2009/05/19 by B. Berg, L. I. Plimak, A. Polkovnikov +3
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreva.80.033624
published as Phys. Rev. A 80, 033624 (2009) · 20 pages, 6 figures
arxiv created 2009/05/19 · arxiv updated 2009/12/01
The applicability of the so-called truncated Wigner approximation (-W) is extended to multitime averages of Heisenberg field operators. This task splits naturally in two. Firstly, what class of multitime averages the -W approximates, and, secondly, how to proceed if the average in question does not belong to this class. To answer the first question we develop an (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 -W equations emerge as an approximation within this 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 -W is trivially generalised 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.