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.

中文翻译：

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在最初耦合的 Tomonaga-Luttinger 液体中淬火：一种共形场理论方法

我们研究了两种耦合的 Tomonaga-Luttinger 液体 (TLL) 中的量子猝灭，从非临界状态到临界状态，依赖于共形场理论方法和已知的单个 TLL 解决方案。我们考虑初始状态的压缩形式，其低能量限制以描述有质量和无质量模式的方式固定，并且我们以适当的时间重新缩放对非平衡动力学进行编码。通过这种方式，我们计算了几个相关函数，这些函数以领先的顺序分解为在不同时间为两种模式评估的多点函数。根据可观察量，有质量模式或无质量模式的贡献可能占主导地位，分别导致时间指数或幂律衰减。我们的结果可以直接应用于所有淬火问题，其中，