论文标题
雅各比相干状态的Krylov复杂性
Krylov Complexity for Jacobi Coherent States
论文作者
论文摘要
我们开发了将Krylov复杂性扩展到迄今为止文献中所考虑的简单哈密顿系统之外的必要计算工具。作为朝着更广泛目标迈出的第一步，我们展示了如何增强迭代性生成Krylov基础的兰开斯算法，以治疗与Jacobi Group相关的相干状态，Jacobi Group是3维真实的Heisenberg-Weyl组的半导体产品， su（1,1）$。这种相干状态在例如量子光学元件中实际意识到了挤压状态。凭借Krylov的基础，$ SU（1,1）$和Heisenberg-Weyl群体都已充分了解，他们的半独立产品也可以部分分析。我们利用它来基准一个方案，以数值计算Lanczos系数，该系数原则上将其推广到更通用的Jacobi组$ H_ {N} \ rtimes sp（2n，\ Mathbb {r}）$。
We develop computational tools necessary to extend the application of Krylov complexity beyond the simple Hamiltonian systems considered thus far in the literature. As a first step toward this broader goal, we show how the Lanczos algorithm that iteratively generates the Krylov basis can be augmented to treat coherent states associated with the Jacobi group, the semi-direct product of the 3-dimensional real Heisenberg-Weyl group $H_{1}$, and the symplectic group, $Sp(2,\mathbb{R})\simeq SU(1,1)$. Such coherent states are physically realized as squeezed states in, for example, quantum optics. With the Krylov basis for both the $SU(1,1)$ and Heisenberg-Weyl groups being well understood, their semi-direct product is also partially analytically tractable. We exploit this to benchmark a scheme to numerically compute the Lanczos coefficients which, in principle, generalizes to the more general Jacobi group $H_{n}\rtimes Sp(2n,\mathbb{R})$.
