Full Counting Statistics and Large Deviations in a Thermal 1D Bose Gas

We obtain the distribution of a number of atoms in an interval (full counting statistics) for interacting bosons in one dimension. Our results are valid in the weakly interacting regime in a parametrically large window of temperatures and interval lengths. The obtained distribution significantly deviates from a Gaussian away from the quasicondensate regime, and, for sufficiently short intervals, the probability of large number fluctuations is strongly enhanced.

Figure 1

Normalized FCS $p(\nu ,R)$ defined in Eq. (2) in the limit of short intervals. The dimensionless temperature is $T/c\overline{n}=\xi /{\ell }_{\phi }=0.1$, 0.25, 0.5, 1.0, and 5.0.

Figure 2

Normalized FCS $p(\nu ,R)$ defined in Eq. (2) in the limit of long intervals. The dimensionless temperatures are the same as in Fig. 1, and $R/{\ell }_{\phi }=5$. Inset: Reduced width $w(x)$ defined in Eq. (18) characterizing fluctuations of the number of particles.

Figure 3

Normalized FCS $p(\nu ,R)$ defined in Eq. (2) for intermediate intervals and high-temperature regime $T/c\overline{n}=\xi /{\ell }_{\phi }\gg 1$. The bold solid line represents exponential distribution, Eq. (9).