Full Counting Statistics of Charge in Quenched Quantum Gases

Unless constrained by symmetry, measurement of an observable on an ensemble of identical quantum systems returns a distribution of values which are encoded in the full counting statistics. While the mean value of this distribution is important for determining certain properties of a system, the full distribution can also exhibit universal behavior. In this paper we study the full counting statistics of particle number in one dimensional interacting Bose and Fermi gases which have been quenched far from equilibrium. In particular we consider the time evolution of the Lieb-Liniger and Gaudin-Yang models quenched from a Bose-Einstein condensate initial state and calculate the full counting statistics of the particle number within a subsystem. We show that the scaled cumulants of the charge in the initial state and at long times are simply related and in particular the latter are independent of the model parameters. Using the quasi-particle picture we obtain the full time evolution of the cumulants and find that although their endpoints are fixed, the finite time dynamics depends strongly on the model parameters. We go on to construct the scaled cumulant generating functions and from this determine the limiting charge probability distributions at long time which are shown to exhibit distinct non-trivial and non-Gaussian fluctuations and large deviations.