Hybrid semiclassical theory of quantum quenches in one dimensional systems

We develop a hybrid semiclassical method to study the time evolution of one dimensional quantum systems in and out of equilibrium. Our method handles internal degrees of freedom completely quantum mechanically by a modified time evolving block decimation method, while treating orbital quasiparticle motion classically. We can follow dynamics up to timescales well beyond the reach of standard numerical methods to observe the crossover between pre-equilibrated and locally phase equilibrated states. As an application, we investigate the quench dynamics and phase fluctuations of a pair of tunnel coupled one dimensional Bose condensates. We demonstrate the emergence of soliton-collision induced phase propagation, soliton-entropy production and multistep thermalization. Our method can be applied to a wide range of gapped one-dimensional systems.