Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation

Berg, B., Plimak, L. I., Polkovnikov, A., Olsen, M. K., Fleischhauer, M. and Schleich, W. P. (2009) Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation. Physical Review A, 80 3: 033624-1-033624-17. doi:10.1103/PhysRevA.80.033624

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Author Berg, B.
Plimak, L. I.
Polkovnikov, A.
Olsen, M. K.
Fleischhauer, M.
Schleich, W. P.
Title Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
1094-1622
Publication date 2009-09-29
Year available 2009
Sub-type Article (original research)
DOI 10.1103/PhysRevA.80.033624
Open Access Status File (Publisher version)
Volume 80
Issue 3
Start page 033624-1
End page 033624-17
Total pages 17
Place of publication College Park, MD, United States
Publisher American Physical Society
Collection year 2010
Language eng
Abstract 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. First, what class of multitime averages the −W 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 −W 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 −W 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.
Keyword Parametric oscillator
Bose-gases
Mechanics
Dynamics
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
 
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Created: Thu, 12 Nov 2009, 12:00:30 EST by Mr Andrew Martlew on behalf of ARC Centre of Excellence for Quantum-Atom Optics