The DOI matches its Crossref record; 15 of the 15 references it cites were found in a registry or an index.
Generalised P-representations in quantum optics
Abstract
A class of normal ordering representations of quantum operators is introduced, that generalises the Glauber-Sudarshan P-representation by using nondiagonal coherent state projection operators. These are shown to have practical application to the solution of quantum mechanical master equations. Different representations have different domains of integration, on a complex extension of the usual canonical phase-space. The 'complex P-representation' is the case in which analytic P-functions are defined and normalised on contours in the complex plane. In this case, exact steady-state solutions can often be obtained, even when this is not possible using the Glauber-Sudarshan P-representation. The 'positive P-representation' is the case in which the domain is the whole complex phase-space. In this case the P-function may always be chosen positive, and any Fokker-Planck equation arising can be chosen to have a positive-semidefinite diffusion array. Thus the 'positive P-representation' is a genuine probability distribution. The new representations are especially useful in cases of nonclassical statistics.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Coherent and Incoherent States of the Radiation Field
Glauber, R. J. (1963) · Physical Review · doi:10.1103/physrev.131.2766 · Cited by 6,797
The Quantum Theory of Optical Coherence
Glauber, R. J. (1963) · Physical Review · doi:10.1103/physrev.130.2529 · Cited by 4,077
Equivalence of Semiclassical and Quantum Mechanical Descriptions of Statistical Light Beams
Sudarshan, E. C. G. (1963) · Physical Review Letters · doi:10.1103/physrevlett.10.277 · Cited by 2,665
Density Operators and Quasiprobability Distributions
Cahill, K. E., & Glauber, R. J. (1969) · Physical Review · doi:10.1103/physrev.177.1882 · Cited by 1,257
Ordered Expansions in Boson Amplitude Operators
Cahill, K. E., & Glauber, R. J. (1969) · Physical Review · doi:10.1103/physrev.177.1857 · Cited by 1,118
Quantum theory of optical bistability. I. Nonlinear polarisability model
Drummond, P. D., & Walls, D. F. (1980) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/13/2/034 · Cited by 553
Self-citationAgarwal, G. S., & Wolf, E. (1970) · Physical Review D · doi:10.1103/physrevd.2.2161 · Cited by 552
Quantum Noise. XI. Multitime Correspondence between Quantum and Classical Stochastic Processes
Lax, M. (1968) · Physical Review · doi:10.1103/physrev.172.350 · Cited by 443
A quantum-mechanical master equation treatment of the dynamical Stark effect
Carmichael, H. J., & Walls, D. F. (1976) · Journal of Physics B: Atomic and Molecular Physics · doi:10.1088/0022-3700/9/8/007 · Cited by 397
Agarwal, G. S., & Wolf, E. (1970) · Physical Review D · doi:10.1103/physrevd.2.2187 · Cited by 285
Cited by
Carusotto, I., & Ciuti, C. (2013) · Reviews of Modern Physics · doi:10.1103/revmodphys.85.299 · Cited by 1,996
Strongly Interacting Photons in a Nonlinear Cavity
Imamoḡlu, A., Schmidt, H., Woods, G., & Deutsch, M. (1997) · Physical Review Letters · doi:10.1103/physrevlett.79.1467 · Cited by 1,090
Dynamical quantum noise in trapped Bose-Einstein condensates
Steel, M. J., Olsen, M. K., Plimak, L. I., Drummond, P. D., Tan, S. M., Collett, M. J., Walls, D. F., & Graham, R. (1998) · Physical Review A · doi:10.1103/physreva.58.4824 · Cited by 434
Self-citationNon-equilibrium Transitions in Sub/second Harmonic Generation
Drummond, P. D., McNeil, K. J., & Walls, D. F. (1981) · Optica Acta: International Journal of Optics · doi:10.1080/713820531 · Cited by 280
Self-citationGauge-independent Wigner functions: General formulation
Serimaa, O. T., Javanainen, J., & Varró, S. (1986) · Physical Review A · doi:10.1103/physreva.33.2913 · Cited by 82
Metadata
- Authors
- Drummond, P. D., & Gardiner, C. W.
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1980-07-01
- Volume
- 13
- Issue
- 7
- Pages
- 2353-2368
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2038366371
- Cited by
- 710
- References
- 15
- FWCI
- 3.98
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Generalised P-representations in quantum optics. https://app.cochat.ai/papers/10.1088/0305-4470/13/7/018
- The paper
- Drummond, P. D., & Gardiner, C. W. (1980). Generalised P-representations in quantum optics. Journal of Physics A: Mathematical and General. https://doi.org/10.1088/0305-4470/13/7/018
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
