# The time evolution of the c.m

**Figure 2.** The time evolution of the c.m. motion of the Bose gas in cases I (solid black line), II (solid green line), III (dashed red line) and IV (solid blue line). The fitting of the c.m. trajectories for cases III and IV (dotted black line in (b) and (d)) from equation (16). The corresponding parameters: *B* = 0.22 μm, 0.1 μm and γ = 22.89 and 10.44 for cases III and IV, respectively, while Ω = 2π **×** 60 and *A* = 3.0 μm for both cases.

**Abstract**

We study the effect of quantum fluctuations on the dynamics of a quasi-one-dimensional Bose gas in an optical lattice at zero temperature using the truncated Wigner approximation with a variety of basis sets for the initial fluctuation modes. The initial spatial distributions of the quantum fluctuations are very different when using a limited number of plane-wave (PW), simple-harmonic-oscillator (SHO) and self-consistently determined Bogoliubov (SCB) modes. The short-time transport properties of the Bose gas, characterized by the phase coherence in the PW basis, are distinct from those gained using the SHO and SCB basis. The calculations using the SCB modes predict greater phase decoherence and stronger number fluctuations than the other choices. Furthermore, we observe that the use of PW modes overestimates the extent to which atoms are expelled from the core of the cloud, while the use of the other modes only breaks the cloud structure slightly, which is in agreement with the experimental observations by Fertig *et al* (2005 *Phys. Rev. Lett. ***94** 120403).