The quantum point contact (QPC) is a one-dimensional constriction with the differential conductance quantised in units of $GQ=2e2/h$. However, the transport behaviour below the first plateau is still not fully understood, including the 0.7 anomaly and the 0.25 anomaly in the linear and non-linear transport regimes respectively.

In this work, we utilise a multiplexing technique and statistically investigate the 0.7 anomaly observed on the first three plateaus respectively in 571 QPCs, fitting well the van-Hove model. The 0.7 anomaly shows the transconductance suppression due to the effective electron interactions which are modified by the local density of states (LDOS). At the maximum of LDOS, the interaction strength becomes strongest,  resulting in the strongest transconductance suppression. The strongest interaction strength is  determined by the ratio of  transverse confinement curvature and  longitudinal barrier curvature.

Moreover, we realise measurements of the effective g factor ($g^*$) and high-field offset ($\Delta E^{hfo}$) in numerous devices in a single cooldown at T=40 mK. The statistical results show both the $g^*$ and $\Delta E^{hfo}$ increase with the potential confinement, which supports the predictions about the role of interaction strength on  $g^*$ and $\Delta E^{hfo}$ in a 1D tight-binding model. We explore the origin of  $\Delta E^{hfo}$ and find that it is only considerable for the first plateau. Using a short and narrow QPC could result in a stronger potential confinement and thus a higher $g^*$, which could be beneficial for its use in spintronic applications.

Last, we investigate the formation and development of the DC-bias-induced 0.75 and 0.25 anomalies for 402 QPCs. We find the anomalies evolve similarly in a magnetic field.  To explain the anomaly behaviours, we propose a phenomenological DC-bias-induced spin-splitting model. In the model, with the increasing DC bias ($V_{DC}$), the 0.75 anomaly occurs first at a differential conductance of 0.75 $G_Q$, while the 0.25 anomaly is formed at a differential conductance of 0.5 $G_Q$ and moves to 0.375 $G_Q$. The spin gap of the first subband opens to be $e|V_{DC}|$, which enables an all-electric manipulation of spin polarisation  simply by applying a DC bias.