Boltzmann-Gibbs statistics meets infinite ergodic theory

Statistical Physics and Complexity Group meeting

Boltzmann-Gibbs statistics meets infinite ergodic theory

  • Event time: 3:00pm until 4:00pm
  • Event date: 1st November 2022
  • Speaker: (Bar-Ilan University, Israel)
  • Location: Online - see email.

Event details

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 a non-normalised Boltzmann Gibbs measure can still yield statistical averages and thermodynamic properties of physical observables, exploiting a model of Langevin dynamics of a Brownian particle in an asymptotically flat potential [1]. The ergodic theory of such systems is known in mathematics as infinite (non-normalisable) ergodic theory, time permitting we will discuss these issues 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).

Event resources