dielectric Module

Dielectric / Density response functions.

dielectric.chi_rpa_matsubara(q, theta, eta, zeta, kf, n)

RPA density response function evaluated for complex (matsubara) frequencies.

Parameters:
  • q (float) – (modulus) of wavevector considered.
  • theta (float) – Degeneracy temperature.
  • eta (float) – \(eta\mu\).
  • kf (float) – Fermi wavevector.
  • zeta (int) – Polarisation.
  • n (int) – nth Matsubara frequency.
Returns:

chi_rpa_n – RPA dielectric function evaluated at nth matsubara frequency.
Return type:

float
dielectric.dandrea_im(omega, q, kf, rs, ef, theta, eta)

Imaginary part of rpa density-density response function in reduced units.

Parameters:
  • omega (float) – frequency
  • q (float) – (modulus) of wavevector considered.
  • kf (float) – Fermi wavevector.
  • rs (float) – Density parameter.
  • ef (float) – Fermi energy.
  • theta (float) – Degeneracy temperature.
  • eta (float) – \(eta\mu\).
Returns:

chi_rpa – Imaginary part of RPA density-density response function.
Return type:

float
dielectric.dandrea_real(omega, q, kf, rs, ef, theta, eta)

Real part of rpa density-density response function.

Parameters:
  • omega (float) – frequency
  • q (float) – (modulus) of wavevector considered.
  • kf (float) – Fermi wavevector.
  • rs (float) – Density parameter.
  • ef (float) – Fermi energy.
  • theta (float) – Degeneracy temperature.
  • eta (float) – \(eta\mu\).
Returns:

chi_rpa – Imaginary part of RPA density-density response function.
Return type:

float
dielectric.im_chi_rpa(omega, q, beta, mu)

Imaginary part of rpa density-density response function.

Parameters:
  • omega (float) – frequency
  • q (float) – (modulus) of wavevector considered.
  • beta (float) – Inverse temperature.
  • mu (float) – Fermi wavevector.
Returns:

chi_rpa – Imaginary part of RPA density-density response function.
Return type:

float
dielectric.im_chi_rpa0(omega, q, kf)

Imaginary part of T=0 rpa density-density response function.

Parameters:
  • omega (float) – frequency
  • q (float) – (modulus) of wavevector considered.
  • kf (float) – Fermi wavevector.
Returns:

chi_rpa – Imaginary part of RPA density-density response function.
Return type:

float
dielectric.im_chi_rpa_dandrea(omega, q, kf, rs, ef, theta, eta)

Imaginary part of rpa density-density response function.

Parameters:
  • omega (float) – frequency
  • q (float) – (modulus) of wavevector considered.
  • kf (float) – Fermi wavevector.
  • rs (float) – Density parameter.
  • ef (float) – Fermi energy.
  • theta (float) – Degeneracy temperature.
  • eta (float) – \(eta\mu\).
Returns:

chi_rpa – Imaginary part of RPA density-density response function.
Return type:

float
dielectric.im_chi_tanaka(x, rs, theta, eta, zeta, l)
Imaginary part of rpa dielectric function in dimensionless form from:
Tanaka and Ichimary, Phys. Soc. Jap, 55, 2278 (1986).
Parameters:
  • x (float) – Momentum considered i.e., k/k_F.
  • rs (float) – Wigner-Seitz radius.
  • theta (float) – Degeneracy temperature.
  • eta (float) –
    math:eta*mu
  • zeta (int) – Spin polarisation.
  • l (int) – Matsubara frequency.
Returns:

Im(chi) – Imaginary part of dielectric function in the RPA.
Return type:

float
dielectric.im_lind(omega, q, beta, mu)

Imaginary part of free-electron Lindhard density-density response function.

Parameters:
  • beta (float) – Inverse temperature.
  • mu (float) – Chemical potential.
  • q (float) – (modulus) of wavevector considered.
  • omega (float) – frequency
Returns:

im_chi – Imaginary part of thermal Lindard function.
Return type:

float
dielectric.im_lind0(omega, q, kf)

Imaginary part of Lindhard Dielectric function at \(T = 0\).

Parameters:
  • q (float) – (modulus) of wavevector considered.
  • omega (float) – Frequency.
  • kf (float) – Fermi wavevector.
Returns:

im_chi_0 – Real part of Lindhard dielectric function.
Return type:

float
dielectric.lindhard_0_mats_n0(q, theta, eta, zeta, kf)

Lindhard function evaluated at zeroth matsubara frequency.

Parameters:
  • q (float) – (modulus) of wavevector considered.
  • theta (float) – Degeneracy temperature.
  • eta (float) – \(eta\mu\).
  • zeta (int) – Polarisation.
  • kf (float) – Fermi wavevector.
Returns:

chi_rpa_n – Lindhard function evaluated at zeroth matsubara frequency.
Return type:

float
dielectric.lindhard_0_matsubara(q, theta, eta, zeta, kf, n)

Real part of free-electron Lindhard density-density response function.

Parameters:
  • q (float) – (modulus) of wavevector considered.
  • beta (float) – Inverse temperature.
  • mu (float) – Chemical potential.
Returns:

re_chi – Imaginary part of thermal Lindard function.
Return type:

float
dielectric.re_lind(omega, q, beta, mu)

Real part of free-electron Lindhard density-density response function.

Parameters:
  • omega (float) – frequency
  • q (float) – (modulus) of wavevector considered.
  • beta (float) – Inverse temperature.
  • mu (float) – Chemical potential.
Returns:

re_chi – Imaginary part of thermal Lindard function.
Return type:

float
dielectric.re_lind0(omega, q, kf)

Real part of Lindhard Dielectric function at \(T = 0\).

Parameters:
  • omega (float) – Frequency.
  • q (float) – (modulus) of wavevector considered.
  • kf (float) – Fermi wavevector.
Returns:

re_chi_0 – Real part of Lindhard dielectric function.
Return type:

float
dielectric.re_rpa_dielectric(omega, q, kf)

Real part of RPA dielectric function.

Parameters:
  • omega (float) – frequency
  • q (float) – (modulus) of wavevector considered.
  • kf (float) – Fermi wavevector.
Returns:

re_eps – Real part of rpa dielectric function.
Return type:

float
dielectric.tanaka(x, rs, theta, eta, zeta, l)
Dimensionless RPA dielectric function factor from Tanaka and Ichimaru J.
Phys. Soc. Jap, 55, 2278 (1986).
Parameters:
  • x (float) – Momentum considered i.e., k/k_F.
  • rs (float) – Wigner-Seitz radius.
  • theta (float) – Degeneracy temperature.
  • eta (float) – :math:eta*mu
  • zeta (int) – Spin polarisation.
  • l (int) – Matsubara frequency.
Returns:

chi(x, l) – Lindhard function evaluated at frequency l (for imaginary frequencies).
Return type:

float