Path integrals for wave intensity fluctuations in random media |
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| Affiliation: | 2. NBER, Cambridge, MA, United States;1. New York University, Microsoft Research and NBER, United States of America;2. Stanford University, United States of America;3. Stanford University and NBER, United States of America;4. Harvard University, United States of America;5. Harvard University and NBER, United States of America;1. Institute for Applied Mathematics FEB RAS, Radio st. 7, Vladivostok, 690041, Russia;2. Far Eastern Federal University, Sukhanova st. 8, Vladivostok, 690950, Russia;3. Klinikum rechts der Isar, Technische Universität München, Ismaningerstr. 22, München 81675, Germany;4. Fakultät für Mathematik, Technische Universität München, Boltzmannstr. 3, Garching bei München 85747, Germany |
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| Abstract: | Approximate expressions for the fourth order moment of a wave propagating in a random medium are derived by using the path integral formulation. These solutions allow the spectrum of intensity fluctuations of a multiply scattered wave to be found, and they are valid at all distances in the medium. The results obtained by path integral methods turn out to be the same as those obtained previously by solving the parabolic partial differential equation for the fourth moment. The spatial frequency spectra of intensity fluctuations are evaluated for a medium in which the irregularities have a single scale and also for one in which there is a range of scale sizes. |
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