Abstract
The applicability of the so-called truncated Wigner approximation is extended to multitime averages of Heisenberg field operators. This task splits naturally in two. First, what class of multitime averages the approximates and, second, how to proceed if the average in question does not belong to this class. To answer the first question, we develop a (in principle, exact) path-integral approach in phase space based on the symmetric (Weyl) ordering of creation and annihilation operators. These techniques calculate a new class of averages which we call time-symmetric. The equations emerge as an approximation within these path-integral techniques. We then show that the answer to the second question is associated with response properties of the system. In fact, for two-time averages, Kubo’s renowned formula relating the linear-response function to two-time commutators suffices. The is directly generalized to the response properties of the system allowing one to calculate approximate time normally ordered two-time correlation functions with surprising ease. The techniques we develop are demonstrated for the Bose-Hubbard model.
- Received 20 May 2009
DOI:https://doi.org/10.1103/PhysRevA.80.033624
©2009 American Physical Society