Physical applications of infinite ergodic theory

Seminar

QUEST Center event

No

Speaker

Eli Barkai, Bar Ilan

Date

29/11/2021 - 14:00 - 12:30Add to Calendar 2021-11-29 12:30:00 2021-11-29 14:00:00 Physical applications of infinite ergodic theory zoom: https://us02web.zoom.us/j/89236785442 Physical applications of infinite ergodic theory Eli Barkai Fermi pointed out that the Hydrogen atom in a thermal setting is unstable, as the canonical partition function of this simple system diverges. We show how non-normalised Boltzmann Gibbs measure can still yield statistical averages and thermodynamic properties of physical observables, exploiting a model of Langevin dynamics of a single Brownian particle in an asymptotically flat potential [1]. The ergodic theory of such systems is known in mathematics as infinite (non-normalisable) ergodic theory, a framework that is widely applicable from laser cooled gases to non-linear systems. [1] E. Aghion, D. A. Kessler, and E. Barkai , Non-normalizable Boltzmann-Gibbs statistics to infinite-ergodic theory, Phys. Rev. Lett. 122, 010601 (2019) Physics Building 203, Room 221 and https://us02web.zoom.us/j/89236785442 Department of Physics physics.dept@mail.biu.ac.il Asia/Jerusalem public

Place

Physics Building 203, Room 221 and https://us02web.zoom.us/j/89236785442

Abstract

zoom: https://us02web.zoom.us/j/89236785442

Physical applications of infinite ergodic theory

Eli Barkai

Fermi pointed out that the Hydrogen atom in a thermal setting is unstable, as the canonical partition function of this simple system diverges. We show how non-normalised Boltzmann Gibbs measure can still yield statistical averages and thermodynamic properties of physical observables, exploiting a model of Langevin dynamics of a single Brownian particle in an asymptotically flat potential [1]. The ergodic theory of such systems is known in mathematics as infinite (non-normalisable) ergodic theory, a framework that is widely applicable from laser cooled gases to non-linear systems.

[1] E. Aghion, D. A. Kessler, and E. Barkai , Non-normalizable Boltzmann-Gibbs statistics to infinite-ergodic theory, Phys. Rev. Lett. 122, 010601 (2019)

Attached file

BIU2021.pdf