论文标题
通过动态参考，在利比利纳气体中放松声子
Relaxation of phonons in the Lieb-Liniger gas by dynamical refermionization
论文作者
论文摘要
我们研究最初在平衡状态下制备的LIEB-LINIGER气体，该状态在声子方面是高斯。由于声子不是哈密顿量的精确特征状态，因此很长时间以来，气体会放松到固定状态。得益于整合性，该固定状态不需要成为热状态。我们表征放松后气体的固定状态并计算其声子种群分布。从技术上讲，这是从Lieb-Liniger Hamiltonian的确切本征态与非相互作用的费米气体的映射（由Bethe方程提供的映射）以及在Hilbert Space低增强部门有效的授权公式之间的映射。我们将结果应用于初始状态是单个声子模式的激发相干状态的情况，并且我们将它们与在硬核极限中获得的精确结果进行了比较。
We investigate the Lieb-Liniger gas initially prepared in an out-of-equilibrium state that is Gaussian in terms of the phonons. Because the phonons are not exact eigenstates of the Hamiltonian, the gas relaxes to a stationary state at very long times. Thanks to integrability, that stationary state needs not be a thermal state. We characterize the stationary state of the gas after relaxation and compute its phonon population distribution. Technically, this follows from the mapping between the exact eigenstates of the Lieb-Liniger Hamiltonian and those of a non-interacting Fermi gas -- a mapping provided by the Bethe equations -- , as well as on bosonization formulas valid in the low-energy sector of the Hilbert space. We apply our results to the case where the initial state is an excited coherent state for a single phonon mode, and we compare them to exact results obtained in the hard-core limit.
