dorsal/arxiv
View SchemaSelf-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves
| Authors | Albert C. Fannjiang |
|---|---|
| Categories | |
| ArXiv ID | physics/0609200 |
| URL | https://arxiv.org/abs/physics/0609200 |
| DOI | 10.1088/1751-8113/40/19/007 |
| Journal | J. Phys. A: Math. Theor. 40 (2007) 5025-5044 |
Abstract
Two-frequency Wigner distribution is introduced to capture the asymptotic behavior of the space-frequency correlation of paraxial waves in the radiative transfer limits. The scaling limits give rises to deterministic transport-like equations. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker-Planck-like differential equation in the phase space. The solutions to these equations have a probabilistic representation which can be simulated by Monte Carlo method. When the medium fluctuates more rapidly in the longitudinal direction, the corresponding Fokker-Planck-like equation can be solved exactly.
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"abstract": "Two-frequency Wigner distribution is introduced to capture the asymptotic\nbehavior of the space-frequency correlation of paraxial waves in the radiative\ntransfer limits. The scaling limits give rises to deterministic transport-like\nequations. Depending on the ratio of the wavelength to the correlation length\nthe limiting equation is either a Boltzmann-like integral equation or a\nFokker-Planck-like differential equation in the phase space. The solutions to\nthese equations have a probabilistic representation which can be simulated by\nMonte Carlo method. When the medium fluctuates more rapidly in the longitudinal\ndirection, the corresponding Fokker-Planck-like equation can be solved exactly.",
"arxiv_id": "physics/0609200",
"authors": [
"Albert C. Fannjiang"
],
"categories": [
"physics.optics",
"physics.gen-ph"
],
"doi": "10.1088/1751-8113/40/19/007",
"journal_ref": "J. Phys. A: Math. Theor. 40 (2007) 5025-5044",
"title": "Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves",
"url": "https://arxiv.org/abs/physics/0609200"
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