Cumulant Expansions and the Spin-Boson Problem

TL;DR

This paper compares three cumulant expansion methods for analyzing the zero-temperature spin-boson problem, introducing a new non-crossing technique that combines their advantages.

Contribution

It presents a new non-crossing cumulant expansion method that improves upon existing techniques for the spin-boson problem.

Findings

The non-crossing cumulant expansion embodies the virtues of standard methods.

Different cumulant techniques have distinct merits and drawbacks.

The new method shows promising results for dissipative two-level systems.

Abstract

The dynamics of the dissipative two-level system at zero temperature is studied using three different cumulant expansion techniques. The relative merits and drawbacks of each technique are discussed. It is found that a new technique, the non-crossing cumulant expansion, appears to embody the virtues of the more standard cumulant methods.