A Lanczos-like method for the time-ordered exponential

• Date: 7. 10. 2021
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Stefano Pozza

The time-ordered exponential (TOE) is defined as the function that solves a system of coupled first-order linear differential equations with generally non-constant coefficients. Despite being at the heart of many problems, the TOE remains elusively difficult to evaluate. The path-sums method formulates any desired entry of a TOE as a branched continued fraction of finite depth and breadth, and it has been successfully used to solve challenging quantum dynamic problems. However, while this approach can provide exact (even analytical) expressions and is unconditionally convergent, it suffers from a complexity drawback. It requires finding all the simple cycles and simple paths of a certain graph G, an #P-complete task. The ⋆-Lanczos algorithm solves this issue by effectively mapping G on a structurally simpler graph. On this graph, the path-sum solution takes the form of an ordinary, finite, continued fraction.