发表机构
Scuola Normale Superiore; NEST; Istituto Nanoscienze-CNR（比萨高等师范学院; 纳米科学与技术研究所在; 意大利国家研究委员会纳米科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对含时哈密顿量的 Fer 展开，将其收敛半径从 2 改进约 30% 至约 2.6058，扩大了该幺正展开的适用条件。
AI 中文摘要
Dyson 级数将含时哈密顿量的传播子按哈密顿量的幂次展开，但其截断通常不是幺正的。Fer 展开将同一传播子写成矩阵指数的无穷乘积，每个因子都是幺正的，其余项随因子数目呈双指数衰减。然而，收敛性仅在有限半径内得到保证：哈密顿量范数的时间积分必须小于 $2$。这是迄今为止已知的最佳值。在此，我们将其改进约 $30\%$，提高到约 $2.6058$。
英文摘要
The Dyson series expands the propagator of a time-dependent Hamiltonian in powers of the Hamiltonian, but its truncations are in general not unitary. The Fer expansion writes the same propagator as an infinite product of matrix exponentials, each of them unitary, and its remainder decays doubly exponentially with the number of factors. Convergence, however, is guaranteed only within a finite radius: the time integral of the norm of the Hamiltonian must be smaller than $2$. This is the best value known to date. Here we improve it by about $30\%$, raising it to about $2.6058$. The result also holds for non-Hermitian Hamiltonians that are Hermitian with respect to a fixed metric.
Comments9 pages, 2 figures. v2: revisited abstract; new Sec. IV on the spectral half-width, Hamiltonians Hermitian in a fixed metric, and general non-Hermitian Hamiltonians
