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

Approximate resolution of linear systems of differential equations with varying coefficients is
a recurrent problem, shared by a number of scientific and engineering areas, ranging from …

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 …

We review recent theoretical work on two closely related issues: excitation of an isolated
quantum condensed matter system driven adiabatically across a continuous quantum phase …

In this paper we address the problem of the numerical integration of the time-dependent
Schrödinger equation i∂ t φ= Ĥφ. In particular, we are concerned with the important case …

Using the adaptive time-dependent density-matrix renormalization group method, we study
the time evolution of strongly correlated spinless fermions on a one-dimensional lattice after …

Time-dependent density-functional theory (TDDFT) extends the basic ideas of ground-state
density-functional theory (DFT) to the treatment of excitations and of more general time …

Recently, there has been a great deal of interest in the construction of exponential
integrators. These integrators, as their name suggests, use the exponential function (and …

In these lecture notes, we present a pedagogical review of a number of related numerically
exact approaches to quantum many‐body problems. In particular, we focus on methods …

Numerical methods based on the Magnus expansion are an efficient class of integrators for
Schrödinger equations with time-dependent Hamiltonian. Though their derivation assumes …