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| related topics |
| {phase, path, phys} |
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| {state, states, coherent} |
| {time, wave, function} |
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Phase-space path-integral calculation of the Wigner function
J. H. Samson
abstract: The Wigner function W(q,p) is formulated as a phase-space path integral,
whereby its sign oscillations can be seen to follow from interference between
the geometrical phases of the paths. The approach has similarities to the
path-centroid method in the configuration-space path integral. Paths can be
classified by the mid-point of their ends; short paths where the mid-point is
close to (q,p) and which lie in regions of low energy (low P function of the
Hamiltonian) will dominate, and the enclosed area will determine the sign of
the Wigner function. As a demonstration, the method is applied to a sequence of
density matrices interpolating between a Poissonian number distribution and a
number state, each member of which can be represented exactly by a discretized
path integral with a finite number of vertices. Saddle point evaluation of
these integrals recovers (up to a constant factor) the WKB approximation to the
Wigner function of a number state.
- oai_identifier:
- oai:arXiv.org:quant-ph/0308119
- categories:
- quant-ph
- comments:
- 16 pages. Small number of typos corrected, including sign in eq A21
- doi:
- 10.1088/0305-4470/36/42/015
- arxiv_id:
- quant-ph/0308119
- journal_ref:
- Journal of Physics A: Mathematical and General, 36, 10637 - 10650
(2003)
- created:
- 2003-08-22
- updated:
- 2003-10-13
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