Time-dependent density-functional theory (TDDFT) describes the quantum dynamics of
interacting electronic many-body systems formally exactly and in a practical and efficient …

We show that the combination of charge and dipole conservation—characteristic of fracton
systems—leads to an extensive fragmentation of the Hilbert space, which, in turn, can lead …

The ability to prepare a physical system in a desired quantum state is central to many areas
of physics such as nuclear magnetic resonance, cold atoms, and quantum computing. Yet …

Due to the significant improvement in computing power and the rapid advancement of data
processing technologies, artificial intelligence (AI) has introduced new tools and …

This book evolved from lecture notes developed over the past 20+ years of teaching this
material, mostly in Applied Mathematics 585–6 at the University of Washington. The course …

Functions of matrices have been studied for as long as matrix algebra itself. Indeed, in his
seminal A Memoir on the Theory of Matrices (1858), Cayley investigated the square root of a …

In principle, the exponential of a matrix could be computed in many ways. Methods involving
approximation theory, differential equations, the matrix eigenvalues, and the matrix …

In this paper we consider the construction, analysis, implementation and application of
exponential integrators. The focus will be on two types of stiff problems. The first one is …

A modification of the exponential time-differencing fourth-order Runge--Kutta method for
solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in …

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it
computes either a small matrix exponential in full, the action of a large sparse matrix …