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Weakly Turbulent Solution to the Schrödinger Equation on the 2D Torus with Potential

Offered By: Erwin Schrödinger International Institute for Mathematics and Physics (ESI) via YouTube

Tags

Schrodinger Equation Courses Quantum Mechanics Courses Fourier Analysis Courses Partial Differential Equations Courses Sobolev Spaces Courses Oscillators Courses Turbulence Courses Mathematical Physics Courses

Course Description

Overview

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Explore a 30-minute conference talk on constructing a smooth solution to the linear Schrödinger equation on the 2D torus with a vanishing potential. Delve into the adaptation of CKSTT 2010 techniques to demonstrate logarithmic growth of the H^1 Sobolev norm in a linear setting. Examine how nonlinear ideas provide new insights into the linear problem through Fourier mode analysis and a discrete resonant system of ODEs. Discover the construction of a special solution resembling a sequence of finite-dimensional linear oscillators, revealing the energy propagation mechanism to higher frequencies. Gain a deeper understanding of the growth rate control and the underlying growth mechanism in this mathematical exploration presented at the Erwin Schrödinger International Institute for Mathematics and Physics.

Syllabus

Ambre Chabert - Weakly turbulent solution to the Schrödinger equation on the 2D torus with potential


Taught by

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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