Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland.
Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.
Phys Rev Lett. 2023 Jan 20;130(3):030401. doi: 10.1103/PhysRevLett.130.030401.
Many experimentally relevant systems are quasi-one-dimensional, consisting of nearly decoupled chains. In these systems, there is a natural separation of scales between the strong intrachain interactions and the weak interchain coupling. When the intrachain interactions are integrable, weak interchain couplings play a crucial part in thermalizing the system. Here, we develop a Boltzmann-equation formalism involving a collision integral that is asymptotically exact for any interacting integrable system, and apply it to develop a quantitative theory of relaxation in coupled Bose gases in the experimentally relevant Newton's cradle setup. We find that relaxation involves a broad spectrum of timescales. We provide evidence that the Markov process governing relaxation at late times is gapless; thus, the approach to equilibrium is generally nonexponential, even for spatially uniform perturbations.
许多与实验相关的系统都是准一维的，由几乎解耦的链组成。在这些系统中，强的链内相互作用和弱的链间耦合之间存在自然的尺度分离。当链内相互作用是可积的时，弱的链间耦合在热化系统中起着至关重要的作用。在这里，我们发展了一种涉及碰撞积分的玻尔兹曼方程形式，该形式对于任何相互作用的可积系统都是渐近精确的，并将其应用于牛顿摇篮实验相关的耦合玻色气体中弛豫的定量理论。我们发现弛豫涉及到广泛的时间尺度。我们提供了证据表明，控制弛豫的马氏过程是无间隙的；因此，即使对于空间均匀的微扰，平衡的趋近通常也不是指数的。
