Квантовая динамика методом рекурсии: последние разработки и перспективы

Recursion method maps quantum dynamics of an observable in an arbitrary many-body system to a seemingly simple problem of a single particle hopping on a one-dimensional semi-infinite lattice. This is done by representing the evolution operator as a tridiagonal matrix by means of the Lanczos algorithm. For a long time, the practical application of the method has been largely hindered by poor understanding of the hopping amplitudes governing the single-body dynamics on the lattice.
Recently, it has been conjectured that the hopping amplitudes far from the origin of the semi-infinite lattice have a universal asymptotic form. The amplitudes in the vicinity of the origin, on the other hand, can be nowadays found by means of highly parallelizable computer calculations. These developments promise to greatly enhance the power and versatility of the recursion method. I will review the method, present some promising results and discuss prospects and challenges.