论文标题
耗散开放量子系统中的操作员生长和Krylov构造
Operator growth and Krylov construction in dissipative open quantum systems
论文作者
论文摘要
受通用操作员生长假设的启发，我们扩展了与马尔可夫浴的耗散开放量子系统中Krylov结构的形式主义。我们的构建基于适当的Lindbladian对Liouvillian超级操作员的修改，从而跟随矢量化的Lanczos算法和Arnoldi迭代。由于环境引起的非热效应，这是有道理的。我们研究了边界振幅阻尼和散装dephasing中横向场模型（可集成和混乱限制）中兰开斯系数的生长。尽管兰开斯算法的直接实施未能给出物理有意义的结果，但Arnoldi迭代仍然通过单独的系数（Arnoldi系数）保留了集成性和混乱的通用性质以及非热性的签名，即使包括散发性环境）。我们的结果表明，Arnoldi迭代在处理开放系统方面更有意义，更合适。
Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian superoperator by the appropriate Lindbladian, thereby following the vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified due to the incorporation of non-Hermitian effects due to the environment. We study the growth of Lanczos coefficients in the transverse field Ising model (integrable and chaotic limits) for boundary amplitude damping and bulk dephasing. Although the direct implementation of the Lanczos algorithm fails to give physically meaningful results, the Arnoldi iteration retains the generic nature of the integrability and chaos as well as the signature of non-Hermiticity through separate sets of coefficients (Arnoldi coefficients) even after including the dissipative environment. Our results suggest that the Arnoldi iteration is meaningful and more appropriate in dealing with open systems.
