一个精确可解电子-声子模型的弛豫动力学
Relaxation dynamics of an exactly solvable electron-phonon model
摘要：
我们解决的问题是否观察到的一个精确的可解模型的电子耦合（光学）声子放松到大的时间稳态值和调查，如果渐近期望值可以使用一个固定的密度矩阵计算。两个初始非平衡的情况被认为是。突然淬火的电子-声子耦合，从非相互作用的正则平衡在温度T的电子以及声子子系统，导致一个相当简单的动力学。如果把初始态看作是声子真空和充满的费米海的乘积，再加上一个高激发的附加电子，我们的模型就有了一组自然的运动常数，其元素与自由度一样多。根据这类模型的早期研究，我们发现，成为平稳的期望值可以描述的密度矩阵的广义吉布斯系综，这不同于一个典型的系综。对于手头的模型，似乎是显而易见的，本征模占用算子应使用在固定的密度矩阵的建设。
英文摘要：
We address the question whether observables of an exactly solvable model of electrons coupled to (optical) phonons relax into large time stationary state values and investigate if the asymptotic expectation values can be computed using a stationary density matrix. Two initial nonequilibrium situations are considered. A sudden quench of the electron-phonon coupling, starting from the noninteracting canonical equilibrium at temperature T in the electron as well as in the phonon subsystems, leads to a rather simple dynamics. A richer time evolution emerges if the initial state is taken as the product of the phonon vacuum and the filled Fermi sea supplemented by a highly excited additional electron. Our model has a natural set of constants of motion, with as many elements as degrees of freedom. In accordance with earlier studies of such type of models we find that expectation values which become stationary can be described by the density matrix of a generalized Gibbs ensemble which differs from that of a canonical ensemble. For the model at hand it appears to be evident that the eigenmode occupancy operators should be used in the construction of the stationary density matrix.
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