A wavefunction that is a solution to the rigid rotor Schrödinger equation (defined in Equation 7.3.1) can be written as a single function Y, ), which is called a spherical harmonic function. Lecture Notes in Physics, vol. 38, pp. 1–111. Describe how the spacing between levels varies with increasing J. (ed.), Time Evolution of Large Classical Systems. Kuksin, S.B.: On turbulence in nonlinear Schrödinger equations. Kuksin, S.B.: Growth and oscillations of solutions of nonlinear Schrödinger equation. Janssen, P.A.: Progress in ocean wave forecasting. In the limit \(L\to \infty \) and \(\alpha \to 0\), under the scaling law \(\alpha \sim L^)\). More precisely, in dimensions \(d\geq 3\), we consider the (NLS) equation in a large box of size \(L\) with a weak nonlinearity of strength \(\alpha \). Our result is the wave analog of Lanford’s theorem on the derivation of the Boltzmann kinetic equation from particle systems, where in both cases one takes the thermodynamic limit as the size of the system diverges to infinity, and as the interaction strength of waves/radius of particles vanishes to 0, according to a particular scaling law (Boltzmann-Grad in the particle case). the kinetic theory of nonlinear wave systems. This solves a main conjecture in the theory of wave turbulence, i.e. We provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear Schrödinger (NLS) equation at the kinetic timescale, under a particular scaling law that describes the limiting process.
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