum of each boson
In conclusion we have found that the shape of the root distribution in the stationary state does not change if the initial state, evolved with the Lieb–Liniger, is a non-rotating or rotating BEC
Summary
In the last ten years, out-of-equilibrium many-body quantum physics has become a very active area of research, especially fuelled by the experimental realizations developed in cold-atomic setups [1,2,3,4]. It is proved that the long time behaviour of local observables is given by the expectation value with respect to a single representative state of the (post-quenched) Hamiltonian This representative state can be obtained as the result of a variational method, exact in the thermodynamic limit, which requires the knowledge of the overlap of any eigenstate of the post-quenched Hamiltonian with the initial state. As a consequence, this method is potentially very useful for interacting integrable models [49,55,56,57,58,59] because it does not require having the expression of the conserved charges, differently from the GGE approach.
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