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We revisit the problem of the calculation of zero-temperature properties for the dilute two-dimensional Bose gas. By using Popov's hydrodynamic approach and perturbation theory on the two-loop level, we recover not only the known expansion for the ground-state energy but also calculate for the first time the condensate density and Tan's contact. [ABSTRACT FROM AUTHOR]

We investigate the non-equilibrium properties of a weakly interacting Bose gas subjected to a multi-pulsed quench at zero temperature, where the interaction parameter in the Hamiltonian system switches between values and for multiple times. The one-body and two-body correlation functions as well as Tan's contact are calculated. The quench induced excitations are shown to increase with the number of quenches for both and . This implies the possibility to use multi-pulsed quantum quench as a more powerful way as compared to the 'one-off' quench in controllable explorations of non-equilibrium quantum many-body systems. In addition, we study the ultra-short-range property of the two-body correlation function after multiple interaction quenches, which can serve as a probe of the 'Tan's contact' in the experiments. Our findings allow for an experimental probe using state of the art techniques with ultracold quantum gases. [ABSTRACT FROM AUTHOR]