How Lagrangian States Evolve into Random Waves

Explore a seminar on spectral geometry that delves into the evolution of Lagrangian states into random waves. Learn about Berry's conjecture regarding eigenfunctions of the Laplacian on manifolds of negative curvature and their behavior in the high-energy limit. Discover how Maxime Ingremau and colleagues investigate a simplified scenario involving Lagrangian states associated with generic phases on negatively curved manifolds. Understand the application of the Schrödinger equation and its long-term effects on these functions in the semiclassical limit. Gain insights into quantum chaos, random superposition of plane waves, and the WKB method. Examine the dynamics, ergodicity, and rescaling involved in this mathematical exploration, and consider the open questions and limitations of the research.

Introduction
Framework
Quantum Organicity Theorem
Barrys conjecture
Two eigen functions
Random fields
Random field
Monochrome field
General idea
Open sets
What is conjecture
Interpretation of Barrys conjecture
Lagrangian States
Space of Lagrangian States
Dynamics
Roman Schubert
Alejandro Rivera
WKB method
Propagation
Why is it finite
Rescaling
Rational Independence
Rescaling around X1
Dynamics and ergodicity
Questions
Limits
Not an open set
Number of summons