Convergence to equilibrium under a random Hamiltonian
Convergence to equilibrium under a random Hamiltonian
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DOI：
10.1103/physreve.86.031101
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发表时间：
2012-09-04
影响因子：
2.4
通讯作者：
Mozrzymas, Marek
中科院分区：
文献类型：
--
作者：
Brandao, Fernando G. S. L.;Cwiklinski, Piotr;Mozrzymas, Marek
我们分析了一个大系统的子系统在随机总哈密顿量下的平衡时间，其中哈密顿量的基取自Haar测度。我们得到平衡时间是玻尔频率算术平均值的倒数量级。为了计算随机基础上的平均值，我们计算置换四个系统的算子重叠矩阵的逆。我们首先得到关于任意有限群表示的这种矩阵的结果，然后将它应用于所考虑的置换群的特定表示。
We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse of the arithmetic average of the Bohr frequencies. To compute the average over a random basis, we compute the inverse of a matrix of overlaps of operators which permute four systems. We first obtain results on such a matrix for a representation of an arbitrary finite group and then apply it to the particular representation of the permutation group under consideration.