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 time scales well beyond the reach of standard numerical methods to observe the crossover between preequilibrated 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.

中文翻译：

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一维系统中量子猝灭的混合半经典理论

我们开发了一种混合半经典方法来研究一维量子系统在平衡内和平衡外的时间演化。我们的方法通过改进的时间演化块抽取方法完全机械地处理内部自由度，同时经典地处理了轨道准粒子运动。我们可以跟踪动力学，直到时间尺度远远超出标准数值方法的范围，以观察预平衡态与局部相平衡态之间的交叉。作为一种应用，我们研究了一对隧道耦合的一维Bose冷凝物的猝灭动力学和相位波动。我们证明了孤子碰撞引起的相传播，孤子熵产生和多步热化的出现。我们的方法可以应用于各种带间隙的一维系统。