discretisedfield.tools.emergent_magnetic_field#

discretisedfield.tools.emergent_magnetic_field(field)#

Emergent magnetic field.

Emergent magnetic field for a (magnetic) unit vector field \(\boldsymbol{m}\) is defined as:

\[F_{kl} = \boldsymbol{m} \cdot (\partial_k \boldsymbol{m} \times \partial_l \boldsymbol{m})\]

Details are given in Volovik, G. E., Rysti, J., Mäkinen, J. T. & Eltsov, V. B. Spin, Orbital, Weyl and Other Glasses in Topological Superfluids. J Low Temp Phys 196, 82–101 (2019).

Parameters:

field (discretisedfield.Field) – Vector field.

Returns:

Emergent magnetic field.

Return type:

discretisedfield.Field

Raises:

ValueError – If the field is not three-dimensional.

Example

  1. Compute topological charge density of a spatially constant vector field.

>>> import discretisedfield as df
>>> import discretisedfield.tools as dft
...
>>> p1 = (0, 0, 0)
>>> p2 = (10, 10, 10)
>>> cell = (2, 2, 2)
>>> mesh = df.Mesh(p1=p1, p2=p2, cell=cell)
>>> f = df.Field(mesh, nvdim=3, value=(1, 1, -1))
...
>>> dft.emergent_magnetic_field(f)
Field(...)