Confining atoms to a single line (1D) results in a system, whose elementary excitations are quasi-particles with properties that may differ significantly from the atoms; in a Bose gas, correlation effects due to interactions in 1D prevent two quasi-particle excitations from occupying the same quantum state. This imposed Pauli exclusion leads to effective fermionization of the quantum Bose gas...

Due to its probabilistic nature, a measurement process produces a distribution of possible outcomes. This distribution — or its Fourier transform known as full counting statistics (FCS) — contains much more information than say the mean value of the measured ob- servable and accessing it is sometimes the only way to obtain relevant information about the system.

In fact, the FCS is the limit...

I will discuss several examples of non-ergodic dynamical systems with anomalous charge fluctuations.