Dimensional effects on the momentum distribution of bosonic trimer states

The momentum distribution is a powerful probe of strongly interacting systems that are expected to display universal behavior. This is contained in the contact parameters which relate few- and many-body properties. Here we consider a Bose gas in two dimensions and explicitly show that the two-body contact parameter is universal and then demonstrate that the momentum distribution at next-to-leading order has a logarithmic dependence on momentum which is vastly different from the three-dimensional case. Based on this, we propose a scheme for measuring the effective dimensionality of a quantum many-body system by exploiting the functional form of the momentum distribution.

Figure 1

LO momentum distribution tail $q^{4}n\left(q\right)$ for ground (upper solid black line) and excited (lower dashed red line) three-body states. Note that the vertical axis is not uniform. The asymptotic dashed lines are the analytical results discussed in Appendix .

Figure 2

NLO momentum distribution comparison of 3D (upper panel) and 2D (lower panel). The 2D momentum distribution is the one of the ground state, but the result is similar for the excited state.

Figure 3

Spectator function $f\left(q\right)$ for the ground state calculated numerically (black solid line) and using the ansatz $f\left(q\right)=A_0\frac{\ln q}{q^2}$ (red dashed line). The solid (black) line tends to oscillate around the dashed (red) one as $q\to \infty$ due to finite numerical precision.

Figure 4

Asymptotic behavior of $f\left(q\right)$ for the ground state.

Figure 5

Same as Fig. 4 for the first excited state.