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:
- Raises:
ValueError – If the field is not three-dimensional.
Example
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(...)