# SPDX-FileCopyrightText: 2024 PairInteraction Developers
# SPDX-License-Identifier: LGPL-3.0-or-later
from __future__ import annotations
from typing import TYPE_CHECKING
import numpy as np
import scipy.constants as const
from typing_extensions import override
from pairinteraction.green_tensor.dynamic_green_tensor import dynamic_green_tensor_homogeneous
from pairinteraction.green_tensor.green_tensor_base import GreenTensorBase
from pairinteraction.green_tensor.utils import evaluate_relative_permittivity
from pairinteraction.units import ureg
if TYPE_CHECKING:
from typing_extensions import Self
from pairinteraction.green_tensor.utils import PermittivityLike
from pairinteraction.units import ArrayLike, NDArray, PintArrayLike
[docs]
class GreenTensorFreeSpace(GreenTensorBase):
"""Green tensor for two atoms in free space.
Examples:
>>> from pairinteraction.green_tensor import GreenTensorFreeSpace
>>> gt = GreenTensorFreeSpace([0, 0, 0], [10, 0, 0], unit="micrometer")
>>> transition_energy = 2 # h * GHz
>>> gt_dipole_dipole = gt.get(1, 1, transition_energy, "planck_constant * GHz")
>>> print(f"{gt_dipole_dipole[0, 0]:.2f}")
-4.79 / bohr
"""
[docs]
def __init__(
self,
pos1: ArrayLike | PintArrayLike,
pos2: ArrayLike | PintArrayLike,
unit: str | None = None,
static_limit: bool = True,
interaction_order: int = 3,
*,
without_vacuum_contribution: bool = False,
) -> None:
"""Create a Green tensor for two atoms in free space.
Args:
pos1: Position of the first atom in the given unit.
pos2: Position of the second atom in the given unit.
unit: The unit of the distance, e.g. "micrometer".
Default None expects a `pint.Quantity`.
static_limit: If True, the static limit is used.
Default True.
interaction_order: The order of interaction, e.g., 3 for dipole-dipole.
Defaults to 3.
without_vacuum_contribution: Reserved for API consistency. Free-space Green tensors
always include the vacuum contribution, so setting this to True is invalid.
"""
super().__init__(
pos1, pos2, unit, static_limit, interaction_order, without_vacuum_contribution=without_vacuum_contribution
)
[docs]
def set_relative_permittivity(self, epsilon: PermittivityLike) -> Self:
"""Set the relative permittivity of the system.
Args:
epsilon: The relative permittivity (dimensionless) of the free space. Default is 1.
"""
self.epsilon = epsilon
return self
@override
def _get_scaled_au(self, kappa1: int, kappa2: int, transition_energy_au: float) -> NDArray:
if kappa1 == 1 and kappa2 == 1:
return self._get_scaled_dipole_dipole_au(transition_energy_au)
raise NotImplementedError("Only dipole-dipole Green tensors are currently implemented.")
def _get_scaled_dipole_dipole_au(self, transition_energy_au: float) -> NDArray:
"""Calculate the dipole dipole Green tensor in cartesian coordinates for free space in atomic units.
Args:
transition_energy_au: The transition energy in atomic units at which to evaluate the Green tensor.
Returns:
The dipole dipole Green tensor in cartesian coordinates as a 3x3 array in atomic units (i.e. 1/bohr).
"""
au_to_meter: float = ureg.Quantity(1, "atomic_unit_of_length").to("meter").magnitude
pos1_m = np.array(self.pos1_au) * au_to_meter
pos2_m = np.array(self.pos2_au) * au_to_meter
epsilon = evaluate_relative_permittivity(self.epsilon, transition_energy_au, "hartree")
omega_hz = ureg.Quantity(transition_energy_au, "hartree").to("hbar Hz", "spectroscopy").magnitude
# unit: # m^(-3) [hbar]^(-1) [epsilon_0]^(-1)
if self.without_vacuum_contribution:
raise ValueError("The Green tensor for free space cannot be provided without the vacuum contribution.")
gt = dynamic_green_tensor_homogeneous(pos1_m, pos2_m, omega_hz, epsilon, only_real_part=True)
to_au = au_to_meter ** (-3) * ((4 * np.pi) ** (-1)) / (const.epsilon_0 * const.hbar)
# hbar = 1, epsilon_0 = (4*np.pi)**(-1) in atomic units
return np.real(gt) / to_au