The three panels in
a–
f indicate the position of the electron wave packet, the charge density and the spin density in the QPC device. Colour bars beneath the panels correspond to scales of charge density between 0 and 2×10
−3, and spin density between −2×10
−3 and +2×10
−3. (
a) Initial state of the wave packet moving in the +
x direction. (
b) After a time evolution of
(
Vh is the hopping energy for electrons), the wave packet is positioned just before the narrowest constriction in the QPC potential. (
c) After a time evolution of
, the wave packet is transmitted through the narrowest constriction. (
d) Initial state of the wave packet moving in the −
x direction. (
e) After a time evolution of
. (
f) After a time evolution of
.