In mathematics and physics, the Artin billiard is a type of a dynamical billiard first studied by Emil Artin in 1924. It describes the geodesic motion of a free particle on the non-compact Riemann surface where is the upper half-plane endowed with the Poincaré metric and is the modular group. It can be viewed as the motion on the fundamental domain of the modular group with the sides identified. The system is notable in that it is an exactly solvable system that is strongly chaotic: it is not only ergodic, but is also strong mixing. As such, it is an example of an Anosov flow. Artin's paper used symbolic dynamics for analysis of the system. The quantum mechanical version of Artin's billiard is also exactly solvable. The eigenvalue spectrum consists of a bound state and a continuous spectrum above the energy . The wave functions are given by Bessel functions. (Wikipedia).
From playlist Art Quizzes
From playlist Art Quizzes
Random Matrices in Unexpected Places: Atomic Nuclei, Chaotic Billiards, Riemann Zeta #SoME2
Chapters: 0:00 Intro 2:21 What is RMT 7:12 Ensemble Averaging/Quantities of Interest 13:30 Gaussian Ensemble 18:03 Eigenvalues Repel 28:08 Recap 29:08 Three Surprising Coincidences 32:44 Billiards/Quantum Systems 36:00 Reimann Zeta ~~~~~~~~~~~~~~~~~~~~~~~~~ Errata + Clarifications ~~~~
From playlist Summer of Math Exposition 2 videos
INTERVIEW AT CIRM : MICHAEL ARTIN
Michael ARTIN participated in the "Artin Approximation and Infinite dimensional Geometry" event organized at CIRM in March 2015, which was part of the Jean-Morlet semester held by Herwig Hauser. Michael Artin is an American mathematician and a professor emeritus in the Massachusetts Ins
From playlist Jean-Morlet Chair's guests - Interviews
Filiz Dogru: Outer Billiards: A Comparison Between Affine, Hyperbolic, and Symplectic Geometry
Filiz Dogru, Grand Valley State University Title: Outer Billiards: A Comparison Between Affine Geometry, Hyperbolic Geometry, and Symplectic Geometry Outer billiards appeared first as an entertainment question. Its popularity increased after J. Moser’s description as a crude model of the p
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
ECR Talk: "A tale of two (or more, integrable) billiards", Sean Gasiorek
SMRI -MATRIX Symposium: Nijenhuis Geometry and Integrable Systems Week 2 (MATRIX): ECR Talk by Sean Gasiorek 14 February 2022 ---------------------------------------------------------------------------------------------------------------------- SMRI-MATRIX Joint Symposium, 7 – 18 Februar
From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems
How to recognize billiard strings #SOME2
For the curious, "Sturmian sequences" are the name for balanced binary strings that are also infinite and not eventually periodic. Sturmian sequences are related in some very cool ways to continued fractions and several other topics. That may be the subject of Part 3, if I ever get that fa
From playlist Summer of Math Exposition 2 videos
Reflections on the Game of Billiards
Asaf Hadari, Gibbs Assistant Professor in the Yale Mathematics Department, gives a lecture during the Math Mornings at Yale on Reflections on the Game of Billiards. Math Mornings is a series of public lectures aimed at bringing the joy and variety of mathematics to students and their fami
From playlist Math Mornings at Yale
Dynamics on the Moduli Spaces of Curves, I - Maryam Mirzakhani
Maryam Mirzakhani Stanford University March 26, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Quantum Ergodicity for the Uninitiated - Zeev Rudnick
Zeev Rudnick Tel Aviv University; Member, School of Mathematics October 26, 2015 https://www.math.ias.edu/seminars/abstract?event=47561 A key result in spectral theory linking classical and quantum mechanics is the Quantum Ergodicity theorem, which states that in a system in which the cl
From playlist Members Seminar
Rose Morris-Wright: Parabolic Subgroups of Infinite Type Artin Groups
Abstract : Parabolic subgroups are the fundamental building blocks of Artin groups. These subgroups are isomorphic copies of smaller Artin groups nested inside a given Artin group. In this talk, I will discuss questions surrounding how parabolic subgroups sit inside Artin groups and how th
From playlist Virtual Conference
Ellipses of small eccentricity are determined by their Dirichlet... - Steven Morris Zelditch
Analysis Seminar Topic: Ellipses of small eccentricity are determined by their Dirichlet (or, Neumann) spectra Speaker: Steven Morris Zelditch Affiliation: Northwestern University Date: April 28, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics