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We study the fluctuation properties of a one-dimensional many-body quantumsystem composed of interacting bosons, and investigate the regimes wherequantum noise or, respectively, thermal excitations are dominant. For thelatter we develop a semiclassical description of the fluctuation propertiesbased on the Ornstein-Uhlenbeck stochastic process. As an illustration, weanalyze the phase correlation functions and the full statistical distributionsof the interference between two one-dimensional systems, either independent ortunnel-coupled and compare with the Luttinger-liquid theory.

Fluctuations and stochastic processes in one-dimensional many-body quantum systems