Nonergodicity of d-dimensional generalized Lévy walks and their relation to other space-time coupled models.

We investigate the nonergodicity of the generalized Lévy walk introduced by Shlesinger et al. [Phys. Rev.

Gas of sub-recoiled laser cooled atoms described by infinite ergodic theory.

The velocity distribution of a classical gas of atoms in thermal equilibrium is the normal Maxwell distribution. It is well known that for sub-recoiled laser cooled atoms, Lévy statistics and deviations from usual ergodic behavior come into play. In a recent letter, we showed how tools from infinite ergodic theory describe the cool gas.

Transitions in the Ergodicity of Subrecoil-Laser-Cooled Gases.

With subrecoil-laser-cooled atoms, one may reach nanokelvin temperatures while the ergodic properties of these systems do not follow usual statistical laws. Instead, due to an ingenious trapping mechanism in momentum space, power-law-distributed sojourn times are found for the cooled particles. Here, we show how this gives rise to a statistical-mechanical framework based on infinite ergodic theory, which replaces ordinary ergodic statistical physics of a thermal gas of atoms.