GreenTensor

Class Methods

__init__()

Initialize a new Green tensor object.

get_spherical(kappa1, kappa2[, omega, ...])

set_from_cartesian(kappa1, kappa2, tensor[, ...])

class GreenTensor[source]

Green tensor for the multipole pair interactions.

This class allows to define custom constant or frequency-dependent Green tensors, which can then be used for the interaction of a SystemPair (see SystemPair.set_green_tensor()).

Examples

>>> import pairinteraction.real as pi
>>> gt = GreenTensorReal()
>>> distance_mum = 5
>>> tensor = np.array([[1, 0, 0], [0, 1, 0], [0, 0, -2]]) / distance_mum**3
>>> tensor_unit = "hartree / (e^2 micrometer^3)"
>>> gt.set_from_cartesian(1, 1, tensor, tensor_unit)
>>> print(gt.get_spherical(1, 1, unit=tensor_unit).diagonal())
[ 0.008 -0.016  0.008]
__init__()[source]

Initialize a new Green tensor object.

The actual tensor can be set afterwards via the set_from_cartesian() method.

Return type:

None

set_from_cartesian(kappa1, kappa2, tensor, tensor_unit=None, omegas=None, omegas_unit=None)[source]
Overloads:

  • self, kappa1 (int), kappa2 (int), tensor (NDArray), tensor_unit (Optional[str]) → None

  • self, kappa1 (int), kappa2 (int), tensor (Sequence[‘NDArray’]), tensor_unit (Optional[str]), omegas (Sequence[float]), omegas_unit (Optional[str]) → None

  • self, kappa1 (int), kappa2 (int), tensor (Sequence[‘NDArray’]), omegas (Sequence[float]), omegas_unit (Optional[str]) → None

Parameters:

  • kappa1 (int)

  • kappa2 (int)

  • tensor (ndarray[tuple[Any, ...], dtype[Any]] | Sequence[ndarray[tuple[Any, ...], dtype[Any]]])

  • tensor_unit (str | None)

  • omegas (Sequence[float] | None)

  • omegas_unit (str | None)

Return type:

None

Set the entries of the Green tensor.

Parameters:

  • kappa1 (int) – The rank of the first multipole operator.

  • kappa2 (int) – The rank of the second multipole operator.

  • tensor (ndarray[tuple[Any, ...], dtype[Any]] | Sequence[ndarray[tuple[Any, ...], dtype[Any]]]) – The green tensor in cartesian coordinates. Either a single tensor to set a constant green tensor or a list of tensors to set a frequency-dependent green tensor.

  • tensor_unit (str | None) – The unit of the tensor. Default None, which means that the tensor must be given as pint object.

  • omegas (Sequence[float] | None) – Only needed if a list of tensors is given. The frequencies of the tensors.

  • omegas_unit (str | None) – The unit of the frequencies. Default None, which means that the frequencies must be given as pint object.

Return type:

None

get_spherical(kappa1, kappa2, omega=None, omega_unit=None, unit=None)[source]
Overloads:

  • self, kappa1 (int), kappa2 (int), omega (Optional[float]), omega_unit (Optional[str]), unit (None) → PintArray

  • self, kappa1 (int), kappa2 (int), omega (Optional[float]), omega_unit (Optional[str]), unit (str) → NDArray

Parameters:

  • kappa1 (int)

  • kappa2 (int)

  • omega (float | None)

  • omega_unit (str | None)

  • unit (str | None)

Return type:

PlainQuantity[ndarray[tuple[Any, …], dtype[Any]]] | ndarray[tuple[Any, …], dtype[Any]]

Get the Green tensor in spherical coordinates for the given indices kappa1 and kappa2.

For kappa == 1 the spherical basis is [p_{1,-1}, p_{1,0}, p_{1,1}]. For kappa == 2 the spherical basis is [p_{2,-2}, p_{2,-1}, p_{2,0}, p_{2,1}, p_{2,2}, p_{0,0}].

Parameters:

  • kappa1 (int) – The rank of the first multipole operator.

  • kappa2 (int) – The rank of the second multipole operator.

  • omega (float | None) – The frequency at which to evaluate the Green tensor. Only needed if the Green tensor is frequency dependent.

  • omega_unit (str | None) – The unit of the frequency. Default None, which means that the frequency must be given as pint object.

  • unit (str | None) – The unit to which to convert the result. Default None, which means that the result is returned as pint object.

Returns:

The Green tensor as a 2D array.

Return type:

PlainQuantity[ndarray[tuple[Any, …], dtype[Any]]] | ndarray[tuple[Any, …], dtype[Any]]