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Quantum evolution by resummations on graphs: The methods of walk- and path-sums

Simon Thwaite (University of Oxford)

14.11.2011 at 14:00 

We present a method of evaluating the time-evolution operator for many-body systems based on a closed-form resummation of various families of terms in the Taylor series for the matrix exponential. This approach, which is inspired by connections between matrix multiplication and walks on directed graphs, corresponds to a discrete analogue of Feynman path integrals, and allows any symmetries and structure present in the Hamiltonian to be taken advantage of. We discuss a recent application to a large system of interacting Rydberg atoms, and propose other systems to which the method of path-sums may be suited.

A 450 Theresienstra├če 37