Abstract
We consider a model of two tunnel-coupled one-dimensional Bose gases with hard-wall boundary conditions. Bosonizing the model and retaining only the most relevant interactions leads to a decoupled theory consisting of a quantum sine-Gordon model and a free boson, describing respectively the antisymmetric and symmetric combinations of the phase fields. We go beyond this description by retaining the perturbation with the next smallest scaling dimension. This perturbation carries conformal spin and couples the two sectors. We carry out a detailed investigation of the effects of this coupling on the non-equilibrium dynamics of the model. We focus in particular on the role played by spatial inhomogeneities in the initial state in a quantum quench setup.
Highlights
We specialize to an initial state that is often used in the literature, see e.g. [46,47,48,49]
We have extended the theory for non-equilibrium dynamics in pairs of elongated, tunnelcoupled Bose gases using a self-consistent time-dependent harmonic approximation (SCTDHA) in the low-energy scaling limit
In contrast to earlier works, we have studied the effect of a relevant perturbation which couples thesymmetric sectors describingsymmetric combinations of the two Bose gas phases
Summary
The study of one-dimensional quantum many-body systems out of equilibrium has seen great progress in the past decades. Our interest lies in the effect of a finite tunnel barrier between the gases [14, 50,51,52] This introduces a relevant perturbation and at sufficiently low energies leads to a decoupled theory of a Luttinger liquid describing the symmetric combination of Bose gas phases (“symmetric sector”) and a sine-Gordon model [53] describing the relative phase (“antisymmetric sector”). Comparison to numerically exact results for this simplified problem indicated that the SCTDHA offers reliable results for early times corresponding to ∼ 3 density-phase oscillation periods Based on those findings, we apply the approximation in the current work to the first few oscillation periods in the presence of sector coupling.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
