We study unitary evolution of bipartite entanglement in a circuit with nearest-neighbor random gates. Deriving compact nonunitary description purity dynamics on qudits we find sudden transition the relaxation rate origin which is underlying boundary localized eigenmodes---the skin effect. provide full solution problem, being one simplest iterations two-site matrices, namely, that each sum only ...

In this paper we discuss the problem of computing the H∞-norm of transfer functions associated to large-scale descriptor systems. We exploit the relationship between the H∞-norm and the structured complex stability radius of a corresponding matrix pencil. To compute the structured stability radius we consider so-called structured pseudospectra. Namely, we have to find the pseudospectrum touchin...

Transfer functions have been shown to provide monotonic approximations to the resolvent 2-norm of A, R(z) = (A − zI), when associated with a sequence of nested spaces. This paper addresses the open question of the effectiveness of the transfer function scheme for the computation of the pseudospectrum of large matrices. It is shown that the scheme can be combined with certain Krylov type linear ...

Abstract Motivated by the substantial instability of fundamental and high-overtone quasinormal modes (QNMs), recent developments regarding notion black hole pseudospectrum call for numerical results with unprecedented precision. This work generalizes improves matrix method QNMs to higher orders, specifically aiming at a class perturbations metric featured discontinuity intimately associated QNM...

To understand the solution of a linear, time-invariant differential-algebraic equation (DAE), one must analyze a matrix pencil (A,E) with singular E. Even when this pencil is stable (all its finite eigenvalues fall in the left half-plane), the solution can exhibit transient growth before its inevitable decay. When the equation results from the linearization of a nonlinear system, this transient...

A unifying framework for methods employed in the approximation of the resolvent norm of nonnor-mal matrices is presented. This formulation uses specific transfer functions, and it provides new information about the approximation properties of these methods and their application in computing the pseudospectrum of matrices. 1. Introduction. We now know that the analysis of matrix-dependent algori...