Figure 1
(a) Three-dimensional configuration of the
field of a knot with Hopf charge
, expressed as
, where
and
. Note that
is related to the order parameter
through Eq. (
2). In the figure, only
on the
,
, and
axes is shown as arrows. The dashed line traces the point
, which is a circle on the
plane with the radius
. The color on the arrows represents the value of
(see the scale). (b) The torus shape on the left side of the figure shows the isopycnic surface of
, which is equivalent to the region where
. The color on the surface shows the phase of
, that is equivalent to
. The white and black tubes are the preimages of
and
, respectively, which are reproduced on the right side of the figure. The two tubes cross once (linking number 1), which is consistent with
. (c) Cross sections of the density of the
(left) and
(right) components in the
plane. The size of each panel is
. The torus shape of the
components appears as double rings in the cross section, which can serve as the signature of a knot.
Reuse & Permissions