Gaussian fluctuations from random Schr\"odinger equation
Yu Gu, Tomasz Komorowski
TL;DR
This paper investigates the effects of weak Brownian forcing on the Schrödinger equation, revealing Gaussian fluctuations modeled by an Ornstein-Uhlenbeck process and showing the exponential distribution of incoherent wave intensity at fixed frequencies.
Contribution
It introduces a novel analysis of Gaussian fluctuations in the Schrödinger equation under stochastic forcing, connecting it to Ornstein-Uhlenbeck processes and exponential intensity distributions.
Findings
Gaussian fluctuations modeled by Ornstein-Uhlenbeck process
Incoherent wave intensity follows exponential distribution
Weak Brownian forcing impacts wave behavior significantly
Abstract
We study the Schr\"odinger equation driven by a weak Brownian forcing, and derive Gaussian fluctuations in the form of a time-inhomogeneous Ornstein-Uhlenbeck process. As a result, when evaluated at a fixed frequency, the intensity of the incoherent wave is of exponential distribution.
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Taxonomy
TopicsRandom lasers and scattering media · Nonlinear Dynamics and Pattern Formation · Terahertz technology and applications