2025/10/22 by Kazutaka Takahashi, Pratik Nandy, Takahashi, Kazutaka +3 · 1 voice · 2 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2510.19436
The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of constructing solvable models from known instances. In doing so, we relate the evolution of deformed and undeformed theories and investigate their complexity. For a certain class of deformations, the resulting Krylov subspace is unchanged, and we observe time evolutions with a reorganized basis. The tridiagonal form of the generator in the Krylov space is maintained, and we obtain generalized Toda equations as a function of the deformation parameters. The imaginary-time-like evolutions can be described by real-time unitary ones. As possible applications, we discuss coherent Gibbs states for thermodynamic systems, for which we analyze the survival probability, spread complexity, Krylov entropy, and associated time-averaged quantities. We further discuss the statistical properties of random matrices and supersymmetric systems for quadratic deformations.