The dynamics of two initially tunnel-coupled chains of bosonic atoms after a quench in the tunneling strength is studied, and the correlation functions of relative phase (directly measured in interference experiments), relative density, and current are computed.
The space-time tunneling bosonization has been introduced to study N-coupled Luttinger liquids. The interaction is separated into a forward exchange and a cooperon part. At T=0 the cooperon part is described by tunneling events which form a Coulomb gas in the plasma phase. At T\ensuremath{\ne}0 we ignore the cooperon part and show that the correlation functions show a Luttinger-liquid behavior. In the limit N\ensuremath{\rightarrow}\ensuremath{\infty}, we extract the two-dimensional behavior and show that for a certain range of parameters the Luttinger liquid survives.
We consider two disconnected Luttinger liquids which are coupled at t=0 through chiral density-density interactions. Both for t<0 and $t\ensuremath{\geqslant}0$ the system is exactly solvable by means of bosonization and this allows us to evaluate analytically the time dependence of correlation functions. We find that in the long-time limit the critical exponent governing the one-particle correlation function differs from the exponent dictated by the equilibrium ground state of the coupled system. We also discuss how this reflects on some physical quantities which are accessible to real experiments.
We study the quantum quench in two coupled Tomonaga-Luttinger Liquids (TLLs), from the off-critical to the critical regime, relying on the conformal field theory approach and the known solutions for single TLLs. We consider a squeezed form of the initial state, whose low energy limit is fixed in a way to describe a massive and a massless mode, and we encode the non-equilibrium dynamics in a proper rescaling of the time. In this way, we compute several correlation functions, which at leading order factorize into multipoint functions evaluated at different times for the two modes. Depending on the observable, the contribution from the massive or from the massless mode can be the dominant one, giving rise to exponential or power-law decay in time, respectively. Our results find a direct application in all the quench problems where, in the scaling limit, there are two independent massless fields: these include the Hubbard model, the Gaudin-Yang gas, and tunnel-coupled tubes in cold atoms experiments.