**Eli Barkai, Physics Dept., Bar Ilan University, Ramat Gan, Israel**

*Lecturer:*Abstract:

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 proper-

ties 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, which in the second

part of the talk is discussed in the context of a gas of laser cooled atoms [2].

References

[1] E. Aghion, D. A. Kessler, and E. Barkai From Non-normalizable Boltzmann-

Gibbs statistics to infinite-ergodic theory Phys. Rev. Lett. 122, 010601 (2019)

[2] E. Barkai, G. Radons, and T. Akimoto Transitions in the ergodicity of subrecoil-

laser-cooled gases Phys. Rev. Lett. 127, 140605 (2021).